Evaluation of the
Further Mathematics
Support Programme
Report on Phase 3
August 2012
Dr Jeff Searle
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
2
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Contents
1. Executive Summary.......................................................................... 4
2. FMSP response to the evaluation report on Phase 2....................... 6
3 Impact of the FMSP on provision and
uptake of Further Mathematics........................................................ 10
3.1
3.2
3.3
3.4
3.5
Achievements against the 2005 baseline.................................................................10
Achievement against the 2009 baseline...................................................................11
Growth in AS and A level Mathematics entries.....................................................13
Growth in the number of establishments offering Further Mathematics...........14
Development and improvement of Further Mathematics
provision in schools and colleges and the sustainability
of Further Mathematics provision...........................................................................16
3.6 Conclusions and recommendations on provision and uptake of Further
Mathematics................................................................................................................19
4. FMSP continued work to extend access
to Further Mathematics.................................................................... 20
4.1
4.2
4.3
4.4
4.5
4.6
The priority schools initiative...................................................................................20
Interviews with Area Coordinators about the priority schools initiative...........21
Interview with teachers in priority schools.............................................................22
The impact of the priority schools initiative...........................................................26
Access to Further Mathematics events....................................................................27
Conclusions and Recommendations on work to
extend access to Further Mathematics....................................................................28
5. Teacher Support ............................................................................... 30
5.1
5.2
5.3
5.4
CPD opportunities provided by the FMSP, including uptake and feedback......30
Teaching Advanced Mathematics (TAM)...............................................................31
Teaching Further Mathematics (TFM)....................................................................35
Conclusions and recommendations on Teacher Support ....................................39
6. Student Support................................................................................ 42
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Review of student survey on tuition through the FMSP.......................................42
Tutor training..............................................................................................................45
Review of online revision..........................................................................................50
Key Stage 4 enrichment events.................................................................................53
Case study – Solihull Further Mathematics Conference 2012.............................55
Senior Team Mathematics Challenge Enrichment Events....................................60
Conclusions and recommendations on Student Support.....................................61
7. Overall conclusions and recommendations..................................... 64
Appendix A............................................................................................ 66
Appendix B............................................................................................ 82
Appendix C............................................................................................ 86
Appendix D............................................................................................ 88
Appendix E............................................................................................ 98
Appendix F ........................................................................................... 120
Appendix G............................................................................................ 126
3
1
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Executive
Summary
Phase 1 of this evaluation covered the period from the formation of the Further
Mathematics Support Programme (FMSP), in August 2009, to February 2010.
Phase 2 covered the period from March 2010 to March 2011. Phase 3 covers the
period from April 2011 to May 2012.
The FMSP continues to make considerable progress towards achieving its aims
of widening access to Further Mathematics, increasing the number of students
who study both AS level and A level Mathematics, and Further Mathematics. It
is developing the knowledge, expertise and confidence of teachers to teach Further
Mathematics in their own schools and colleges.
To date, the FMSP has achieved all of the Key Performance Indicator success
measures agreed with the Department for Education relating to the Phase 3 period.
These are referred to throughout this report.
An analysis of entry and achievement data from both the Department for
Education and the Joint Council for Qualifications shows that student numbers
in both Mathematics and Further Mathematics continue to grow strongly year on
year. Further Mathematics has been among the four fastest growing A level subjects
throughout the period of the FMSP.
The number of schools and colleges offering Further Mathematics also continues to
grow significantly. Since the formation of the FMSP in 2009 the number of statefunded establishments offering A level Further Mathematics has risen by 9.9%
(from 1150 in 2009 to 1264 in 2011). Over the same period the number of statefunded establishments offering AS level Further Mathematics has risen by 15.5%
(from 1169 in 2009 to 1383 in 2011). When setting up a Further Mathematics
course an establishment necessarily starts with a cohort of students taking AS level
Further Mathematics, so this is an indicator that there is a significant number of
establishments working towards offering full A level Further Mathematics.
Phase 3 focused on the FMSP’s continuing work to extend access to Further
Mathematics. A significant aspect of this is the ‘priority schools’ initiative, in which
the FMSP has been given the task of introducing Further Mathematics into
specified target schools not offering Further Mathematics and attended by students
from deprived backgrounds. This is working effectively, with a number of priority
schools now receiving support as a result of this initiative. Telephone interviews
with teachers from some of these schools indicated that they welcome the support
available from the FMSP and the effect that it is having on the provision and
profile of mathematics in their establishments. At the time of writing it appears
that, as a result of this initiative, Further Mathematics will be made available in a
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
significant number of these establishments for the first time from September 2012.
The ‘Access to Further Mathematics’ events arranged by the FMSP in March
2012 aimed to provide advice to schools and colleges not yet offering Further
Mathematics or in the early stages of provision, on introducing Further
Mathematics into the curriculum or extending and improving their current
provision. University academics took part in these events to illustrate the benefits of
studying Further Mathematics to students contemplating STEM subjects in higher
education. These events were very well-attended and feedback was excellent.
The Teaching Advanced Mathematics and Teaching Further Mathematics CPD
courses were reviewed in Phase 3. In general course participants reported the
courses had a very positive impact on their teaching.
A survey of students who had experienced tuition through the FMSP indicated
that they were generally very positive and grateful for the opportunity to study
Further Mathematics. There were a small number of criticisms and the FMSP
should investigate these cases further, but the large majority of students found both
the mode of study and the mathematics studied to have helped them when starting
higher education courses. This was evidence reinforced by subsequent telephone
interviews with a small sample of students.
Phase 3 also focused on the FMSP online revision programme and student
enrichment events. In both cases the uptake was considerable and the feedback
excellent. Of those students who gave feedback, 98% said they would recommend
FMSP online revision sessions to others. Over 3000 students attended FMSP
enrichment events during 2010 and a similar programme was offered during 2011
and 2012
The findings of this report indicate that the various activities of the FMSP are very
effective and it is succeeding in its key aims. Teachers value what it does and want
it to continue. Students value the opportunities it offers that might not otherwise
be available to them. It is clear that the work of the FMSP is an important factor
in the continued uptake of Further Mathematics. The work of the FMSP should
be continued and opportunities sought for further expansion. Conclusions and
recommendations for further development are made at the end of each section of
this report with an overview at the end of the report.
Note: Any references to Key Performance Indicators in this report refer to those
agreed between the Department for Education and FMSP relating to the period
from 1st April 2011 to 31st March 2012.
5
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FMSP response to the
evaluation report on Phase 2
The recommendations from the evaluation report on Phase 2, together with the
responses from the FMSP, are given below.
1. The FMSP should continue to be funded so that it can continue to support
both students and teachers of Mathematics and Further Mathematics.
The DfE agreed funding for the FMSP from 1st April 2012 to 31st March 2014.
This funding enabled the FMSP to appoint more Area Coordinators and to expand
the programme to deliver more student enrichment events, more continuing
professional development (CPD) and support for both students and teachers at
KS4 and with Sixth Term Examination Paper (STEP) and Advanced Extension
Award (AEA) Mathematics.
2. If the FMSP is to continue to support the mathematics of the level 3
Diploma in Engineering, then information about its services needs to reach the
teachers who actually deliver the course, particularly in colleges. There is also a need
to review the compulsory mathematics within the Diploma in terms of volume of
content, accessibility to students and its relevance to engineering.
In the agreement with the DfE beginning in April 2011 the FMSP is no longer
required to support the mathematics of the level 3 Diploma in Engineering.
3. There needs to be a review geographically and by type of institution as to
where and how Further Mathematics is being offered and who is taking it up.
This should enable future effort to be targeted at helping schools and colleges
move towards provision if they do not currently offer Further Mathematics.
It should also help to identify how AS Further Mathematics is offered to
students, whether this be as a one year course offered in Year 12 and / or Year
13, or as a two year course or not offered at all. It may also help to redress the
gender balance between male and female students who choose to study Further
Mathematics. In such a review, the FMSP should have access to reliable data
on student take up of AS level and A level Further Mathematics. This could
involve access to school and college census data, and reconciling this with
achievement data from the Department for Education, and also information
from the school or college itself, if registered with the FMSP. Local Area
Coordinators could also seek this type of information from the establishments
in their area.
The ‘priority schools’ initiative, described in section 3.1, focuses FMSP support
on those schools still not offering Further Mathematics and attended by students
from deprived backgrounds. The FMSP believes that this has been a very effective
way to target support and further extend access to Further Mathematics. The
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FMSP continues to collect data on Further Mathematics provision (both at AS
and A level) through its registration procedure and via Area Coordinators. AS level
Further Mathematics figures at national level are still very difficult to interpret.
4. For professional development and other events, it is recommended that
the FMSP ensures that standard feedback forms are used and that they are
summarised in a standard way that facilitates aggregation. Such aggregated
information could be analysed so that a national picture of provision and take
up can be established to inform and focus future planning and provision on
need. A survey of teachers’ perceived requirements both in terms of content
and style of delivery would also inform future planning.
The FMSP should continue its development of Knowledge Networks and consider
supplementing these with online forums for both teachers and pupils. The FMSP
should also continue its support and involvement with the Senior Team Maths
Challenge.
The FMSP has worked to make sure that standard feedback forms are used for
FMSP CPD events. These are aggregated and summarised and the resultant data
are subject to frequent review. Content of locally-provided CPD is determined by
Area Coordinators’ local knowledge of demand. The FMSP continues to support
post-16 Teacher Networks (formerly Knowledge Networks) running 15 such
networks covering England during 2011/12.
The FMSP has continued its involvement in the Senior Team Mathematics
Challenge.
During the period of the FMSP, the number of schools competing in the challenge
has risen from 905 during 2009/10 to 1025 during 2010/11.
During 2011/12, the FMSP set up associated events called Senior Team
Mathematics Challenge Enrichment Events to help students prepare for the main
competition and to encourage more engagement in mathematical problem-solving.
These events are reviewed in section 5.7 of this report.
5. The FMSP should consider the implications of the revised GCSE in
mathematics on take up in both AS level Mathematics and Further
Mathematics. The FMSP should offer guidance to teachers and students as to
whether there is a minimum grade or pre-16 experience of mathematics that
should be a pre-requisite to studying Mathematics or Further Mathematics.
The FMSP should consider the provision of bridging resources and / or
courses should these prove to be necessary. It should also encourage those
7
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
students who doubt their ability or who feel they might lack the self-discipline
to make a success of supported self-study, that they can succeed in Further
Mathematics, especially through taking an AS level over two years, or in Year
13.
The FMSP has been given access to data which will help to analyse the relationship
between performance at KS4 and performance in A/AS level Mathematics and
Further Mathematics. The results of this analysis will be available soon. In the
new agreement with the DfE, the FMSP is providing a programme of CPD and
resources to help with extension and enrichment at KS4. This will also address
issues around transition from GCSE mathematics to AS/A level Mathematics and
Further Mathematics. Close attention has been paid to ensuring that good practice
is embedded in school programmes of study as a result of this CPD.
6. The FMSP should seek ways to continue to raise the profile of mathematics
in Key Stages 3 and 4. The FMSP could develop further guidance in terms of
ideas for ‘extra–curricular’ activities and resources that promote an interest in
mathematics as a fun, fascinating and challenging subject to pursue further, and
that it leads to many career opportunities.
Under the new agreement with the DfE, the FMSP is providing more enrichment
events targeted at KS4 students. These continue to receive excellent feedback. The
FMSP is reviewing how resources can be provided to those schools attending so
that their teachers can run related activities before or after the events.
The FMSP continues to provide and update general resources for student
enrichment via the FMSP website.
8
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
9
3
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Impact of the FMSP on
provision and uptake of Further
Mathematics
3.1 Achievements against the 2005 baseline
The figures used in Table 1 below, to show the growth in the number of candidates
entering for a qualification in Further Mathematics, are those of the Joint Council
for Qualifications. These are published annually, each August, following the
summer examinations. They are less authoritative than the figures released later by
the Department for Education (DfE), but are suitable for comparative purposes,
both for year-on-year growth, and for comparison with Wales and the Northern
Ireland, whose figures are also published by the Joint Council for Qualifications.
The original baseline year has been taken as 2005 and this is compared firstly to the
figures for 2009, as the former Further Mathematics Network was fully operational
for the period 2005 to 2009. The Further Mathematics Support Programme
followed from the Network in the Autumn of 2009, so the 2009 figures formed
a new baseline with which to compare the present growth under the Support
Programme, up to 2011.
The number of candidates entering for AS and A level Further Mathematics has
increased in England, Wales and Northern Ireland between each of the dates of
interest. The largest numerical and percentage increases have generally been seen in
England, where AS level Further Mathematics numbers increased by 275% and A
level Further Mathematics numbers increased by 110% between 2005 and 2011.
There has been growth in both Wales and Northern Ireland with the growth in
Wales being somewhat higher. It is notable that a support programme for Further
Mathematics has recently been initiated in Wales, which may account for some of
the growth.
When comparing increases, it should be noted that the candidate entry numbers
for Wales and Northern Ireland are much smaller than in England. A level Further
Mathematics entries in 2011 in these countries were 309 and 173 and 11805,
respectively. A small change in entry numbers in Wales or Northern Ireland can
have a large effect on the percentage increase from year to year. For example an
increase of 59 students taking A level Further Mathematics in Wales between 2009
and 2011 produced a 24% increase, which is greater than England where there were
an extra 1732 students and the percentage increase was 17%.
Note that full details of the entries and attainment year on year as published by the
DfE are given in Appendix B to this report. These figures are from the Department
for Education official statistical release, and apply to candidates aged 16, 17 and 18
who took these examinations in England.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table 1 Number of candidates entering A level and AS level Further
Mathematics from 2005 to 2011
2005
2009
2005-2009
percent
change
2011
2005-2011
percent
change
2009-2011
percent
change
A level
5627
10073
79%
11805
110%
17%
AS level
4809
12710
164%
18045
275%
42%
A level
186
250
34%
309
66%
24%
AS level
118
245
108%
289
145%
18%
A level
120
150
25%
173
44%
15%
AS level
127
209
65%
221
74%
6%
England
Wales
Northern
Ireland
Source JCQ
3.2 Achievement against the 2009 baseline
Tables 2 and 3 below show the baseline entry figures and the percentage of students
who achieved a pass grade for the FMSP baseline year 2008/09, and the subsequent
two years. These figures are from the Department for Education official statistical
release, and apply to candidates aged 16, 17 and 18 who took these examinations in
England.
It is seen in Table 2 that the growth in the number of candidates taking the AS
level has increased substantially in 2010/11 compared to the previous year, with
3006 more entries overall.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table 2 GCE AS level Further Mathematics entries
Academic
year
All student entries - percentage achieving grade
A
B
C
D
E
Pass
rate
Total
entries
Percentage increase
2010/11
40.7
17.8
13.9
10.1
7.5
90.0
12427
31.9%
2009/10
41.9
19.2
13.8
10.6
6.9
92.5
9421
12.2%
2008/09
41.0
19.7
14.9
10.4
7.0
93.1
8399
48.5%
It should be noted that there is some ambiguity in the figures for AS level Further
Mathematics because of the variety of ways in which schools and colleges can
choose to enter students for certification. Some students who complete a full A
level in Further Mathematics do not certificate AS level Further Mathematics at
all, whilst other students certificate AS level Further Mathematics at the end of
year 12, before certificating A level Further Mathematics in year 13. Furthermore,
some students choose to take AS level Further Mathematics only, with some
taking it in year 12, some studying it over years 12 and 13 and some taking it up
in year 13. It would be useful to know how many students take AS level Further
Mathematics only, without progressing to the full A level, but these data are not
currently available.
Table 3 GCE A level Further Mathematics entries
Academic
year
All student entries - percentage achieving grade
A*
A
B
C
D
E
Pass
rate
Total
entries
Percentage
increase
2010/11
27.5
31.2
21.0
10.3
5.7
3.0
98.7
11408
5.5%
2009/10
29.3
30.1
20.2
11.4
5.4
2.8
99.3
10813
14.5%
2008/09
-
59.1
20.2
11.0
5.4
3.2
99.0
9443
11.8%
Source DfE
As shown in Table 3, the growth in the number of A level Further mathematics
entries continued into 2010/11. In total, there were 595 more entries in 2010-11
than in the previous year, a 5.5% increase. The rate of growth has slightly lessened
compared with previous years but it should be noted that, in annual percentage
terms, Further Mathematics is the only subject to have been among the four fastest
growing A level subjects in all of 2009, 2010 and 2011. The five fastest growing
subjects (including some subject groupings such as ‘other social studies’ and ‘other
modern languages as defined by the Department for Education) are given below.
The FMSP’s work in promoting Mathematics to KS4 students is also likely to
contribute to the increases in entries for A level Mathematics.
Position
1st
2009
2010
2011
Economics
Other social studies
Other modern languages
2nd
Mathematics
Economics
Mathematics
3rd
Further Mathematics
Further Mathematics
Chemistry
4th
Other modern languages
Business Studies
Further Mathematics
5th
Government and Politics
Biological Sciences
Government and Politics
Source DfE
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Tables 4 and 5 below show the baseline entry figures and the percentage of
students who achieved each grade since the baseline year 2008/09. This is the year
before the first year of operation of the FMSP. The figures are broken down into
male and female students for AS level Further Mathematics and A level Further
Mathematics respectively.
Table 4 GCE AS level Further Mathematics entries by gender
Academic year
Male student entries - percentage achieving grade
A
B
C
D
Pass
rate
E
Total
entries
Percentage
increase
2010/11
39.9
17.5
13.8
10.4
7.5
89.0
8199
38.7%
2009/10
40.3
18.9
13.9
10.9
7.4
91.4
5911
13.9%
2008/09
39.3
19.1
15.5
10.6
7.8
92.4
5190
45.5%
Female student entries - percentage achieving grade
2010/11
42.2
18.4
14.1
9.5
7.5
91.7
4228
20.5%
2009/10
44.6
19.7
13.7
10.1
6.2
94.3
3510
9.4%
2008/09
43.8
20.7
14.1
9.9
5.7
94.2
3209
53.8%
Source DfE
Table 5 GCE A level Further Mathematics entries by gender
Academic year
Male student entries - percentage achieving grade
A*
A
B
C
D
E
Pass
rate
Total
entries
Percentage
increase
2010/11
27.9
31.0
20.7
10.3
5.8
2.9
98.7
7819
6.1%
2009/10
30.0
29.3
20.3
11.1
5.5
3.1
99.2
7369
13.5%
2008/09
-
59.4
19.7
10.4
5.8
3.6
98.9
6493
10.6%
Female student entries - percentage achieving grade
2010/11
26.7
31.5
21.7
10.3
5.5
3.1
98.8
3589
4.2%
2009/10
27.7
31.9
20.1
12.0
5.3
2.3
99.3
3444
16.7%
2008/09
-
58.6
21.3
12.4
4.6
2.3
99.2
2950
14.5%
Source DfE
About 75% of the increase in entries for both AS and A level Further Mathematics
were from male candidates. The FMSP, as well as continuing its work in promoting
the take up of Further Mathematics in general, should consider in particular how to
attract more females to take the full A level.
The ratio of male to female candidates for both the full A level and the AS level in
mathematics is about 3:2, which is a little closer to a 50-50 split in gender than for
Further Mathematics.
3.3 Growth in AS and A level Mathematics entries
The influence of the FMN and subsequently the FMSP has extended beyond just
Further Mathematics to mathematics education in general and in particular to
GCE A level Mathematics and AS level Mathematics. It is thus considered that A
level Mathematics should form part of the baseline as the FMSP has the support of
A level Mathematics as part of its brief.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Tables 6 and 7 below show the total entry figures and the percentage of students
who achieved each grade since the baseline year of 2008/09 in AS level and A level
Mathematics respectively.
Table 6 GCE AS level Mathematics entries
Academic
year
All student entries - percentage achieving grade
A
B
C
D
E
Pass rate
Total
entries
Percentage
increase
2010/11
24.3
15.8
15.1
14.0
12.1
81.3
104586
31.6%
2009/10
23.5
16.5
15.5
14.2
12.3
81.9
79458
7.8%
2008/09
23.3
15.3
15.1
14.9
12.9
81.5
73728
11.4%
Source DfE
Table 7 GCE A level Mathematics entries
Academic
year
All student entries - percentage achieving grade
A*
A
B
C
D
E
Pass
rate
Total
entries
Percentage
increase
2010/11
18.2
26.9
21.9
15.6
10.4
5.6
98.6
75547
8.2%
2009/10
17.0
27.9
22.0
15.5
10.1
6.0
98.5
69803
8.2%
2008/09
-
45.4
21.7
15.3
10.1
5.8
98.3
64517
12.0%
Source DfE
In Tables 6 and 7 it is seen that the large increases year on year in student entries
were sustained into 2010/11. Between 2004/05 and 20010/11 the number of
entries increased by 29 513 students at A level and 49614 students at AS level,
increases of 64.1% and 90.3% respectively.
The government target of 56000 A level Mathematics students by 2014 was passed
in 2007/08. In 2009 this target was revised to 80000.
Part of the challenge to the FMSP, through its various support activities, is to
support continued growth in AS and A level numbers in both Mathematics and
Further Mathematics. All the above figures are evidence that substantial growth has
occurred in recent years. Although this growth cannot causally be attributed to the
FMSP it is likely, given the positive feedback from teachers and students about the
activities of the FMSP.
3.4Growth in the number of establishments offering
Further Mathematics
Table 8 below shows the number of establishments offering A level Further
Mathematics and those offering AS level Further Mathematics in the baseline
year of 2008/09 and the subsequent two years. The number of Academies offering
Further Mathematics has increased substantially in the last year, which is likely to
be due to some schools changing their status to become an Academy. This probably
accounts for the small decrease in the number of Foundation schools offering
A level Further Mathematics. Across the state sector as a whole, the number of
14
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
establishments offering both the A level and AS level has continued to increase.
In 2010/11, there were 113 more state establishments offering the full A level
compared to the baseline year, a growth of about 10%, whilst there was an increase
of 215 state establishments offering the AS level, a growth of about 18%. These
increases in the number of establishments offering Further Mathematics reflect the
growth in candidate entries, and are likely to be due to the influence of the FMSP
in initiating Further Mathematics in state schools and colleges where it was not
previously offered.
Table 8 Establishments offering Further Mathematics
A level Further Mathematics
Type of establishment
Academy
City Technology College
AS level Further Mathematics
2008/09
2009/10
2010/11
2008/09
2009/10
2010/11
17
26
52
19
28
66
1
2
2
3
3
2
Community School
415
441
468
437
458
521
Foundation School
294
300
295
282
292
315
Further Education
163
164
169
174
175
182
Independent school
418
414
413
286
310
335
0
2
3
1
1
1
Voluntary aided school
209
210
219
208
208
242
Voluntary controlled school
50
51
52
44
45
50
Other government funded
1
4
4
1
2
4
Total all establishments
1568
1614
1677
1455
1522
1718
Total all state establishments
1150
1200
1264
1169
1212
1383
Non-maintained special school
Source DfE
The chart below shows the proportion of state-funded establishments offering A
level Mathematics that also offer Further Mathematics. The percentage of such
schools has risen from below 40% to well over 60% over the period of the FMN
and FMSP. Recent increases in this percentage have not been as large but this is
probably due to a large number of establishments setting up new post-16 provision.
Such establishments tend to offer Mathematics straightaway, but do not offer
Further Mathematics until their post-16 provision has become more established.
Key Performance Indicator 1c relates to this, see Appendix A for full details.
State-funded establishments offering A level Mathematics that also
offer Further Mathematics
100%
75%
50%
25%
0%
2004/05
2005/06
2006/07
Offering Further Mathematics
2007/08
2008/09
2009/10
2010/11
Not Offering Further Mathematics
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
3.5Development and improvement of Further
Mathematics provision in schools and colleges and
the sustainability of Further Mathematics provision
Key Performance Indicator 6a, relates to the percentage of establishments that are
able to offer Further Mathematics without any tuition provided by the FMSP. This
has risen from 52.9% in 2009/10 to 57.1% in 20010/11. These figures will only
provide estimates to the true figures, again due to difficulties with AS level data
(see section 3.1). For details of how this percentage is calculated based on DfE and
FMSP data see Appendix A.
The chart below shows the number of students receiving some tuition in Further
Mathematics through the FMSP from 2005/06 to 2011/12.
Number of students receiving some tuition
through the FMSP 2005/06 to 2011/12
1400
Number of students
1200
1000
800
600
400
200
0
2005/06
2006/07
2007/08
2008/09
2009/10
2010/11
2011/12
Source FMSP
It is evident that after an initial increase in numbers, since 2007/08 there has been a
decline. The graph shows that the number of FMSP-tutored students has dropped
over the last three years, whilst overall the number of students studying Further
Mathematics has risen. This suggests that more schools and colleges are now able to
teach their own students.
The FMSP tries to engage with all suitable schools and colleges across England
to raise awareness of Further Mathematics, and mathematics in general.
Establishments can register with the FMSP by completing a short online form.
One aspect of this registration is to request the ‘FM Status’ of the registering
establishment, as set out in the categories below (note that the wording below is
not that which is given in the online form, but that which is used to match with
Key Performance Indicators).
16
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FM status
FM offered?
Further Mathematics (FM) tuition
1
Y
When there is demand for FM, all FM teaching is performed ‘in house’ either by
the school/college itself or through a consortium. There is no reliance on support
from the FMSP.
2
Y
When there is demand for FM, all FM teaching is performed ‘in house’ either
by the school/college itself or through a consortium. The school/college or
consortium receives CPD from the FMSP to support its teaching.
3
Y
When there is demand for FM, the school/college /consortium only teaches some
FM modules that are essential to the delivery of AS and/or A level FM; others are
taught externally. This category does not include cases where external tuition is
used to provide alternative, but non-essential, module options (e.g. high level
mechanics).
4
Y
When there is demand, all teaching is provided by the FMSP.
5
Y
The school/college does not offer FM to its students, or there is no evidence to
suggest the subject is offered.
Key Performance Indicator 1a of the FMSP agreement with the DfE for this
period relates the FMSP keeping up-to-date records of FM status.
The evaluation considered how the Further Mathematics status of an establishment
changed from 2009/10 to 2010/11 and from 2010/11 to 2011/12. Table 9 below
shows how the status changed between the two years being comp1ared. It should
be noted that categories 1 and 2 are amalgamated in Table 9 as they both indicate
that Further Mathematics is taught ‘in-house’ (but in category 2 the school/college
receives CPD from the FMSP).
Table 9 Change in Further Mathematics (FM) status of
establishments registered with the FMSP 2009-10 to 2011-12
2009/10 Further Mathematics status
1/2
3
4
5
total
1/2
810
46
24
77
957
3
13
12
8
4
37
4
2
2
27
7
38
5
9
2
3
36
50
total
834
62
62
124
1082
2010/11 Further
Mathematics status
2010/11 Further
Mathematics status
2009/10 Further Mathematics status
1/2
3
4
5
total
1/2
1323
25
12
42
1402
3
13
20
6
5
44
4
6
4
31
12
53
5
23
3
4
172
202
total
1365
52
53
231
1701
Source FMSP
Key to Table 9
number of establishments
2009/10 to 2010/11
2010/11 to 2011/12
Further Mathematics provision improved
166
102
Further Mathematics provision stayed the same
885
1546
Further Mathematics provision reduced
31
53
1082
1701
Total establishments
Further Mathematics provision seems likely to be sustainable for some schools and
colleges who are in categories 1 and 2 where there is ‘in-house’ provision of Further
Mathematics. Some of these schools and colleges are likely to have offered Further
Mathematics for many years and always attracted students in sufficient numbers to
make at least one viable teaching group.
1 The total number of establishments involved in the 2010/11 to 2011/12 analysis was much greater than that for 2009/10 to
2010/2011 (1701 compared to 1082). Establishments could only be included in the analysis if they had an FM Status for the
two consecutive years considered. There were many establishments who were registered with the FMSP in 2009/10 who did
not have an FM Status attributed to them. Following a specific effort by the FMSP considerably more establishments had an FM
Status recorded for 2010/11 (and similarly in 2011/12) so they could be included in the 2010/11 to 2011/12 figures.
17
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
It is notable that 79 establishments moved into categories 1 and 2 from a lower
category between 2010/11 and 2011/12. This represents excellent progress for those
establishments but it should be noted that the FMSP has a vital role in supporting
them in future. These schools and colleges could still benefit from association with
the FMSP. Schools and colleges with status 2 already make some use of CPD
opportunities. Telephone interviews conducted with teachers during both Phase
2 and Phase 3 of the evaluation, indicated that they found the CPD they had
experienced beneficial to themselves and their students. CPD through the FMSP
had refreshed and strengthened their knowledge, and given them opportunity to
share ideas for introducing and developing topics. Such CPD might be particularly
useful for relatively new members of a department who might wish to become
involved in teaching Further Mathematics, or where there is a general staff
development policy to increase the staff capacity to teach post-16 mathematics.
Students and teachers can also benefit from having access to the Integral2 website
resources by registering with the FMSP.
However, some of these schools and colleges are likely to have small numbers of
students taking Further Mathematics and few teachers capable of teaching Further
Mathematics. If student numbers drop to a non-viable level, or key teaching staff
move on or retire, then they may need support from the FMSP. This is supported by
analysis reported in a previous phase of the evaluation of the FMSP, in which it was
found that the modal entry for a school or college for A level Further Mathematics
was one student; this indicates that there is likely to be significant variability in the
provision from year to year in many schools and colleges.
It can be seen in the Table 9 that between 2010/11 and 2011/12, 42 establishments
dropped out of category 1/2, of which 23 changed to category 5. These 23
establishments may only be about 3% of the schools and colleges that were
in category 1/2 in 2010/11, but if Further Mathematics is to continue to be
offered, support from the FMSP needs to be available. In addition a further
seven establishments changed to category 5 from categories 3 and 4. Thus 30
establishments that were previously offering Further Mathematics have now moved
to category 5 and are no longer doing so. This may be temporary due to a drop in
numbers in the period 2010/11 to 2011/12, but the reasons aren’t known and it is
something which the FMSP Area Coordinators should investigate. They should
also investigate why the 172 schools that remained in category 5, are not offering
Further Mathematics. It would be informative to look and see how many of these
schools have been categorised as ‘priority schools’ under the DfE / FMSP definition
(Section 4).
It can also be seen in Table 9 that currently there are 44 establishments in category
3 and 53 in category 4. These establishments also need support from the FMSP
to be available, more so to those in category 4, which are totally dependent on
support from the FMSP. The 97 schools currently in these categories represents
just 6% of the establishments in the analysis, but if the students who attend them
are to continue to be taught Further Mathematics and it be offered in future, then
it would appear this is only sustainable if the FMSP provides at least some of
2 See Appendix C for details of what access to Integral provides.
18
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
the teaching. It was noted in the Phase 2 report that schools and colleges in the
position of having recently taken Further Mathematics provision ‘back in-house’
following support from the FMSP are vulnerable to not being able to maintain
provision and may fall back to a position where they again need support from the
FMSP.
3.6Conclusions and recommendations on provision
and uptake of Further Mathematics
•The number of students studying A and AS Mathematics and Further
Mathematics has grown considerably over recent years. It is likely that the
various activities and initiatives of the former FMN and the FMSP have
been influential in that growth occurring.
•The number of state funded establishments that offer Further
Mathematics has also continued to grow.
•In many schools and colleges Further Mathematics is well established in
the sixth form curriculum offer.
•In schools where student numbers are small and/or there are a limited
number of teachers capable of teaching a Further Mathematics module
and possibly none, tuition from the FMSP in some form is essential if
these schools and colleges are to continue to offer Further Mathematics
to their students.
•It would be informative to research the size of the Further Mathematics
student cohorts for AS and A level Further Mathematics across all state
schools and colleges in England.
•All teachers can benefit from the professional development opportunities
that are available through the FMSP and that benefit can enhance their
students’ learning experience.
•Schools and colleges that are in the early stages of moving to offer
Further Mathematics to their students are able to seek advice and support
from the FMSP and can request tuition.
•The FMSP has a vital role to play in initiating and supporting the offer of
Further Mathematics in schools and colleges that do not currently offer it.
19
4
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FMSP continued work to extend
access to Further Mathematics
4.1 The priority schools initiative
The FMSP has worked with the Department for Education to identify schools and
colleges which are attended by students deemed to be from deprived backgrounds
and which do not currently offer Further Mathematics. Key Performance Indicator
3a of the agreement with the Department for Education for this period relates to
this, see Appendix A. Such schools and colleges are referred to as ‘priority schools’
by the FMSP.
A method of defining such schools and colleges was agreed between the DfE and
the FMSP, see Appendix A. This definition identified 199 priority schools. Where
the data required to determine whether an establishment satisfied this definition
was not available, the FMSP Area Coordinators could request that establishments
be added on the basis of the data that was available. As a result, the number of
priority schools ultimately rose to 204.
The FMSP Area Coordinators were given the task of making contact with these
schools and colleges in order to establish a dialogue that would lead to them
agreeing to offer Further Mathematics. One of the Key Performance Indicators
specified by the DfE for the FMSP for this period is that 40 of these schools and
colleges should be offering Further Mathematics from September 2012. Progress
towards this Key Performance Indicator is described in section 4.4. The Area
Coordinators kept their FMSP regional manager informed of progress with the
priority schools they had been allocated.
The evaluation of the priority schools initiative was in two parts. Firstly the
evaluator interviewed each of the 20 Area Coordinators about how they had gone
about making contact with their allocated priority schools and the progress they
were making with them. Secondly the FMSP selected priority schools which
were in a dialogue with the FMSP and where it was believed a teacher would be
willing to participate in a telephone interview with the evaluator about the status
of Further Mathematics in their school or college. The target number with teachers
from priority schools was 20 interviews; 15 actually took place. It should be noted
that all interviews that were conducted as part of this evaluation followed the
Durham University ethics code of practice; all interviews were arranged in advance
with the interviewee given full information as to the purpose of the interview, and
informed that they could withdraw at any time if they so wished. All interviews
followed a pro-forma.
20
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
4.2Interviews with Area Coordinators about the priority
schools initiative
Each interview covered the number of priority schools an Area Coordinator had
tried to contact and the outcomes of those attempts.
The number of priority schools allocated to each Area Coordinator varied
considerably between the regions probably due to the varying nature of local post16 provision. One of the Area Coordinators commented that where the secondary
school structure is predominantly 11-16 schools with sixth form colleges providing
provision for post-16 study, there were relatively few priority schools. She suggested
that this is because Further Mathematics is well established in most sixth form
colleges and went on to comment that only faith schools in these areas tended to
have sixth forms.
Many schools are changing their status to become Academies and within that
they can set up a sixth form, and it seems there are many such schools with an
embryonic sixth form where Further Mathematics might be introduced. However,
in many parts of England there are 11-18 schools not currently offering Further
Mathematics.
Several of the Area Coordinators expressed surprise at some of the schools or
colleges in their allocation, saying they had been in contact with some of them for
a while and knew that Further Mathematics was already under development and so
they didn’t see them as a priority. They did however have schools in their region that
they would have deemed to be priority and so would have liked further consultation
with the FMSP about the rationale for the choice of schools. This will be at least
partly due to the possibility that a school or college had no Further Mathematics
certifications in August 2010 but a Further Mathematics course has existed since
then. Conversely there may be schools or colleges that had Further Mathematics
certifications in August 2010 and as a result of this are not a priority school, but
have had no Further Mathematics students since.
For schools and colleges that were new to the Area Coordinators, first contact
was made by e-mail. Sending an e-mail to a generic address usually resulted in no
response, whereas if it was sent to a named head of department, head of sixth form,
Key Stage 5 coordinator or a curriculum deputy head, a response was much more
likely, particularly if the person was known to the Area Coordinator.
If the Area Coordinator did not receive a timely response, s/he sent follow up
e-mails, made telephone calls and gave invitations to regional FMSP events. These
sometimes led to contact being made. Some resorted to sending the ‘official letter’
21
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
on DfE headed paper. Seventeen such letters were sent to head teachers and in four
cases this led to further dialogue.
Where contact was established and the Area Coordinator was able to talk to
a teacher at the school or college, this often led to interest in offering Further
Mathematics and the Area Coordinator was able to explain how the FMSP could
support the initiation of provision. Most of these schools undertook to offer
Further Mathematics from September 2012, by assigning timetable time in an
option block, or by using FMSP live online tuition or by arranging face-to-face
tuition with a FMSP tutor. The Area Coordinators reported that many of these
schools were in a similar position to the ‘back in-house’ schools or colleges reported
in Phase 2 of the evaluation; that is, there is a balance between attracting students
who want to study Further Mathematics, having capable staff with sufficient time
to deliver the course and the support of the senior management.
4.3 Interview with teachers in priority schools
The contact details for 24 teachers from selected priority schools were supplied to
the evaluator. At the time, many priority schools had only just started a dialogue
with the FMSP. Given this, these 24 schools and colleges had been chosen by the
FMSP in consultation with the Area Coordinators as those where FMSP support
was in place or had been agreed. They were e-mailed in advance by the FMSP,
outlining the purpose of the interview and the questions that would be asked, and
giving notification that the evaluator would be in touch. The evaluator contacted
all of these 24 teachers, and 15 interviews took place. Two teachers declined,
saying they no longer had any students taking Further Mathematics. This was
disappointing as their views would have been of interest, particularly as regards
their intention for offering Further Mathematics in future. There was no response
from eight of the selected teachers, despite repeated reminders.
•What support are you looking for from the FMSP?
•What are the long term objectives for the development of your
mathematics department?
•How did you hear about the FMSP and why did you decide to get in
touch with it?
•What support have you received so far, if any? How effective has it been?
Interviewees were also invited to make any other comment about the FMSP.
What support are you looking for from the FMSP?
There was a varied response to this question, but all teachers are looking for advice
and guidance of some sort. Further Mathematics was already being offered and
taught in some of these schools, albeit with small numbers of students.
One teacher noted that she is the only qualified mathematician in the school, and
that she wanted to ensure she was teaching and using the resources appropriately.
In one school the teacher wanted the FMSP to ‘do the teaching’ as she was just
getting A level Mathematics started in her school which had recently established a
22
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
sixth form; there were two students taking Further Mathematics at this school with
an FMSP tutor.
Several teachers explained that they were delivering the course but were
meeting regularly with the Area Coordinator for advice about their delivery and
management of the course and effective use of the resources from the Integral
website3. In some schools the Area Coordinator was doing some of the teaching.
Several teachers noted that they had only a small number of staff who could
teach any Further Mathematics and there was concern as to what would happen
if such staff left the school. They were reassured that the FMSP could provide
tuition support at short notice, should it prove necessary so the students didn’t lose
continuity.
One teacher noted the lack of school time to give to Further Mathematics and
was looking for support for out of hours teaching. She also wanted development
opportunities for inexperienced staff.
In one school, the teacher wanted the FMSP to visit and stimulate the Key Stage 3
and 4 pupils. He noted they are a rural school and there is a big college a few miles
away, to which they “lose” a lot of Year 11 students. He wants to retain students
by convincing them that the school can deliver A level Mathematics and Further
Mathematics. At the time of the interview, he had two students taking Further
Mathematics, and they were largely teaching themselves.
Another teacher also talked about retention. He was the teaching and learning
consultant in a new Academy that had ‘national challenge’ status and he was
looking to make big improvements, which meant retaining students so the school
could develop a sixth form. He saw A level Mathematics and Further Mathematics
as an important aspect of that. He hoped to offer Further Mathematics from
September 2013.
What are the long term objectives for the development of your
mathematics department?
All the teachers hoped that their numbers would grow both for A level
Mathematics and Further Mathematics. Some noted that realistically the numbers
are unlikely to become large in their school, mostly due to competition for post-16
students from neighbouring schools and colleges where there is a substantial post16 offer. Some teachers mentioned the issue of convincing senior management of
the importance of Further Mathematics when small numbers made its provision
look non-viable.
In schools where Further Mathematics isn’t currently being offered it was hoped
that it would be introduced in either 2012 or 2013. For schools where there is
currently some provision, they hoped to move to a full timetable offer within sixth
form option blocks and move away from ‘out of hours’ or online provision, although
this was still considered to be important in supporting students. As part of this,
many mentioned the need for professional development of colleagues, so that they
3 See Appendix C for details of what access to Integral provides.
23
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
were able and confident to teach Further Mathematics modules. The views of senior
management on Further Mathematics were seen as crucial in bringing about these
developments.
Three factors emerged as crucial to the introduction of Further Mathematics, one
of which is the need for support from senior management. Secondly there must
be pupils currently in Year 11, and possibly Year 12, who wish to study Further
Mathematics in their current school. Several teachers described the need to
encourage and inspire Key Stage 4 students to study mathematics in the post-16
phase and referred to the FSMP’s enrichment activities and others (e.g. the Royal
Institution’s master classes) as being important in this respect. Thirdly, there must
be at least one teacher able and willing to support the students either through
teaching some of the course and/or pastoral support.
One teacher explained how, with FMSP advice, he was changing the approach to
teaching mathematics in his department from Key Stage 4, to help students make
connections between topics and, by using appropriate resources and teaching ideas,
to motivate them to continue with studying mathematics.
How did you hear about the FMSP and why did you decide to get in
touch with it?
Most of the teachers said they had come across or heard about the FMSP through
colleagues or networking and had followed this up with a visit to the website, or
had responded to an enquiry from the Area Coordinator. Some teachers first met
their Area Coordinator at a teacher meeting and support had developed from there.
One teacher explained how the Local Authority had organised a subject leaders’
meeting to which the FMSP Area Coordinator had been invited to make a
presentation. The teacher had subsequently made contact seeking advice and the
relationship had developed from there, with the FMSP now providing support.
Another teacher noted that the Local Authority adviser had recommended the
FMSP website to her, and she followed that up and registered her school with
the FMSP. She has subsequently met with the Area Coordinator to discuss the
development of A Level courses in mathematics and is now receiving support from
her.
Several of these 15 teachers said that information on the FMSP website had
inspired them to make a first enquiry which led to registration with the FMSP.
Two teachers had come across the FMSP through their involvement with MEI.
They had seen the link to the FMSP website on the MEI website which they had
followed up, and were very pleased gain access to the resources on the Integral
website4 as a result of registering with the FMSP.
One teacher explained how one of the current Area Coordinators was a former
colleague at another school, and they had stayed in touch. The Area Coordinator
was working with her ‘out of region’; she described the support as “brilliant” and
noted that one student was now thinking about taking a degree in mathematics.
4 See Appendix C for details of what access to Integral provides.
24
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Another teacher had been to a FMSP enrichment event which had both inspired
her and her pupils; she was hoping many of them would progress to level 3
mathematics.
Another teacher explained how a group of students from his school had been to a
university open day and been told about the importance of Further Mathematics;
the students asked why their school didn’t offer it. As a result, the Head Teacher
contacted the Area Coordinator, who helped initiate provision outside school time.
In this school, provision will move onto the timetable in September 2012
What support have you received so far, if any? How effective has it
been?
The 15 teachers interviewed were generally very pleased with the support they had
been given by the Area Coordinators. The FMSP had provided tuition for several
modules across these schools, had introduced students and teachers to the Integral
website and shown them how to make effective use of it. Some also appreciated the
advice on assessment and appropriate supporting textbooks.
Other teachers mentioned local professional development sessions with the FMSP;
one teacher was particularly impressed with a session on practical mechanics
from which he took ideas and used them with students. Some teachers noted the
enrichment events they had been to. They described how they and their students
found them inspiring and how they had given them ideas to pursue as teachers.
Some of these teachers had been to an Access to Further Mathematics event
(Section 4.5), which they said had increased their confidence to introduce Further
Mathematics as well as giving them information with which to convince students
and senior management of its importance.
Most of these teachers found the regular contact with the Area Coordinator
just to discuss progress and any issues arising reassuring. Many appreciated the
personal visits that Area Coordinators had made to their school. Area Coordinators
had provided some teaching or had talked to Key Stage 4 students about the
importance of mathematics and given them some challenging mathematics
problems to work on.
Some teachers were content to maintain contact by phone and by e-mail but
generally the teachers spoke of the reassurance they got from knowing that support
was available from the Area Coordinator if they needed it. Some teachers were
grateful for tuition help from the Area Coordinator when they felt under pressure
from the rest of their teaching or department managerial duties. One teacher was
grateful for having various resources and ideas brought to his attention.
Do you have any other comment on the FMSP?
The teachers generally reiterated their gratitude for the support they had received in
getting Further Mathematics up and running or planning for it to be on offer in the
near future and wanted this to continue.
25
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Several said that without the FMSP support, Further Mathematics wouldn’t be on
offer at their school.
One teacher noted that just meeting people involved with the FMSP and
discussing possibilities was stimulating and she was really pleased with the way
things were developing in her school. Her school was now retaining students
against post-16 competition from elsewhere. Another teacher noted the enthusiasm
of those involved with FMSP and how this inspired her, expressing appreciation at
being able to talk to people who understood the issues in mathematics education.
One teacher explained how she was hoping to collaborate with other schools and
the Area Coordinator to establish a local consortium. Another teacher noted how
she found the Integral website very helpful when she needed to refresh her own
subject knowledge.
Another teacher reiterated the important role that the FMSP was playing in
motivating Key Stage 4 students to continue their study of mathematics post16. It was noted how FMSP speakers are able to engage students’ interest in
mathematics whilst also showing them the importance of mathematics and the
career opportunities it can open up.
Some of these 15 teachers hoped to become more involved with FMSP activities.
Some had not yet taken any students to an enrichment event, but aimed to do
so. Others, who had visited an enrichment event, said they wanted to go to more.
Some teachers also noted the need for professional development, not just for
themselves but for colleagues, noting it was important to involve several teachers in
the mathematics department in the teaching of A level Mathematics and Further
Mathematics.
One teacher mentioned the Access to Further Mathematics event he had been
to (section 4.5). He valued the opportunity to meet with other teachers and the
FMSP officers and Area Coordinators noting the benefits of the discussion, the
sharing of ideas and networking opportunities and hoped that similar events could
be staged in the future, and not just for schools new to Further Mathematics.
4.4The impact of the priority schools initiative
The FMSP has kept a detailed register of the progress it is making with priority
schools. Key Performance Indicator 3b of the agreement with the DfE for this
period relates to this, see Appendix A.
The register was set up in September 2011 and is used to record progress with these
establishments. FMSP strategies for engagement with priority establishments have
involved e-mails, phone calls and visits from FMSP Area Coordinators, as well as
central mailings. Records of these are kept in the register.
Key Performance Indicator 3c of the agreement with the DfE for this period relates
to the number of priority schools that are able to offer AS FM to their students in
2012/13, see Appendix A.
Data provided by the FMSP shows that, as of May 2012, all of the 204 priority
26
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
schools and colleges had been contacted by the FMSP and 92 have replied. Of
those that have replied, 65 have had a meeting with a representative of the FMSP
to discuss and set up support. Of these, 36 are receiving a package of support from
the FMSP that will involve some or all of CPD, promotion of mathematics and
general advice and guidance.
The selection of the priority schools was based on August 2010 data according to
FMSP records. It transpired that some of the selected schools and colleges had
some Further Mathematics provision in place from September 2011, often as a
result of working with their Area Coordinator during 2010/11. Many of these have
continued to receive support from the FMSP this year (2011/12).
It is expected that the target of 40 priority and colleges schools offering Further
Mathematics in 2012/13 will be met.
4.5Access to Further Mathematics events
During March 2011 the FMSP held an event called ‘Access to Further
Mathematics’ in four English universities located in London, Manchester,
Warwick, and York. These events aimed to encourage the introduction of Further
Mathematics in schools and colleges that don’t currently offer it and to help
improve and develop provision in those that do. These events were not publicised
on the FMSP website, but rather delegates from targeted schools were invited.
Delegates included school senior managers as well as teachers of mathematics.
Feedback from the exit evaluation forms was positive, suggesting that the events
were successful (details given below).
This event was repeated in the same four locations in March 2012. The evaluator
attended the event in York. See Appendix D for the standard programme.
A full report on the event at York by the evaluator is available in Appendix D.
The evaluator found the event to be very comprehensive in making the case for
Further Mathematics. Feedback from the events that took place in March 2011 is
given in Table 10 below.
Table 10
London
Manchester
Warwick
York
Total
London
Manchester
Warwick
York
Total
London
Manchester
Warwick
York
teachers
22
17
22
22
83
information
received in
advance
3.5
3.3
3.6
3.3
3.4
more likely to
offer Further
Mathematics
yes
17
11
12
14
feedback forms
managers
1
2
0
1
4
3.7
3.7
4.0
3.6
3.8
total
23
19
22
23
87
suitability of
venue and
equipment
3.7
3.6
4.0
3.9
3.8
no
1
1
1
4
n/a
0
3
0
0
organisation
during course
attendees
managers
total
3
32
3
23
3
28
4
27
13
110
lunch/
suitability of
usefulness of
dinner and
accommodation
the event
refreshments
3.5
3.5
3.9
2.9
3.8
3.6
3.4
3.9
4.0
3.3
3.7
3.5
3.3
3.7
3.7
teachers
29
20
25
23
97
no answer
5
4
9
5
total
23
19
22
23
Source FMSP
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
It can be seen that the number of delegates was similar in each of the four venues.
Numbers were kept deliberately small to encourage interaction and discussion.
Senior managers as well as teachers were present at all events although teachers
predominated. Feedback forms were returned by 87 out of the 110 delegates, which
is return of about 75%.
The delegates were asked to rate the event under the six aspects shown, using the
following four point scale:
Excellent: 4 Good: 3 Adequate: 2 Poor: 1
The numbers shown in Table 10 for the six aspects are the average scores in each
location, and overall. The most important question in terms of meeting the aims of
the FMSP was about the usefulness of the event; that the average response was 3.7
indicates that this aim was met successfully.
The events appear to have met the aim of the FMSP to encourage schools and
colleges to offer Further Mathematics. Most of the delegates who responded to
the question on whether they were now more likely to make this offer, responded
positively with just a few responding negatively.
Delegates were also invited to offer further feedback and these generally reflected
the positive ratings. However, some delegates felt there were aspects of providing
Further Mathematics that were left out of the event and the FMSP should consider
these and other feedback comments, when designing the programme for future
events.
4.6Conclusions and Recommendations on work to
extend access to Further Mathematics
Engaging with schools and colleges attended by students from
deprived backgrounds
•The Area Coordinators in all areas of the country made considerable
efforts to establish contact with the priority schools they were given in
their region.
•There were varying degrees of success from no response to positive
development where it seems likely Further Mathematics will be offered
from September 2012, if it is not already offered.
•Area Coordinators should be involved in identifying the priority schools
in their area, as in some schools it seemed they had been working with
the FMSP for some time, and Further Mathematics was becoming well
established.
•Where a school or college did fail to respond, the FMSP needs to
consider a strategy of how best to try again, without alienating the school
into rejecting the offer of support. An Access to Further Mathematics
type event could be organised regionally for such schools.
•Of the 15 teachers interviewed, most want advice from the FMSP on
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
various aspects of provision from course management, to the use of
resources and the professional development opportunities available.
•Most of the teachers were grateful for the help and advice they
have already had from the FMSP, and having the Area Coordinator
available to help if required is giving them confidence to develop
Further Mathematics; they want their provision to become established
in the post-16 offer however few students this may attract in their
establishment.
Access to Further Mathematics events
•The feedback from the four Access to Further Mathematics events held in
March 2011 indicates these events are very successful.
•The event attended by the evaluator in March 2012 was very well
organised, gave a lot of information to the delegates and the case for
offering Further Mathematics was put very convincingly. Delegates
had plenty of opportunity to try out resources, discuss issues and ask
questions.
•The FMSP should follow up the teachers from the schools and colleges
who attended to see if their school or college has now started to offer
Further Mathematics, and if so how, and extent of the take up by
students.
•The events should be repeated in 2013. The date should be reconsidered
as March may be too late in the year for provision to be offered in the
following September.
•An event customised towards the priority schools might convince some of
those schools that they should work with the FMSP to offer provision.
29
5
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Teacher Support
5.1 CPD opportunities provided by the FMSP, including
uptake and feedback
The FMSP provides continuing professional development courses to support
teachers to develop their knowledge and skills for teaching both A level
Mathematics and Further Mathematics. Some of these are face-to-face events
whilst other courses take place online.
Attendance is measured in teacher days (one teacher attending a one day (or
equivalent) course). According to FMSP data, during 2010/11 700 teacher days
of CPD were provided via regional face-to-face events, 201 teacher days of CPD
were provided via live online courses and 204 teacher days of CPD were provided
through the FMSP’s Teaching Further Mathematics course (see section 5.3 below).
At the time of writing, according to FMSP data, the FMSP has provided or has
planned at least the same quantity of CPD for 2011/12. In addition to this 59
teachers are taking FMSP’s Teaching Advanced Mathematics Course and 43
teachers are taking the Teaching Further Mathematics course.
Teachers provide feedback on all FMSP CPD they attend using a four point scale
as shown below:
Excellent: 4 Good: 3 Adequate: 2 Poor: 1
Average figures for 2010/11 and 2011/12 to date are shown in Table 12
Table 12
Course content
Standard of delivery
Averages for 2011/12*
3.59
3.64
Averages for 2010/11
3.60
3.61
*This is based on the feedback that has been summarised and collated at the time of
writing (from 38 courses).
Source FMSP
KPIs 5a, 5b and 5c relate to the provision of CPD by the FMSP. The FMSP is on
course to meet all the success factors specified in these KPIs, see Appendix A for
full details.
Phase 3 of the evaluation focused on two particular CPD courses. The Teaching
Advanced Mathematics (TAM) course and the Teaching Further Mathematics
course (TFM).
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
5.2 Teaching Advanced Mathematics (TAM)
The TAM course is designed to support teachers who are teaching A level
Mathematics for the first time.
Participants are required to take an active role in eight study days, spread across the
year, focusing on A level Mathematics pedagogy. In addition, they study the content
of five A level modules, from a teaching and learning perspective, with support
using the online virtual classroom software Elluminate. They receive two school or
college visits from the course tutors. Participants have access to an extensive website
of teaching and learning materials and this access continues for two years after
course completion.
During the course, teachers are asked to compile a portfolio of mathematics
assignments and personal reflections on the course study days. Those wishing to
receive a Postgraduate Certificate submit additional work in the form of essays.
5.2.1 Gateway report
In 2008, the report ‘A Gateway to Teaching Advanced Mathematics’ was published;
it was based on feedback from teachers who had taken the TAM course at least
one year previously. In 2011 recent course participants were contacted and asked to
respond to the same questions. Feedback has been received from 52 participants.
The responses are universally consistent in their praise of the TAM course.
Phrases such as “inspirational teaching”, “brilliant lesson resources” and “excellent
preparation” are common in these responses and these previous participants are
actively putting into practice their experiences from the course in their current
teaching. One teacher described the TAM course as “the most effective professional
development I have participated in”. Some teachers noted how taking TAM gave
them the confidence to apply for posts at schools with sixth forms and they have
successfully taken up such posts and are now teaching A level Mathematics. One
teacher noted “The TAM course is what made it possible for me to teach A level; I
would not have done so without it”.
One teacher from an 11-16 school highlighted the effect of TAM on their GCSE
teaching, noting “I use many of the teaching techniques I have learned from TAM
such as types of questioning, forcing them to think more deeply in group work and
solving their own problems.” Another noted “TAM has undoubtedly increased my
confidence, opened my eyes to a wider range of resources and genuinely given me
a greater understanding and love of mathematics.” The following quote sums up
what these participants have said about the TAM course and how it has enhanced
their subject knowledge and understanding and their confidence to teach A level
Mathematics.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
“I am teaching to AS and A2 now. The TAM course was excellent. It gave me the
confidence to teach beyond GCSE. It improved my teaching not just for A level but overall
as a mathematics teacher. Moreover, it enhanced my understanding of the subject and
made me more passionate about maths.”
The above quotes are typical of the 52 responses received and show the TAM
course to be an exceptionally successful professional development course from
which its participants have benefitted greatly. Most of these previous participants
have subsequently taken another form of professional development and some are
now taking a course to support the teaching of Further Mathematics.
5.2.2Observation in school of a participant teaching
The evaluator visited a school in October 2011 where a teacher is a current TAM
participant and three of his colleagues are former TAM participants. The teacher
was observed delivering a lesson by the TAM Course Leader (CL), who gave
him feedback immediately following the lesson. The TAM course leader was
also observed by a colleague who herself is training to observe TAM participants
teaching a lesson and to give them feedback. As well as being present during the
lesson and subsequent feedback, the evaluator was also able to interview the three
teachers who had previously taken the TAM course, to elicit their views on the
course; these are included in section 5.2.5 below.
The feedback immediately followed the observed lesson, and consisted of
constructive criticism. There was praise for various aspects of the lesson, as well
as advice on what might have been done differently and how. The feedback was
supplied in written form as well soon after the lesson, with some clear points
for the teacher to think about both in terms of the seating arrangement in his
classroom, as well as the actual mathematics and its teaching. The teacher received
the verbal feedback positively and he seemed to find the feedback generally
encouraging. He subsequently sent an e-mail to the TAM CL thanking him for his
feedback and noting that he would act upon it.
This form of induction for those new to carrying out TAM schools visits proved
highly effective and this particular observer has gone on to carry out over 20 visits
in 2011/12 and will continue to do so in 2012/13. In this way the TAM course is
able to expand whilst maintaining high quality feedback to observed teachers.
5.2.3 Course providers meeting
The evaluator was present at a meeting of the course organisers at the three
universities currently offering the course, London South Bank, Manchester
Metropolitan and Warwick Universities, together with the TAM CL. This meeting
provided opportunity for the course organisers to meet with the CL and to discuss
various aspects of the course. In particular the content of the course days for
participants being held at the three venues was on the agenda which had been
circulated in advance of the meeting. The representatives from Manchester and
Warwick were relatively new to TAM so the meeting gave them good opportunity
to give their initial impressions of the course, and discuss them with the more
experienced representative from LSBU and the TAM CL. Several points were
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
raised in the discussion, including how participants need encouragement in
being reflective and having the confidence to take back ideas from TAM to their
classrooms, and not just with A level classes, but to consider KS3 and KS4 as well.
It was noted that some participants are reluctant to do the assignments for the
Masters degree aspect of TAM, and there was discussion on how they might be
encouraged to study the pedagogy as well as the mathematics at this level.
The TAM CL and the representative from LSBU brought ABC Maths (Awareness
of Big ideas in the Mathematics Classroom) to the attention of the other two; this
was an EU-funded project with colleagues in Germany and Austria. There was
discussion on this project and how it was influencing TAM, and the thinking of
those involved. It was suggested ABC ideas could be a focus during the course days.
There was considerable discussion over the eight course days, the required prereading by participants and the content and organisation of the days. The TAM CL
had supplied a draft programme for the eight days, which was amended following
discussion, so that the same programme would be followed at the three venues.
There was also discussion about encouraging participants to complete the
postgraduate work through completing the required assignments, with suggestions
made on how to achieve this.
The organisers were informed by the CL that TAM now has funding to 2014,
but participation will be encouraged from priority schools. These priority schools
are part of the wider remit of the FMSP, to encourage the take up of Further
Mathematics in schools where it is not at present offered. The schools are currently
being agreed between the FMSP and the DfE. Participants from the priority
schools will have the first opportunity to enrol on the TAM course for 2012/13.
This was a constructive meeting for the course organisers, with a lot of ideas being
put forward, and agreement reached on taking TAM forward for the current
participants. It is a model that will be valuable as the TAM course expands to
include new universities. The TAM CL supplied minutes of the meeting soon
afterwards, including action points for each of the organisers to follow up.
5.2.4Course days for participants
The evaluator was an observer at the second day of two consecutive university days
at LSBU. Day 2 of the course days was attended by 19 participants, together with
the TAM CL, the course organiser from LSBU and his colleague. Also present
was another colleague who is training to give feedback to TAM participants when
they are practising the teaching of A level Mathematics. When the participants
were given various tasks during the day she was able to get first-hand experience
of supporting them and helping them overcome difficulties, in the same way that
these teachers will ultimately support and help their own students. Group work
and interactive participation was encouraged, this being facilitated by the seating
arrangement in which the participants were organised into four groups, each round
a table.
Throughout the day the CL worked together with the university colleague to
33
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
support teachers with subject knowledge, teaching ideas (particularly questioning
skills, group work and use of dynamic imagery), reflecting on the experience and
focusing on Masters level work.
The participants on this course day had certainly engaged in a great deal of work,
but they were mostly engaged for the whole day. The feedback to the TAM CL
which has been shared with the evaluator reinforced this. Many said that although
after the two days they were exhausted, they felt they had been stretched and
challenged but had got a lot out of being present. In particular working with
colleagues, and sharing ideas in the solving of problems was found to highly
beneficial. Many had clearly already started the reflection process of how they could
put some of the ideas that they had encountered into practice in their own teaching.
5.2.5 Interviews with previous participants.
The evaluator interviewed eight previous participants; three at the school
mentioned in section 5.2.2 above and five by telephone. All interviews followed
the Durham University ethics code of practice in seeking the agreement of the
interviewee and informing them of the purpose of the interview. The participants
represented a range of age and experience, came from a wide range of mathematical
and teaching backgrounds, and worked in a range of settings (11-16 and 11-18
schools and sixth form colleges).
Common themes emerged and these are given below. The individual case studies
are available in Appendix E.
Whilst all of the participants enrolled on the course for support with learning
and then teaching A level Mathematics, most were not interested in the option of
Masters level accreditation and only two took that opportunity. It was felt there
was a good balance between subject knowledge and teaching ideas across all aspects
of the course. The participants particularly valued the university course days, the
opportunity to work with other teachers in similar positions, the ‘brilliant’ website
resources which are very widely used, and the recordings of the online sessions
to provide ideas of how to teach a topic before teaching it themselves. The lesson
observations were supportive and constructive. All eight would recommend the
TAM course to others.
5.2.6 Interviews with current participants
Telephone interviews were conducted with eleven participants from the 2011/12
TAM course at LSBU. Six of these focused specifically on the online sessions and
the Integral website and resources and five on the TAM course in general. The
questions used can be found in Appendix E.
Online sessions and the Integral website and resources
All the interviewees were very positive about the presentation of the mathematical
ideas in the online sessions with one describing it as “absolutely brilliant”. Several
noted they try to mimic the presentation style of the TAM CL in their own
teaching, as they believe through doing that they are teaching to enhance students’
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
understanding of a topic. All of them make some use of the recordings, with
some doing so extensively. Most of the participants will view a recording about a
particular topic before teaching it themselves, as an aid to lesson planning and how
they will present the topic to their students.
The Integral resources are widely used. Whilst some found the website easy to
navigate, others commented on finding it difficult possibly due to there being a lot
of material on the site. Of particular use were interactive applets, ‘key concepts’,
lesson plans, student-centred activities, and resources supporting the use of software
such as Autograph and GeoGebra.
Additional comments received from these six teachers about the TAM course in
general were similar to those made by previous participants; all were very positive
about their experience.
The TAM course in general.
These were quite extensive interviews; the five individual case studies can be seen in
the Appendix E.
These five participants had all come to the TAM course from quite contrasting
backgrounds, but they were all clearly benefitting from taking the course. They are
getting a lot from TAM in terms of awareness of the resources available on the
Integral website and elsewhere, and ideas for using these resources in their teaching.
It was notable how they liked to copy the style of the presentations seen in the
online sessions, but somewhat regrettable that they were not able to participate
more fully in these sessions. However, having the recordings available is clearly
invaluable to these teachers. It is apparent that commitment is essential to the
successful completion of TAM, and it is a pity that some of these participants had
to give up on the Masters degree through lack of available time rather than interest
in following it.
As far as teaching A level mathematics is concerned, these teachers all felt their
knowledge of the topics had improved and their confidence to teach them using
innovative ideas was increasing. Generally the lesson observations had gone
well, and they found the feedback very supportive, being comprehensive with
constructive ideas for improvement. Many commented on the positive impact the
course has had on their teaching at Key Stages 3 and 4
These participants like the way the TAM course is structured, and the opportunities
it brings to discuss and share ideas with like-minded teachers and the support
they get from each other and the tutors. They would all recommend the course
to others. Thus it is concluded that TAM is a very successful course that needs
no amendments, and the FMSP should continue to offer it in its present format,
including the Masters degree option.
5.3 Teaching Further Mathematics (TFM)
The evaluator was supplied with the names of 21 former participants who had taken
the TFM course during the past three years 2008/09 (7 participants), 2009/2010
35
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
(10 participants) and 2010/11 (4 participants). From these the evaluator selected
and contacted 10 participants on a pro-rata basis and requested an interview to
elicit their views of the course and the impact it had on their teaching and career.
The structure, but not the content, of TFM changed slightly for July 2012 to fit
with a new Masters link with Plymouth University, as described currently on the
FMSP website. As these participants took the TFM course prior to this, the aims
and structure of the course as described here are taken from what was previously on
the website and relate to the period up to July 2012.
Course Aims
The aim was to provide professional development for teachers who have some
experience of teaching A level Mathematics and who are starting to teach Further
Mathematics or considering teaching it in the near future. The course focuses on
the content of A level Further Mathematics modules from a teaching and learning
perspective. The emphasis is very much on expanding the participants’ mathematical
horizons and giving them a deeper understanding of the links within mathematics.
Course Structure
The course consists of three units. Each unit has a lead tutor who delivers a series
of tutorials using the online learning platform Elluminate. There is a study day for
each unit when participants meet at a university venue for a day of more intensive,
interactive study with their tutor and the course leader.
Teachers enrolled on the course receive a textbook for each unit of the course, two
years access to the Integral online resources, which includes the student and teacher
resources for the Further Pure Mathematics modules for all specifications, material
written specifically for the course and accessible only to course participants and
forums for support where they can communicate with the module tutor and each
other.
As well as delivering the online tutorial and study day, the tutor posts regular
messages with guidance and support on the forum and offers e-mail support.
Participants are encouraged to make contact with their local FMSP Area
Coordinator and, where possible, attend revision days and relevant lessons.
Assessment
At the end of each unit participants submit a handwritten solution of an exam-style
paper which is annotated with student misconceptions with reference to principal
examiners’ reports and either a detailed investigation into an aspect of the module
or interactive teaching resource for a topic in that module set within the context of
a detailed lesson plan or unit of work.
TFM can be studied as part of a Post Graduate Certificate in Teaching and
Learning Further Mathematics through the University of Warwick. This involves
participants submitting two essays (1000 and 3000 words) in addition to their
TFM portfolio and an action research ‘classroom based enquiry’.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
The Interviews
All interviews followed the Durham University ethics code of practice.
Interviewees were asked to give their reflective views on the course, using a proforma in which they were asked about:
•their background in terms of qualifications and teaching experience and
why they took the TFM course,
•their expectations on the taking the TFM course and the extent to which
these were met,
•what aspect(s) of the course they thought was particularly good,
•what aspect(s) could have been better and in what way(s),
•the impact of the course on their teaching, and on that of colleagues,
•the impact on their career,
•anything else they wished to add.
Teaching experience, qualifications and why take the TFM course?
Six participants had a degree in mathematics, whilst the others had a degree in
another area, three in an aspect of engineering and one in law. Teaching experience
varied from two to twenty years, and some of these participants had made career
changes into teaching after an earlier year in industry or commerce. Most had some
experience of teaching Further Mathematics and one participant said she wanted
to demonstrate to her head of department that she was capable of teaching it.
One teacher noted that she had taught up to GCSE but not A level, however she
wanted her international school to know she had the capability to teach students
beyond age 16. She also taught additional mathematics and wanted to be better
informed to advise students about the mathematics they could progress onto in
more advanced work. The teachers were unanimous in their reasons for taking
the course. These reasons comprised being brought up to date on curriculum and
assessment requirements, refreshing themselves about the mathematical content
and acquiring ideas to teach it. One participant noted that after a long career in
industry he wanted to reinvigorate himself through teaching Further Mathematics
so he needed to update his knowledge and skills.
What were your expectations of TFM and were they met?
The expectations included becoming more familiar with the resources available
for teaching, becoming familiar again with the content and developing a deeper
understanding of the mathematics and links between topics and an increased
confidence to teach Further Mathematics. All interviewees expected the course
to be demanding in terms of the work and time commitment, and that is what
they found, but that wasn’t a problem. The course had met the expectations of
all the interviewees and many found the experience very rewarding. There was
some comment that the online lectures were somewhat biased towards content
with little on how to teach a topic, but it was appreciated that to cover all content
was necessary. One participant commented that she found the pace of the online
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
lectures rather fast.
What did you think was particularly good about TFM?
Some of the 10 interviewees made an overall comment at first including, “the
course was put together very well”, “the course was brilliant”, “the course was
fantastic” and “the course was excellent”. Most went on to say they had got a lot
out of the university days, one of which was part of the Mathematics in Education
and Industry (MEI) conference. The opportunity to meet other like-minded
participants together with the course tutors was appreciated. The discussion and
sharing of experiences and ideas for teaching was clearly valued. Most of these 10
teachers said they had adopted and developed the ideas in their teaching. Some
would have liked more university days. One participant noted how he now has
a support role in his local area network. Several participants have continued to
network via forums. Some participants also mentioned the online sessions; they
liked the interactive nature and as one participant put it “I had to think quickly”.
Another liked the way she could choose her own level of participation. One
participant commented that at first he felt it unsatisfactory that some aspects of the
online sessions were left incomplete, but noted he had learnt a lot by completing
unfinished problems himself. Other aspects mentioned were the online resources,
the assignments that required creativity in investigations and opportunity to go
beyond the curriculum and looking at mathematics topics in different ways.
Could any aspect of TFM been better? If so, how?
There was little criticism of the TFM course. Most of the 10 interviewees again
mentioned a positive aspect of the course for them, such as being shown the ‘flash
resources’ and the interactive matching puzzles. One participant said the course
was “exactly what he wanted”, and he was able to fit professional and family
commitments around it. Another noted that she was very happy with the course
and the support she got from the tutors; “it couldn’t be better”. One interviewee was
disappointed by the low level of interaction with other participants in the online
sessions, whereas another thought it great that everyone joined in. One commented
on the basic level of mathematics in some of the sessions but appreciated that the
course catered for a variety of abilities. One noted that Saturday for the university
day was not convenient but was a manageable problem, as was the distance some
participants had to travel. One participant, who was relatively new to teaching
thought the course could be better aligned to the teaching year, leaving the summer
for completing assignment work.
To what extent has the TFM course impacted on your teaching?
Most of the 10 interviewees mentioned their increased confidence to teach the
FP2, 3 and 4 modules. One noted that through understanding the topics better he
believes that he teachers them better and he gets students thinking through using a
variety of approaches to a topic. One participant noted how he is able now to work
more closely with the very able students. Many also noted how they now make
regular use of interactive lessons and activities and less use of lecture style lessons
38
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
and dependence on a text book. One participant noted how this approach has
helped students overcome a feeling of failure and that most will engage positively
in a lesson. Some noted that through discussion and sharing with colleagues this
approach is spreading across KS3and 4. The numbers of students taking A level
Mathematics and Further Mathematics has increased in some schools and the
interviewees were supporting colleagues in their teaching at this level. Although
interviewees were uncertain as to why the increase had taken place there was one
suggestion that this increase had followed the interviewee’s participation in the
TFM course.
To what extent has the TFM course impacted on your career?
Some interviewees are very content in their current role, enjoying their teaching
of A Level Mathematics and Further Mathematics. One teacher is moving on
to a school where he will be offered more Further Mathematics teaching and
opportunity to work with some very able pupils. Another is hoping to be offered
some Further Mathematics teaching in her current school. One interviewee
is contemplating a Masters degree. Two interviewees noted they had moved
into promoted posts as KS5 lead teachers and thus had responsibility for the
organisation of Further Mathematics within their school and the professional
development of A Level teachers of mathematics.
Do you have any further comments on the TFM course?
All interviewees said that they would recommend the course to others and many
had already done so. One participant noted “in quality, it is way above any other
CPD course he has done”. Some reiterated the significant time and workload
commitment, but were grateful for having done the course; “it was a juggling act to
manage it all and it was hard work, but I would very much recommend this course”.
There were some suggestions for change or alternative ways of presentation. One
asked if the course could be modularised, so it might be taken in parts to reduce
the intensity of the workload. Two interviewees would have liked more face-to-face
contact and one suggested a residential weekend. Many again stressed the benefits
to them personally of having done the course and to their school or college through
being able to share ideas and help the professional development of other teachers.
One interviewee said “it is such a well thought out course from all aspects from
teaching to assessment”. One interviewee summed up the general feeling of these
participants; “it was a really useful and beneficial course”.
5.4Conclusions and recommendations on Teacher
Support
39
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Teaching Advanced Mathematics
•TAM is a very successful professional development course. The
participants interviewed and those who responded to the Gateway
report are unanimous in their appreciation of it in terms of their career
development.
•The organisation of the course and the ways in which it is delivered is
very effective for the majority of participants.
•The FMSP might consider online sessions or a special university day
aimed at those participants who have no pre-TAM experience of teaching
A level, to boost confidence when such participants are working with
more experienced colleagues.
•The TAM course should clearly continue to be offered in the current
three university locations.
•The FMSP should consider how the TAM course could be offered in
other university locations so it is accessible to more teachers.
•Teaching Further Mathematics
•All the feedback from the telephone interviews indicated that this was a
very successful course and did not need to be changed.
40
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
41
6
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Student Support
6.1Review of student survey on tuition through the
FMSP
Students who had received tuition in Further Mathematics through the FMSP
during 2010/11 were asked by the FMSP to complete an online feedback form
during the summer following their tuition. Forty four students responded. Students
received their tuition either through face-to-face sessions with their tutor, through
live online sessions using computers or both (see Table 12).
Table 12 How FMSP students received tuition in 2010/11.
Face-to-Face
Live Online Tuition
Both
Total
16
19
9
44
Source FMSP
The students were asked to rate the quality of the support they received under five
aspects of the tuition:1. The overall standard of tuition provided by the FMSP.
2. Your enjoyment of the course.
3. The setting and follow up of homework.
4. The usefulness and quality of the Integral online resources for Further
Mathematics.
5. The availability and accessibility of your FMSP tutor to support you with any
individual queries you may have had.
Students were asked to respond on a four point scale as shown below:Excellent: 4 Good: 3 Adequate: 2 Poor: 1
The results of the survey are summarised in Table 13.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table 13 Responses to the survey on tuition through the FMSP
Number of responses and percentage of total
Aspect
Excellent
Good
Adequate
Poor
Not applicable
Total
1
24
56%
16
37%
2
5%
1
2%
1
2%
44
2
17
39%
23
52%
2
5%
2
0%
0
0%
44
3
14
33%
22
52%
2
5%
4
5%
2
5%
44
4
20
48%
18
43%
2
5%
2
5%
2
5%
44
5
27
64%
11
26%
2
5%
2
5%
2
5%
44
Source FMSP
Table 13 shows that students are generally very satisfied with the tuition they
received. In all five aspects of the tuition survey, the responses indicate that 85%
of the students rated them as either good or excellent, and with the exception of
aspect 3, the setting and following up of homework, 90% of the students rated
them as good or excellent.
Students were invited to comment further on any particular aspect of the tuition
they had rated as inadequate or poor. There were 13 such responses. Four referred to
“poor teaching”, which was generally a reference to students thinking that teachers
were teaching too fast and/or at too high a level. Four referred specifically to lack
of clear explanations which related to difficulties in explaining some concepts,
the desirability of face-to-face sessions to supplement online sessions or finding
the explanations on the Integral website unhelpful. Four referred to the lack of
homework and follow up. As well as the comments on homework, one student
mentioned that he would have benefited from written feedback on his solutions
noting all the text book told you was whether your answer was right or wrong.
Another student commented that he had no choice in his modules as the school
made the decisions.
These were isolated cases, the responses from students were overwhelmingly
positive, but they none the less affected the students concerned and so the FMSP
who have the detailed responses having requested such feedback, should follow
them up.
Students were also invited to make any further comment on any aspect of their
experience, and 16 students did so. Of these, 12 were positive in nature with
students being grateful for the opportunity to study Further Mathematics and
the support they had received both during the course and in preparation for the
43
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
examinations. Comments from individual students varied from being general to
highlighting a particular aspect of their course. Some examples are:
“Really a great service and something of a life saver in my case.”
“The revision session for Decision Maths was extremely good, covering everything in the
course rapidly but thoroughly, exploring good exam questions as examples.”
“Overall I think the programme was excellent in not only helping me to achieve my
Further Maths grade but also my Core Maths grade.”
“My online tutor held a face-to-face session…I found this day very useful as it gave me
some extra time to catch up on areas of the course I had struggled with.”
There were several comments on the good support the students had received from
their FMSP tutors some noting that the response from tutors to e-mail enquiries
was swift and very helpful and that they had enjoyed the course.
“The FMSP online lessons and Integral resources site has been of great use to me.”
“I have had some fantastic tutors who were every helpful.”
“The tutors were helpful and knowledge able. I found their responses to any e-mails
containing problems, swift and informative.”
“I would like to say thanks for the support and excellent preparation for Further Maths
exams.”
“Overall the programme was fantastic; the help I received from my tutors was really good;
I enjoyed the course.”
However, two students expressed disappointment at the level of support they had
received.
“My college brought in maths tutors to teach us; they had no desire for us to do well and
the teaching was incredibly poor.”
“Overall I was extremely disappointed with the support I was given through the FMSP
and thoroughly regret being part of it; I had to teach myself the modules because the lessons
were so poor.”
“I think more time is needed for certain modules; for the FP3 exam we only started in
January and had only 1 hour a week…. There was a lot of content to cover particularly for
student who wanted to learn more than just three of the five options”.
Although the responses were overwhelmingly positive, it is important that the
FMSP follows up on any negative responses reported by students.
Interviews with students
Part of the evaluation plan was to pursue further some of the students’ responses.
Based on the response to the students’ survey, the evaluator selected ten students
with a view to interviewing them by telephone with a further ten as backup should
there be a lack of response. In fact invitations were sent out through the FMSP to
44
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
all 20 students, but only three responses were received by the evaluator. These three
students have been interviewed and all three indicated that they were grateful for
the opportunity to take Further Mathematics that the FMSP had offered them.
They were pleased with the support they received from their tutors, one more so
than the other two, with one student thinking he would have got a better grade
with more support. The students had experienced a mix of online tuition and faceto-face tuition. As there were only three responses, they were treated as three case
studies. Full details are available in Appendix E.
Conclusion
Although only three interviews took place, the contrasting circumstances of these
students illustrates the flexibility of the FMSP in meeting students’ needs. The
female student was full of praise for her tutors and the support she had received
through the FMSP; given that she hadn’t heard of Further Mathematics until her
Head of Department at school suggested she study it with the FMSP, to be doing a
degree is quite an achievement for all concerned.
Although the two male students made some criticism of the tutorial support they
received, all three students are pleased to have had the opportunity to take Further
Mathematics and believe it was influential in securing their progress to higher
education. They all highlighted that the topics they had met during their Further
Mathematics course has helped them in the first year of their degree courses, which
reinforces what was said in the Access to Further Mathematics event (Sections 4.5
and 4.6) about the benefits of studying Further Mathematics.
6.2 Tutor training
In 2010 and 2011, the FMSP organised two events for FMSP tutors, one in
London and one in Manchester.
The evaluation of the 2011 event consisted of four parts:
1. Attendance and purpose of the events.
2. Visit by the evaluator to the Tutor Event at Manchester University.
3. Analysis of feedback from the tutors via exit evaluation forms.
4. Feedback from tutors via telephone interviews.
Attendance and purpose of the events
There were 25 attendees in total at London and 11 attendees at Manchester,
together with three professional officers from the FMSP.
Table 14 shows the attendance by region and the classification of the delegate.
Delegates were classified as being experienced tutors (Ex’d; at least one year’s
experience), new tutors (New; in first year of tutoring), potential tutors (Pot’l;
considering becoming a tutor) or Area Coordinators (AC).
45
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
South East
South West
1
4
2
1
1
5
Total
East of England
4
London
West Midlands
East Midlands
Yorkshire and
the Humber
North West
North East
Table 14 Delegates from the FMSP regions who attended the tutor
events.
London
Ex’d
1
New
2
12
9
Pot’l
2
AC
1
1
2
2
Manchester
Ex’d
1
New
1
Pot’l
1
AC
Total
1
1
1
6
1
1
1
3
2
2
2
1
0
3
7
2
3
7
9
2
36
Source FMSP
Attendance varied quite considerably by region. Although tutors are strongly
recommended to attend, attendance is purely voluntary. It may be that well
established tutors see no reason to attend, but maybe Area Coordinators could do
more to encourage attendance as those who did attend found value in meeting with
other tutors and the FMSP professional officers. Travel expenses for tutors were
paid by the FMSP and the tutor also received a fee for attending, or their school
was reimbursed for cover costs.
In the information sent out in advance of the event it was said to be designed to:
1. Provide essential information about tutoring for the FMSP.
2. Enable discussion of Further Mathematics teaching and learning.
3. Enable FMSP tutors to meet and get to know other tutors.
4. Give information about getting involved in live online tutoring.
5. Give FMSP tutors the opportunity to feedback to the FMSP team.
The programme for the day was the same at each venue and allowed time for
informal networking, questions and discussion as well as formal input from the
FMSP officers.
The evaluator attended the event held at the University of Manchester. A full report
on the event by the evaluator can be found in Appendix F.
In the opinion of the evaluator, the aims of the event were met.
Attendees were invited to complete an exit evaluation form. An analysis of their
responses from both the Manchester and London is given below.
46
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
The tutors were asked to rate the event under six aspects:
1. Information received in advance of the course.
2. The organisation during the course.
3. The course content.
4. Standard of delivery.
5. Suitability of venue and equipment.
6. Refreshments.
At the London event 23 of the delegates completed exit evaluations forms. At the
Manchester event 7 were completed.
The information from the exit evaluation forms is summarised in Table 15.
Delegates rated six aspects of the event on a four point scale:
Excellent: 4 Good: 3 Adequate: 2 Poor: 1
Table 15 Tutors’ response to six aspects of the Tutor Event
London
Number of responses
Aspect
1
Excellent
Good
Adequate
Poor
Average rating
11
11
1
0
3.4
2
17
6
0
0
3.7
3
11
12
0
0
3.5
4
11
12
0
0
3.5
5
10
12
1
0
3.4
6
5
17
1
0
3.2
Manchester
Aspect
1
Number of responses
Excellent
Good
Adequate
Poor
Average rating
4
2
1
0
3.4
2
6
1
0
0
3.9
3
3
4
0
0
3.4
3.7
4
5
2
0
0
5
3
2
2
0
3.1
6
6
1
0
0
3.9
Source FMSP
It is seen that tutors and others attending these events were very positive about
their experience with the majority of the responses on the 30 completed feedback
forms being either good or excellent. The responses were very similar between the
London and Manchester events.
The respondents were invited to make any further comment on aspects 1 to 6. Most
respondents left this blank, but four comments focused on access to computers (no
hands-on facility at London; noise in the computer room at Manchester due to
students being present).
www.cem.org
47
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Respondents were also asked:
1. What was the most useful aspect of the day?
2. What changes, if any, would you suggest we make, when planning future
events?
3. Are there any other comments you would like to make?
1. What was the most useful aspect of the day?
All tutors responded to this question. Responses varied but the most frequent
was meeting and talking with other tutors and the FMSP professional officers.
Others noted the sharing of ideas and getting helpful hints about being a tutor
and discussion of the role in general, the updates on the FMSP activities and the
resources on the Integral website. The practical demonstration of an online tutorial
was also valued by two tutors at the London event and one new tutor noted the
support given by the FMSP.
2. What changes, if any, would you suggest we make,
when planning future events?
There were only four responses to this question. Two from London suggested the
need for hands on experience and training in the use of the Integral website. One
tutor requested more detail on online tutoring, and one hoped to meet his Area
Coordinator in person. FMSP should consider strongly encouraging the Area
Coordinators to attend these events.
3. Are there any other comments you would like to
make?
Again there was little response but some tutors did take the opportunity to say they
enjoyed the day and to say thank-you.
Overall the tutors’ feedback from the two events was very positive. There were a few
negative comments for the FMSP to take note of and to respond to.
Feedback from tutors via telephone interviews
In order to gather further feedback information on the tutors’ views of the events,
the evaluator contacted 12 tutors, six from each event, including experienced
tutors (7), new tutors (4) and a potential tutor and invited them to participate in a
telephone interview. Nine interviews were conducted, 6 with experienced tutors, 2
with new tutors and one with a potential tutor. All interviews followed the Durham
University ethics code of practice. The interviews were conducted using a pro-forma
which invited tutors to comment on:
1. Why they had attended the event
2. The suitability of the programme.
3. How it had affected their role as a tutor.
48
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Why attend the event?
Some of the nine tutors mentioned that they attended out of a sense of obligation,
feeling it is expected of them. Others took the opportunity to feel more part of the
organisation noting tutors are managed at a distance and that they can feel remote.
One mentioned “a need to belong” and some mentioned that they wanted to see
and share the commitment and enthusiasm of those involved with the FMSP.
Another reason for attending was to get an update on what is happening in the
FMSP. The most common reason was the opportunity to meet other tutors and
FMSP team members together with opportunity to share experiences.
Suitability of programme
The attendee who was considering becoming a tutor didn’t think the programme
was appropriate to him. He was disappointed not to have been “followed up” after
initial contact and surprised no-one had checked his qualifications. He5 would have
liked to observe the resources being used in a “live” online session.
The new tutor thought the event was her induction and training course. She
thought the split of new and experienced tutors in London was useful, but still
valued the input from the experienced tutors and the opportunity to talk to them
informally about the role and self-management.
Experienced tutors noted a good balance between formal and informal discussion.
One observed that no actual mathematics had been included this year, which he
thought was an improvement on the 2010 event.
The experienced tutors generally agreed that they do need a refresher on what is
expected of them, and information on new developments like the Live Interactive
Lectures. Most would have liked more input on managing the students’ teaching
and learning on limited time for the modules, including use of online tests and the
Integral website. Some tutors acknowledged that although study plans are provided
on the website, they would have liked to explore ways of using the website resources
more imaginatively. One tutor emphasised how he would have liked more on “how
to…” rather than just receiving information; for example, how best to get work
from students; what is the best mechanism by which to receive work?
Some of the nine tutors noted that the IT session could have been more focused
for those not familiar with the Integral website and the resources there. Some
emphasised the need to know how to navigate so they could advise students and
they would have liked more opportunity for guided hands-on experience. Some also
mentioned it would be helpful similarly to have some guided hands on experience
with GeoGebra.
Most tutors thought that an annual event seemed appropriate although most
would attend another event if they considered it looked useful. Some suggested
an additional event(s), regionally based, where there would be a focus on using
the Integral website to support the teaching and learning of specific topics and
modules.
5 It should be noted that before this potential tutor is offered any tutorial work, his qualifications would be checked by the FMSP.
49
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Role as a tutor
Tutors are generally (semi) retired mathematics teachers or from an IT industrial
background; they know the mathematics, or at least agree that they should. They
had received no specific training as such, but had been guided and advised by their
local Area Coordinator. The event gave some reassurance they were doing things
“right” as a tutor.
Some of the nine tutors would have liked feedback on their performance;
particularly the outcome of module examinations for the students. Also, some
would like advice on how tutors should fit in with a school’s reporting system,
particularly on predicted grades, and what is required of them as tutors in this
respect.
Some concern was raised about less able students with respect to whether they
receive adequate support through online tutoring and queried whether the FMSP
could do anything to encourage such students to seek further support through their
tutor.
Support for tutors themselves was felt to be generally good, both from the local
Area Coordinator and the FMSP administration at Trowbridge. The newsletter is
appreciated but one tutor asked if there could be “headline” updates via e-mail.
However, some tutors noted that as tutoring goes online, there is less, if any,
attachment to an Area Coordinator. The question was raised about whether
the FMSP should monitor tutor performance and offer an annual performance
management review.
Some tutors voiced concern over the time it took to get the students organized,
noting their courses did not start until October half term.
Some tutors noted that they generally put in more time than they are paid for.
6.3 Review of online revision
The FMSP provides a comprehensive series of live online revision sessions during
December/January and May/June each year to coincide with the winter and
summer examination series. These revision sessions cover all the modules that can
form part of a Further Mathematics qualification for all specifications. The sessions
are free to attend for students and teachers in schools and colleges registered
with the FMSP. At the end of a session, students are asked to complete an online
feedback form.
The analysis below is for the feedback for revision sessions held during 2010/11.
There were 583 respondents but 16 of these did not refer specifically to an
examination board and/or a particular module and 3 referred to the A level module
C1, which is not a possible Further Mathematics module. These 19 responses were
excluded from the analysis.
Table 16 shows an initial breakdown of these responses by examination board.
50
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table 16
Examination board
Number of responses
percent
AQA
140
25%
Edexcel
165
29%
MEI
143
25%
OCR
116
21%
Total
564
100%
Source FMSP
It is seen in Table 16 that attendance at online revision sessions in 2011 was quite
evenly spread over the four examination boards.
It should be noted that both students and teachers were invited to make a response,
and although some teachers did this (17), the vast majority of the responses were
from students (547). The respondents were asked to rate the revision session on
three aspects:
1. The course content.
2. Quality of delivery.
3. Elluminate as a platform for delivering the session.
Students and teachers were asked to respond on the four point scale:
Excellent: 4 Good: 3 Adequate: 2 Poor: 1
Students and teachers were also asked:
4. Would you recommend this revision session to other students?
5. Do you feel better prepared for your examination after this revision session?
6. Did you have any problems accessing Elluminate?
7. Are there any areas that were not covered in the revision session with which
you feel you need support?
Table 14 shows the responses for course content
Table 14
Examination
Board
Excellent
Good
Adequate
Poor
Total Responses
AQA
55.0%
40.7%
4.3%
0%
140
Edexcel
53.9%
40.6%
5.5%
0%
165
MEI
55.9%
42.7%
1.4%
0%
143
OCR
57.8%
37.1%
5.2%
0%
116
Overall
55.5%
40.4%
4.1%
0%
564
Source FMSP
The vast majority of respondents, 96%, rated the course content of the sessions as
good or excellent across the four examination boards.
51
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table 15 shows the responses for delivery quality
Table 15
Examination
Board
Excellent
Good
Adequate
Poor
Total Responses
AQA
61.4%
34.3%
3.6%
0.7%
140
Edexcel
63.6%
30.3%
5.5%
0.6%
165
MEI
61.1%
36.1%
2.8%
0.0%
144
OCR
60.0%
32.2%
6.1%
1.7%
115
Overall
61.7%
33.2%
4.4%
0.7%
564
Source FMSP
Table 15 indicates that more respondents rated the delivery of their revision session
as excellent compared to the content, but also there was a little more criticism,
with overall 29 respondents (about 5%) rating the session to be adequate or poor.
The content and delivery quality of a revision session are controlled by the session
presenter so it would be useful for the FMSP to investigate the negative responses
to determine whether they were due to factors associated with the examination
board or the presenter.
Table 16 shows the responses for Elluminate quality
Table 16
Examination
Board
Excellent
Good
Adequate
Poor
Total Responses
AQA
58.3%
38.1%
2.9%
0.7%
139
Edexcel
44.8%
47.9%
7.3%
0.0%
165
MEI
58.7%
32.9%
8.4%
0.0%
143
OCR
54.3%
37.1%
7.8%
0.9%
116
Overall
53.6%
39.4%
6.6%
0.4%
563
Source FMSP
Table 16 indicates that the vast majority rated this positively but about 7% as
adequate or poor. It appears that some students and teachers may have experienced
problems. This might be more difficult for the FMSP to address as the respondents
may have had technical problems with their own computing equipment or may not
have followed advice about setting the equipment up. The FMSP could offer a presession test run, so that respondents can check their computing equipment.
Table 17 shows how many would recommend their session to other students
Table 17
Examination Board
Yes
No
Total Responses
AQA
97.9%
2.1%
140
Edexcel
98.2%
1.8%
165
MEI
100%
0%
143
OCR
95.7%
4.3%
116
Overall
98.0%
2.0%
564
Source FMSP
52
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
The responses in Table 17 indicate that virtually all the respondents were
sufficiently satisfied with their session to recommend it to others. However,
the FMSP should find out which revision session the negative responses were
associated with and investigate further.
Table 18 shows how many thought they were better prepared for their examination.
Table 18
Examination Board
Yes
No
Total Responses
AQA
97.1%
2.9%
137
Edexcel
90.9%
9.1%
164
MEI
95.1%
4.9%
143
OCR
91.2%
8.9%
116
Overall
93.5%
6.5%
557
Source FMSP
Table 18 again indicates that the majority of responses were positive but the
FMSP should identify the sessions associated with the negative responses to see if
improvements are necessary.
About 25% of the respondents made a comment on the session content or the
quality of the delivery, most of which were very positive in nature, saying how
helpful the session had been and praising the presentation and knowledge of the
teacher running the session with some saying it was particularly good to get a
fresh perspective on the topics. There were some comments about sessions running
out of time or being somewhat rushed, particularly in the decision mathematics
sessions, and here too the FMSP could look in more detail to see if there is scope
for improvement.
6.4 Key Stage 4 enrichment events
During 2010 the FMSP ran a series of mathematics enrichment events for Key
Stage 4 students at various locations around England. Some of these were funded
by a grant provided by the Clothworkers’ Foundation. The events aimed to inspire
Key Stage 4 students’ interest in mathematics and to encourage them to consider
going on to study AS level and A level Mathematics and Further Mathematics
after their GCSEs.
Feedback from students and teachers who attended these events was obtained and
summarised for 30 such events on the FMSP website. An analysis of this feedback
is shown in Table 19 below. It can be seen that the events were spread around
England and across the calendar year. They were held mostly on university premises,
but were also held in schools, FE colleges and other venues as well.
Table 19 indicates that the number of students attending the events varied
considerably from 20 to 280, but also that half of the events were attended by about
100 or more students. Students, and the teachers who attended the events with
them, were asked to rate the contents of the day on a four point scale as shown
below:
Excellent: 4 Good: 3 Adequate: 2 Poor: 1
53
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
The figures shown in the column “content of the day” are the average ratings for the
students and teachers. The number shown in brackets in the “students” column is
the number of returned feedback forms (where this information is available).
With the exception of four events, these events were rated good or excellent, and
were highly likely to be recommended to other students.
The students were also asked whether the event had influenced their thoughts
about studying mathematics post-16. Where this information is available, with two
exceptions, at least a third of students attending said they were more likely to study
mathematics post-16 following the event, and at some events this percentage was
considerably higher.
Event
Date of
Event
Region
Venue
Students
Teachers
Content of
the day
Recommend
to other
students
more or
less likely
to study
mathematics
post 16?
Table 19 Analysis of feedback forms from Key Stage 4 Enrichment
Events 2010
1
30/03/2010
SW
University of Plymouth
96
6
3.1
yes
84%
2
09/06/2010
SE
University of Southampton
57
5
3.2
100%
3
10/06/2010
SE
University of Southampton
54
6
3.2
100%
4
5
23/06/2010
23/06/2010
NW
London
University of Liverpool
University of Greenwich
14
12
3.0
3.0
6
23/06/2010
SW
Bournemouth University
20
7
29/06/2010
NE
The Workplace, Newton Aycliffe
8
29/06/2010
NW
University of Manchester
9
07/07/2010
EM
Nottingham University
10
11
08/07/2010
08/07/2010
London
Y&H
Royal Holloway University of London
University of Leeds
12
09/07/2010
EofE
University of Cambridge
13
14
13/07/2010
16/07/2010
SW
Y&H
New College, Swindon
York University
84
107 (94 )
280
(152)
134
(124)
116 (34)
160
(124)
112 (26)
80 (77)
167
(136)
80 (78)
78 (63)
15
15/09/2010
EM
Keele University
16
16/09/2010
EM
Staffordshire University
no
10%
n-a
6%
91%
81%
7%
11%
2%
8%
more less same n-a
37% 6% 50% 7%
No
No
No
No
info' info' info' info'
No
No
No
No
info' info' info' info'
40% 2% 54% 4%
38% 2% 54% 6%
3.0
92%
5%
3%
46%
5%
47%
2%
16
3.0
84%
10%
6%
37%
4%
54%
5%
13
3.3
97%
3%
50%
3%
47%
18
3.0
91%
9%
52%
4%
44%
19
9
3.7
3.1
96%
90%
4%
6%
4%
85%
34%
2%
11%
60%
4%
4%
25
3.2
91%
7%
2%
41%
1%
54%
3%
8
10
3.0
3.0
9%
4%
31%
41%
6%
2%
59%
57%
4%
74 (46)
6
3.4
3.1
no
info
6%
2%
5
no
info
3%
44%
101 (91)
87%
100%
no
info
91%
54%
No
info'
54%
No
info'
19%
1%
No
info'
2%
45%
No
info'
81%
17
17/09/2010
EM
University of Northamptonshire
36
5
3.4
92%
18
17/09/2010
London
Kingston University
8
3.5
98%
19
24/09/2010
SE
University of Sussex
16
3.3
93%
3%
4%
76%
2%
18%
4%
20
01/10/2010
SE
Aylesbury High School
14
2.9
87%
8%
5%
41%
5%
52%
2%
21
22
23
24
25
26
27
28
29
30
15/10/2010
21/10/2010
22/10/2010
27/10/2010
02/11/2010
13/11/2010
19/11/2010
10/12/2010
13/12/2010
14/12/2010
Y&H
SW
EM
London
NW
SW
SE
NW
SW
SW
The Lawns, Hull University
Town Hall, Chippenham
Franklin College, NE Lincs
University College London
University of Manchester
South Wilts Grammar School, Salisbury
Ousedale School, Milton Keynes
Holmes Chapel Cheshire
Tremough Campus, Cornwall.
Cornwall College, St Austell.
54
149
(105)
225
(196)
70
96
84 (77)
60
100 (28)
102 (90)
20
50 (8 )
90 (76)
98 (52)
7
9
7
0
9
9
5
9
6
5
3.0
3.1
3.2
3.3
2.9
2.9
3.1
2.9
3.1
3.2
91% 9%
92% 8%
91% 9%
96% 2%
93% 7%
82% 17%
75% 25%
100%
94% 1%
94% 2%
23%
55%
49%
72%
32%
34%
65%
25%
66%
46%
7% 70%
2% 41% 2%
2% 48% 1%
3% 25%
7% 61%
11% 51% 4%
5% 35%
63% 23%
33% 1%
52% 2%
8%
2%
1%
5%
4%
Source FMSP
54
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Key Stage 4 enrichment events 2011/12
The FMSP has continued to offer enrichment events with the same aims as above.
The programme for 2011/12 can be found in Appendix F. Key Performance
Indicators 4a, 4b and 4c relate to this, see Appendix A. At the time of writing, the
FMSP is on target to achieve the success factors described for these KPIs.
The events are spread across the academic year and held at various venues across
England. The titles of the events vary and the nature of the events is not the same
in each venue, but they all have the same principal aim.
The evaluator visited one event, (the Further Mathematics Conference held at
Solihull Sixth Form College), to observe the students’ reaction and degree of
participation. This was followed up by telephone interviews with teachers who had
attended one of the 2011/12 events with their students. Against a target of ten
interviews, 15 teachers were contacted and invited to participate in a telephone
interview and nine interviews were conducted, again all following the Durham
University ethics code of practice. The events attended by the nine interviewees are
shown in the programme in Appendix G.
6.5 Case study – Solihull Further Mathematics
Conference 2012
The Conference was sub-titled “Maths in Sports and More…”. The event was
attended by 139 students from 10 different schools, mostly from Solihull and
Birmingham with one from further away. This included four 11-16 schools.
The day included a sessions on a variety of topics. Details can be found in Appendix F
The evaluator found the event to be very well organised and the sessions attended
entertaining and stimulating. There were some concerns about the amount of
mathematics directly related to the school curriculum in one of the sessions. The
final plenary session was particularly excellent with the presenter expertly blending
entertainment with more serious teaching. A full report on the conference can be
found in Appendix F.
Some feedback from teachers on this event
Participants returned feedback forms to the event organiser who summarized the
responses. The teachers were generally very happy with the venue and the content
of the afternoon. The students had enjoyed the presentations and particularly
the plenary session on mathematics in sport. The teachers were asked what they
thought their students had learnt from the day. The following are some of the
responses:
•‘bringing maths to life’
•‘interesting applications to the real world, such as coding’
• ‘problem solving; life of maths after GCSE’
•‘how widely maths is used every day’
•‘inspired to further studies; seen broader applications of maths’.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Some teachers commented that they would have liked the event to be a whole day
so their students could have experienced more of the sessions. This was the main
criticism. One teacher did ask for a “welcome pack” to be sent out in advance of the
event, so that students could be better prepared and another asked if there could be
a resource pack, based on the sessions, to take away at the end. The organiser noted
that this is the first time she has seen such requests, noting further that perhaps
teachers’ expectations of these enrichment events are rising.
Telephone interview with one teacher who had attended the Solihull
event
This teacher had taken 15 students from year 11 to the event.
Her comments on the activities experienced by herself or fed back from the
students are as follows:
•Code breaking was good but couldn’t see the relationship to A level.
•Statistics was an open ended task and the students needed help to
progress with it.
•The balloons based activity was fun, but there wasn’t a lot of maths.
•The projectiles really needed a longer time to get into the maths and
understand it.
•The road show was fun but really what was the point?
•Evolution; couldn’t see the point.
•The plenary session on maths in sport was brilliant.
The teacher felt that a full day would have been a better experience for her so
that they could have experienced more of the activities. She also felt the sessions
could have been longer to allow more development of the associated mathematics.
She felt that her students did benefit from attending the event but this could
have been enhanced by some pre-event preparatory work had suitable materials
been available. Although the students had enjoyed the event, she didn’t think that
their mathematics knowledge and understanding had improved and she found it
difficult to relate the mathematics at the event to A level Mathematics and Further
Mathematics. She emphasised that she would have liked longer sessions with
greater mathematical content.
This teacher’s views do raise an issue for the FMSP to consider, and that is about
what is the right balance between fun and entertainment and the mathematics
and its relevance to A level work. More so, can such a balance be achieved across a
range of several different activities? However, if the emphasis is on applications of
mathematics not usually met in school being used to inspire pupils, then relevance
to A level work is perhaps not a prime consideration.
Despite her criticisms the teacher, however, said she would certainly take another
group of students to a similar event, feeling the overall experience was good for her
students, particularly the gifted and talented. She felt some had been inspired by
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
the enthusiasm of the presenters, and that it was good for the students to meet and
work with students from other schools. In this respect, for this teacher, the event
would appear to have achieved its aim.
Interviews with teachers who had attended other events in 2011/12
All the telephone interviews with teachers followed a pro-forma which covered the
following points:
•Pre-event organisation and administration.
•Which students attended? Was there any pre-event preparation?
•What were your expectations of the event? Were they met?
•What aspect was particularly good; what could have been better?
•Impact on your students; what do you think your students learnt from the
day?
•Any other comments?
Pre-event organisation and administration
This was generally felt to be very good. Initial information was obtained through
the regional FMSP website and/or flyers sent to the school. Organisers, who were
often FMSP Area Coordinators, were quick to respond to any queries. One teacher
commented that there had been plenty of time to get the paperwork required for
out-of-school visits organised. In some cases a programme had been sent out in
advance, so teachers knew what to expect and some had been given guidance on the
sort of mathematics that would be involved.
Which students attended? Was there any pre-event preparation?
These were either a group of Year 10 students or Year 11 students and usually
from the top two sets in mathematics. Students who had shown enthusiasm for
mathematics tended to be chosen where places were limited. Numbers attending
varied considerably from less than 10 students from a school to over 50 from
another. It was noted in some cases schools were allowed to increase their quota but
this depended on responses from schools and the size of the venue.
Little classroom based preparation was reported, with most teachers just telling
their students to expect a range of activities.
What were your expectations of the event? Were they met?
Most of the nine teachers said they expected a mix of lectures and activities and
challenges to the students. Some teachers were more specific; one hoped her
students would experience “widening horizons” and be shown mathematics beyond
the school curriculum. There was a similar response from another who wanted his
students to see mathematics in a context different to that usually met in school.
One teacher particularly wanted his more able students to be challenged. Another
teacher hoped the event would be motivating for her students and that they would
see that “mathematics is more than just numbers”.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
All felt that generally their expectations had been met and that their students had
been actively involved in all aspects of the event.
One teacher felt her students benefitted more from listening to lectures, which
they found to be really good, rather than the challenges which they found to be too
difficult. This teacher noted that the challenges didn’t seem to relate to the lectures,
whereas another teacher thought it was brilliant that her gifted and talented
students were really challenged. Getting the level challenge ‘right’ so that students
don’t find an activity too difficult or too easy and so deter them from further study
in mathematics, is another issue for the FMSP to consider.
Most teachers felt that their students had seen various aspects of mathematics
and its uses that they would not have met in school. These ranged from origins
of numbers and the philosophy of mathematics to some practical mechanics
and to the mathematics of nurturing the eggs of penguins. Several had seen the
presentation on juggling, noting students’ surprise that it involved mathematics.
Several also mentioned that the students had found a lecture on codes and code
breaking to be very interesting. This feedback generally indicates the positive
impact of the enrichment events, and the way in which they can inspire interest in
mathematics.
What aspect was particularly good; what could have been better?
One teacher commented that she was very impressed with the whole thing; it was
very well organised. Other teachers mentioned particular lectures or activities.
One mentioned again the ‘story of maths’ and where numbers came from noting
the speaker was entertaining in his presentation. There were similar comments
on the presentation on the philosophy of mathematics. One teacher highlighted
the practical mechanics and how different it was to anything students experience
in GCSE. The presentation on juggling was again mentioned by many, with one
teacher noting a group of students pursued this further back at school through
the presenter’s website. Other teachers mentioned the lecture on mathematics and
music where the presenter brought out the links between the two. The teachers’
feedback here again indicates the positive impact of the events and meeting the
aim of inspiring students with applications of mathematics they wouldn’t meet in
school.
In terms of what was not so good, some teachers said they had no criticism and that
they and the students had enjoyed the whole event. One teacher felt that the talk
on careers was not well geared for Year 10 students and it needed to be simplified.
Another thought the lecture on the importance of mathematics and its relationship
to careers was more like a speech and was too long and not motivating. One teacher
noted that the lecture on rainbows and their curvature was very interesting, but it
would have been better with a related activity. One teacher, who had taken a group
of Year 11 students to an event, thought they found the mathematics too easy, and
thought there could be different events for Year 10 and 11 pupils, again suggesting
the FMSP needs to consider carefully the level of challenge associated with
activities in an event.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Impact on students; what do you think your students learnt from the
day?
The response here was generally very positive. Several teachers referred to students
as “buzzing” after the event and there was a lot of discussion related to the event
on the way home. Many teachers said that students had developed increased
confidence to take on a challenge and this fed through to them wanting to do A
level mathematics; a ‘can-do’ attitude was developing.
One teacher noted that his students had really enjoyed it but would have liked
some even more challenging activities rather be lectured on the importance of
maths, again raising the issue of an appropriate level of challenge in an activity.
Many teachers felt that their students’ perspectives on mathematics had been
broadened and that it was beneficial to interact with students from other schools.
There were comments such as “students realise there is more to mathematics
than what is met in school and there are many applications in the real world”.
Another teacher mentioned the inspirational presenters, thinking it was good
for her students to see these clever people who clearly love mathematics. One
teacher summed up the event and its effect on her Year 10 students as absolutely
brilliant, noting at least half those attending were now talking about taking A level
Mathematics. Whether this can be put down to attendance at the event alone is
doubtful, as able students might already be considering A level mathematics, but it
was very likely the event was influential.
Any other comments
In response to the invitation to make any further comment, all the teachers
reinforced their positive views about the event attended. Many said they would
certainly attend another event with some asking about whether there could be
more such events. One teacher wanted such events available to younger gifted and
talented students as well as Key Stage 4 students, noting how they all could benefit
from some inspiring presentations. In contrast, another teacher thought pupils
who were not gifted and talented and in the top sets could benefit from attending
such an event stating that he had a problem as to which students to bring next
time. Another teacher noted how she heard about her event by chance, so perhaps
publicity could be improved, and that she would like to see more rural schools,
like hers, becoming involved. Another teacher, from an inner city school, noted
how eye-opening it was for students to experience going out to a university for the
event. Another teacher, noted that this was the first enrichment event she has been
to and that it was fantastic to see new perspectives on mathematics; the event had
opened up a new world for her. One teacher commented that she liked the way in
which some problems had been left open, for students to think about some more
and that this had resulted in some follow up activities in school. Some teachers
mentioned the enjoyment their pupils had got out of attending the event and that
this had increased their enthusiasm for mathematics which was in turn influencing
their peers in the classroom. One teacher summed up the general feeling of these
eight teachers, when she said the event was really valued; it was a great opportunity
to interest those who are good at mathematics in what mathematics has to offer, or
as another put it more succinctly, “it was brilliant; can we have more?”.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
6.6 Senior Team Mathematics Challenge Enrichment
Events
These pilot enrichment events were offered free of charge to schools around the
country, through flyers sent by e-mail by Area Coordinators to their contacts in the
local schools. The purpose of the events was to help students prepare for the STMC
competition, through activities that focus on the skills and techniques needed in
each round of the competition. The events were particularly designed to attract new
participants and previous participants who had not done very well.
The events were mainly planned for October 2011 and, as the programme
was devised during the summer, notification to schools was not possible until
September 2011. Of the original 18 events planned, only eleven went ahead due
to lack of response to the others. The events were evaluated using exit feedback
forms as it was not possible for the evaluator to observe an actual event due to
cancellation. Feedback was also obtained through telephone interviews with ten of
the organisers.
Attendance at events varied from two to eleven schools. Four students attended
from each school, although there were some variations as some brought two
‘teams’- or ‘extra’ team members. Some organisers noted there was some last minute
drop out of schools from their event. The students were generally accompanied by
a teacher, and most university based events also had support from PGCE trainee
teachers. It is notable that at one event, a team from the local FE college had asked
to participate on their own volition.
All organisers understood that the focus of the invitation to participate had been
to schools that hadn’t previously entered STMC, or had not done particularly well,
although all events except one were open to all schools. Most organisers invited all
schools on their contact list as registered with the FMSP or those that had taken
part previously in the competition. The targeting seemed to work well with a good
response from the target schools and little interest from teams that traditionally do
well, such as independent schools. Some new schools that came to an enrichment
event did take part in the actual competition and at one event, three 11-16 schools
sent a team.
Organisers saw the day as giving the students from the target schools an
opportunity to be introduced to the challenge and to develop “belief in themselves”
and that they can participate and should not be intimidated by the “high flying”
schools.
All organisers considered that their event had gone very well, with the students
fully engaged in the activities. The resources provided were generally felt to be
excellent. Feedback from both students and their teachers was very positive.
Students had enjoyed the experience of working on types of mathematics problems
they hadn’t seen before, and learning strategies for the actual competition, like
working under time pressure and developing team work, and working with students
from other schools. Some teachers noted their students were “buzzing” after the
event and wanted more of the same, and definitely to be in the competition. This
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
enrichment aspect of the event had certainly worked well. It was also noted how the
supporting trainee teachers also benefited from the experience. These events were
felt to be very worthwhile despite the relatively low numbers. All the organisers
felt they wanted to put on a similar event next year, noting issues of planning and
timing which need to be addressed.
Participating students did not report attendance on a Saturday as being
problematic although it might have put others off. Most organisers felt that the
length and content of the day were appropriate and expressed concern that, if
held on a weekday, students and teachers may not be released to attend. One of
the enrichment events did take place on a weekday. Some organisers are going
to consider the feasibility of ‘twilight sessions’. It would appear that further
consultation with schools about the optimum time and format for similar
enrichment events is required.
Another issue mentioned by some was whether to guarantee a place in the
competition to priority schools. In some areas of the country it was noted that
places fill up very quickly. It is notable that some students and their teacher were
willing to travel to a neighbouring region so that they could take part in the
competition, which says a lot about the success of the event for them.
6.7 Conclusions and recommendations on Student
Support
Student tuition
•Feedback was generally very positive but there were issues with some
tutors which the FMSP should follow up.
•Students should be asked at the time of the survey if they are willing to be
interviewed about their experiences with the FMSP.
Tutor training
•This was certainly found worthwhile by those attending. The FMSP
should consider how to increase attendance.
•The FMSP should consider hosting regional events to encourage liaison
between tutors and Area Coordinators.
•The FMSP should review the programme to include more on “how to”.
For example, how to manage students’ learning on limited contact time
and how to conduct online tutoring. The programme might include
less information that could be provided using an alternative mode of
communication, for example a printed notes.
•Hold a separate event for hands-on training on the Integral website with
focussed tasks for the inexperienced.
•Tutors are concerned about not receiving formal feedback on their
performance. The FMSP could issue a policy document on this,
incorporating an annual review, and informing tutors of the examination
results of their students.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Online revision
•The FMSP offers revision sessions across a substantial number of modules
offered by the four examination boards.
•Feedback from students and teachers indicated that, in general, they were
very satisfied with the content and quality of these sessions, and that they
helped to prepare them well for the relevant examination.
•The FMSP should further explore negative feedback to assess whether
changes should be made. Similarly they should consider comments
relating to any omission from the sessions or suggestions on how sessions
might be improved.
•There were some reported technical difficulties with the virtual classroom
software and associated hardware. The FMSP could offer a pre-session
test run.
Key Stage 4 enrichment
•The feedback from teachers about the impact of these events on their
pupils was generally very positive.
•There was certainly a demand for more such events, and a case for
broadening them out to a wider range of pupils both by age and ability.
•There were some issues, particularly as highlighted by the teacher who
attended the Solihull event, of striking the right sort of balance between
challenging problems and accessibility of the mathematics to the students
and between relevance of the mathematics and topics to the pupils and
the relationship to post-16 study. However, there is considerable evidence
in general from the teacher feedback, that most presenters are getting this
balance about right.
STMC enrichment events
•These are worth repeating in 2012.
•The FMSP should consider when best to hold these events.
•The events should be promoted in the summer term, with reminders
issued early in the autumn term.
•The FMSP should consider guaranteeing a place in the competition
to schools and colleges that have attended an enrichment but have not
competed before or are new to the competition.
•There is demand for more places at STMC events.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
63
7
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Overall conclusions and
recommendations
During the time that the previous Further Mathematics Network and the
current Further Mathematics Support Programme have been in existence, the
number of students studying both AS level and A level Further Mathematics and
Mathematics has increased substantially. Between 2004/05 and 2010/11 numbers
taking A level Further Mathematics rose from 5192 to 11408 (an increase of
120%), and numbers taking AS level Further Mathematics rose from 3388 to
12427 (an increase of 267%); numbers taking A level Mathematics rose from 46034
to 75547 (an increase of 64%) and numbers taking AS level Mathematics rose from
54972 to 104586 (an increase of 90%).
The number of state funded establishments offering Further Mathematics has also
increased over this period. In 2010/11 there were 1264 state funded establishments
offering A level Further Mathematics, an increase 10% from 2008/09, and 1383
state funded establishments offering AS Further Mathematics, an increase of 18%.
The FMSP would thus appear to have had substantial influence in bringing about
this growth and its work should continue. In particular the FMSP should continue
to offer tuition to students who would otherwise be unable to access study of
Further Mathematics. Students who have received tuition through the FMSP are,
in general, very grateful for having had the opportunity to do so.
The priority schools initiative should continue, with a greater involvement of the
Area Coordinators in selecting the target schools and colleges. Teachers from
priority schools where Further Mathematics has been, or is about to be, introduced
are grateful for the support from the FMSP. Teachers who attended the ‘Access to
Further Mathematics’ events similarly gave very positive feedback about the advice
and support they received from the FMSP, and so these events should be repeated
in 2012/13.
The FMSP should continue to offer professional development opportunities to
all teachers, whether they be experienced teachers or new to A level teaching. The
CPD courses Teaching Advanced Mathematics and Teaching Further Mathematics
have been very successful in enhancing teachers’ classroom practice, and should
continue and be expanded. The FMSP should continue to offer and develop other
CPD opportunities, both face-to-face and online and facilitate teacher networks.
The FMSP tutors who attended the training events, in general benefitted from
doing so. Sharing practice, ideas and concerns with other tutors is clearly valued as
is meeting with representatives from the FMSP. The FMSP should encourage more
tutors to attend, offer them professional development opportunities, and encourage
liaison between regionally based tutors and their local Area Coordinator.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
The FMSP should continue to offer its online revision programme across all
examination boards and modules. These are clearly valued by the students who
attended them with the vast majority believing they were better prepared for their
examinations as a result, and said that they would recommend their revision session
to other students.
The FMSP plays an important role in encouraging an interest in mathematics
through its enrichment programmes for both pre-16 and post-16 students. The
nature of this provision needs to be reviewed as to its aims, but it is clear that, in
general, the aim of inspiring young people through meeting mathematics and
mathematicians they would not normally meet in school is effective.
The FMSP is continuing to make considerable progress towards achieving its aims
of widening access to Further Mathematics and increasing the number of students
who study both AS level and A level Mathematics, and Further Mathematics. It
is developing the knowledge, expertise and confidence of teachers to teach Further
Mathematics in their own schools and colleges.
The FMSP is making an important contribution to the development of
mathematics education in England and its work should continue.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Appendix A
FMSP Progress Report for DfE - overview of period from 1st April 2011 to 31st
March 2012, including reports against Key Performance Indicators (KPIs) for the
Agreement covering this period
Below is a summary of progress against KPIs for the Agreement covering the
period from 1st April 2011 to 31st March 2012. These KPIs are included as an
appendix to this report for convenience of reference. Figures in 1c, 6a, 6b are from
the DfE national pupil database. The date of this document is 11th May 2012.
66
KPI
Actual Progress
1a
Achieved
1b
Achieved
1c
Figure not yet available. The target for the proportion of FM-eligible institutions with students taking
A level FM during 2011/12 is 70%. The latest available figure is for 2010/11. This figure was 62.90%,
This has already been discussed with DfE: the number of FM-eligible institutions rose significantly from
2009/10 to 2010/11 (from 1,874 to 2,008), having remained at a fairly constant level from 2006-2010
(1,900 +/- 30). For this reason, the target in 1c for 2012/13 has remained at 70% in the set of KPIs for
the current FMSP Agreement.
1d
Achieved
2a
Achieved
2b
Achieved
3a
Achieved
3b
Achieved
3c
Success factor is measured in September 2012. A report on this KPI will follow ASAP in a FMSP
bimonthly report to the DfE after that date
4a
Achieved
4b
Achieved
4c
Some events are still to take place. The average feedback rating for those that have taken place so far
between ‘good’ and ‘excellent’.
5a
Achieved
5b
Achieved
5c
Success factor is measured in September 2012. A report on this KPI will follow ASAP in a FMSP
bimonthly report to the DfE after that date.
6a
Figure not yet available. The target for the proportion of FM-eligible institutions teaching FM during
2011/12 is 58%. The latest available figure for this is for 2010/11. This figure is 57%. This has already
been discussed with DfE: the number of FM-eligible institutions rose significantly from 2009/10 to
2010/11 (from 1,874 to 2,008), having remained at a fairly constant level from 2006-2010 (1,900 +/- 30).
For this reason, the target in 6a for 2012/13 has remained at 58% in the set of KPIs for the current FMSP
Agreement.
6b
Figure not yet available. The target for the proportion of students taking AS/A level Mathematics and
also taking AS/A level Further Mathematics in 2011/12 is 16%. The latest available figure for this is for
2010/11. This figure is 13.51%. This has already been discussed with the DfE: the last increase (from
2009-10 to 2010-11) in the number of students in state-funded institutions taking A level Mathematics
was significantly higher than in the previous year (11.5% compared to 8.2%). For this reason, the target
in 6b for 2012/13 has remained at 16% in the set of KPIs for the current FMSP agreement.
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
A detailed description of FMSP activity in relation to the objectives and KPIs
follows:
Objective 1:
The FMSP provides universal availability of FM
The FMSP ensures that any student in England can study Further Mathematics. It
does this in two ways:
•by supporting schools/colleges to provide an FM course for its students,
possibly in collaboration with other schools/colleges,
•where this cannot be arranged, by providing an external tutor.
The FMSP has met all requests to provide an external tutor during 2011/12.
External tutors either provide face-to-face tuition, online tuition or tuition using a
blend of the two.
The amount of tuition provided by the FMSP has reduced steadily over the past
three years as more schools/colleges have been able to provide tuition themselves
(see objective 6):
Year
Students
Total units
Face-to-face units
Live online units
2009/10
816
1977
1780
197
2010/11
607
1525
1207
318
2011/12
435
1113
879
227
The FMSP continues to attempt to engage with all schools/colleges not offering
FM, both through central mailings and contact via Area Coordinators. Records of
these transactions are kept on the FMSP database.
KPI 1a: FMSP national leadership team and FMSP Area Coordinators
maintain and extend their records of the FM status of FM-eligible institutions*
in each FM Area.
Success Factor: The FM status of 90% of all FM-eligible institutions* recorded
by the FMSP by 1 September 2011 has been updated by December 2011.
Actual: On 22 December 2011, the FM status of 94% of such institutions had
been updated.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
KPI 1b: FMSP Area Coordinators contact FM-eligible institutions* not offering
FM (or with unknown FM status) and encourage them to offer FM.
Success Factor: 75% of those not offering FM (or with unknown FM status)
have been contacted by the FMSP between September 2011 and December
2011 and 100% by March 2012.
Actual: On 24 October 2011, all schools/colleges were sent a hard copy mailing
including a letter describing the support the FMSP can offer, an advice and
guidance leaflet for teachers and an advice and guidance leaflet for students.
FMSP Area Coordinators also send e-mails and letters to their local schools/
colleges. Records of this are kept in the FMSP database and in termly returns
provided by the FMSP Area Coordinators. Three regional newsletters are
distributed to schools/colleges each year.
It should be noted that Area Coordinators have been encouraged to focus their
attention on priority schools/colleges (see objective 3).
In summary, 100% of those not offering FM (or with unknown FM status) were
contacted by March 2012.
KPI 1c: The proportion of FM-eligible institutions* with students taking A level
FM (in-house or externally) is increasing.
Success Factor: The national target is that 70% of FM-eligible institutions* have
students that complete A level FM in academic year 2011/12 according to DfE
data and FMSP records.
Actual: The 2011/12 figure is not yet available. The most recent available figures
for the proportion of schools/colleges offering FM (either in-house or external)
are:
2008/9: 59.75%
2009/10: 62.49%
2010/11: 62.90%
The 2011/12 figure will not be available until January 2013.
These figures have already been discussed with DfE: the number of FM-eligible
institutions rose significantly from 2009/10 to 2010/11 (from 1,874 to 2,008),
having remained at a fairly constant level from 2006-2010 (1,900 +/- 30). For
this reason, the target in 1c has remained at 70% in the set of KPIs for the
current FMSP Agreement.
KPI 1d: Excluding management and development costs, tuition delivered by the
FMSP is self-financing.
Success: Cost of provision is less than income received.
Actual Progress: Based on current figures the income generated from tuition
during 2011/12 will meet the cost of provision.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Objective 2:
All schools and colleges are aware of the support
available from the FMSP
Schools and colleges are made aware of the support of the FMSP in a variety of
ways:
•through the FMSP registration process,
•through central mailings,
•through local mailing and phone calls from Area Coordinators,
•via local FMSP newsletters,
•through KS5 teacher networks,
•via the FMSP website,
•through FMSP representation at teachers’ meetings and conferences.
As at 3 May 2012, the number of school/colleges registered with the FMSP is 2738
of 375 are 11–16 schools (roughly 40% of all 11-16 schools).
Under the current Agreement (that beginning in April 2012) the FMSP will be
working more closely with schools/colleges to provide support at KS4. The FMSP
is hoping to increase the number of registrations from 11-16 schools/colleges.
The FMSP has set up KS5 Teacher Networks and has encouraged teachers in
schools/colleges not offering FM to attend. At network events, teachers can benefit
from others’ experiences of setting up FM as well as from advice from their FMSP
Area Coordinator.
KPI 2a: Up-to-date information about the FMSP’s offer and programmes
reaches every state funded school or college teaching post-16 students and every
state-funded 11-16 school.
Success Factor: All post-16 institutions are sent an up-to-date direct mailing by
end October 2011. All 11-16 institutions are sent an up-to-date direct mailing
by end February 2012.
Actual: On 24 October 2011, all schools/colleges were sent a hard copy mailing
including a letter describing the support the FMSP can offer; an advice and
guidance leaflet for teachers and an advice and guidance leaflet for students.
On 17 Feb 2012, all 11-16 institutions were sent an FMSP letter promoting
the support that we can offer registered schools. This included an advice and
guidance leaflet for 11-16 institutions.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
KPI 2b: The FMSP collects information about good practice in FM and makes
it available through the FMSP website.
Success Factor: Comprehensive information on good practice is maintained and
kept updated on the FMSP website.
Actual: The FMSP website contains advice and guidance for both students and
teachers. This is regularly updated.
Advice to students includes: explaining the benefits of doing FM, help with
deciding whether to do FM, student case studies, a student study guide, maths
enrichment materials and advice/information about university admissions.
Work is underway to provide webpages which collect together advice about
specific progression opportunities resulting from doing FM, linking to other
organisations websites as appropriate.
Advice to teachers includes information about: offering Further Mathematics
(partly via case studies from other schools/colleges); university admissions; how
to access CPD events/support; revision events and maths enrichment events; and
how to access tuition for students via the FMSP.
Students and teachers can access leaflets/posters, enrichment/extension materials
for GCSE mathematics, resources about applications of mathematics in the real
world and links to other mathematics websites.
Objective 3:
The FMSP targets support to FM- eligible institutions*
not offering FM that have students from the most
deprived backgrounds
The FMSP refers to these institutions as ‘priority institutions’.
FMSP strategies for engagement with priority institutions have involved e-mails,
phone calls and visits from FMSP ACs, as well as central mailings. Records of these
are kept on the FMSP database.
The FMSP has sent a DfE-endorsed letter to 17 priority schools offering support.
This has been an effective strategy in cases where the FMSP found it difficult to
engage otherwise. In four cases it has resulted in engagement with the local Area
Coordinator leading to support being put in place.
In March 2012, the FMSP ran four ‘Access to Further Mathematics’ events.
Priority schools/colleges were given the first opportunity to book places at the
events. Following this, places at the events were opened up to all schools/colleges
with preference given to those not currently offering Further Mathematics. 57
schools/colleges attended the events of which 15 were priority schools/colleges.
The events featured speakers from universities; schools/colleges that have worked
with the FMSP to offer Further Mathematics in their institution; students who
studied Further Mathematics and are now undertaking STEM degrees; FMSP
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
central team members and Area Coordinators. The teachers and senior leaders who
took part all reported that they had found the events extremely useful.
The FMSP Progress Report for March/April 2012 for contains details of the
feedback from these events.
KPI 3a: The FMSP, in agreement with the DfE, establishes a mechanism for
identifying those FM eligible institutions* not offering FM that have students
from the most deprived backgrounds.
Success Factor: The mechanism is agreed by the end of June 2011.
Actual: This mechanism was agreed in May 2011 as follows:
A priority school/college is one which had more than 3 A Level Mathematics
but no AS or AL FM certifications in August 2010 (as per DfE Data) and either
had a deprivation index of at least 50% (according to the tax credit measure) or
is in a ward in which more than 20% of pupils are eligible for Free School Meals
(according to bespoke information provided by the DfE).
Where some of the above data are not available for an institution, but it is clear
that the institution is not offering FM and that it is attended by students from
deprived backgrounds, the FMSP will prioritise support.
KPI 3b: The FMSP maintains and updates a register of FM-eligible institutions*
not offering FM that have students from the most deprived backgrounds.
Success Factor: Data are updated on an on-going basis, and all records are
checked and updated where necessary at least once by March 2012.
Actual: The register was set up in September 2011 and is used to record progress
with these institutions (see KPI 3c below).
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
KPI 3c: The FMSP engages with FM-eligible institutions not offering FM that
have students from the most deprived backgrounds and helps them to offer FM.
Success Factor: By academic year 2012/13, 40 of these FM-eligible institutions
offer AS FM to their students.
Actual: All of the 204 priority schools/colleges have been contacted by the
FMSP and 92 have replied. Of those that have replied, 65 have had a meeting
with a representative of the FMSP to discuss and set up support. Of these, 36 are
receiving a package of support from the FMSP that will involve some or all of
CPD, maths promotion and general advice and guidance.
Because priority school allocation was based on August 2010 data, some priority
schools/colleges had a Further Mathematics provision in place from September
2011, often as a result of working with their Area Coordinator during 2010/11.
Many of these continue to receive support from the FMSP this year.
It is expected that the target that 40 priority/colleges schools will be offering
Further Mathematics in September 2012 will be met. A detailed report on this
will be included in the FMSP progress report that follows this date.
Objective 4:
The FMSP promotes the study of FM and level 3
mathematics to students in Key Stage 4
The FMSP promotes the study of FM and level 3 mathematics to students in Key
Stage 4 in a variety of ways:
•through enrichment events; typically these consist of a series of
presentations, workshops and quizzes and are aimed at KS4 students;
the mathematics covered ranges from pure mathematics and abstract
problem-solving through to applications of mathematics and mathematics
in careers,
•through in-school taster sessions provided by FMSP staff,
•through KS4 extension materials which show how GCSE mathematics
progresses in A level Mathematics and FM; these are available via the
FMSP website,
•through other student resources available via the FMSP website stressing
the importance and relevance of mathematics,
•the FMSP also supports stretch and enrichment at KS4 by making MEI’s
online resources for the FSMQ Additional Mathematics (OCR) and the
Level 2 Certificate in Further Mathematics (AQA) available to registered
schools/colleges.
In the current Agreement (that beginning on 1st April 2012), FMSP support for
KS4 stretch and enrichment will be increased.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
KPI 4a: FMSP KS4 enrichment opportunities are available throughout England.
Success Factor: KS4 enrichment offered by the FMSP is available in all FMSP
Areas.
Actual: The FMSP ran 23 enrichment events for Key Stage 4 students covering
all regions. 11-16 schools were given priority when assigning places at the
events. FMSP Area Coordinators and Associates provided taster sessions and
enrichment sessions in schools/colleges when requested. Records of this are
kept in the FMSP database and in termly returns provided by the FMSP Area
Coordinators. FMSP staff contributed to other enrichment series such as Maths
Inspiration.
KPI 4b: The FMSP Area Coordinators run enrichment events to promote the
study of FM and level 3 mathematics to students in Key Stage 4.across England,
targeted in particular at students from 11-16 schools.
Success Factor: 20 enrichment events for KS4 students are run by FMSP Area
Coordinators across England, targeted in particular at students from 11-16
schools.
Actual: The FMSP is running 23 enrichment events during 2011/12 for Key
Stage 4 students covering all regions. 11-16 schools are given priority when
assigning places at the events.
KPI 4c: The enrichment events are of high quality.
Success Factor: The average feedback rating is ‘good’ or ‘‘excellent’.
Actual: Some events have yet to take place. All the events that we have received
the feedback for so far have had an average score greater than 3 (students
were asked to rate the content of the day as a whole on the scale: 1 – Poor, 2 –
Satisfactory, 3 – Good, 4 – Excellent) with the exception of one event which had
an average score of 2.98.
Of the students that have attended events 65% have indicated that they are more
likely to study A level Mathematics as a consequence and 90% indicated that
they would recommend the day to others.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Objective 5:
The FMSP provides a CPD programme that enhances
teachers’ skills in teaching FM and level 3 mathematics.
The FMSP provide CPD in several forms:
•day or half-day CPD events focusing on subject knowledge and pedagogy,
•online courses focusing on subject knowledge and pedagogy,
•informal advice and guidance on teaching and learning provided through
phone calls, e-mails and school visits,
•teachers attending FMSP revision days and enrichment days as CPD.
KPI 5a: FMSP CPD opportunities are available throughout England.
Success Factor: CPD offered by the FMSP is available in all FMSP Areas.
Actual: Totals for 2010/11: Regional face-to-face events: 55 CPD events took
place around the country. These were attended by 750 teachers from 413 schools/
colleges.
Live Online Professional Development (LOPD): LOPD courses are available to
all teachers from any part of the country. 113 teachers completed LOPD courses,
an increase of over 100% on the previous year.
Teaching Further Mathematics (TFM) 36 teachers studied all or part of the
TFM course with 20 completing assessed work and being awarded certificates in
autumn 2011.
Current totals for 2011/12
Regional face-to-face events: 43 events have taken place to date with a further 22
planned to take place this term.
Live Online Professional Development (LOPD): 130 teachers have taken part in
LOPD courses so far this year.
Teaching Advanced Mathematics: 59 teachers are currently taking part in the
TAM course at the three universities.
Teaching Further Mathematics: 43 teachers are currently taking part in TFM
and are due to complete the course in September.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
KPI 5b: The FMSP national leadership team and FMSP Area Coordinators
make the opportunities for professional development known to teachers at FMeligible institutions*.
Success Factor: All FM-eligible institutions* have received information
concerning FMSP CPD by Dec 2011.
Actual: FMSP CPD opportunities are described in the advice and guidance
leaflets that were sent to all schools/colleges on 24 October 2011. Local CPD
opportunities are described in regional newsletters which schools/colleges receive
three times per year. Schools/colleges can find out about the CDP offered
through the FMSP via its website.
KPI 5c: The CPD offered by the FMSP is widely taken up.
Success Factor: In academic year 2011/12 the FMSP delivers at least 800
teacher days of CPD, excluding the ‘Teaching Advanced Mathematics’ (TAM)
course, and of the 60 teachers starting the TAM course, at least 50 complete it.
2010/11:
Regional face-to-face events: 700 teacher days
Live Online Professional Development: 201 teacher days.
TFM: 204 teacher days
Total: 1105
2011/12
It is anticipated that the targets for 2011/12 will be met. Actual figures for
September 2011 – July 2012 will appear in a FMSP Progress Report for the DfE
when available.
KPI 5d: The CPD is of high quality and meets NCETM’s values and emerging
principles.
Success Factor: The average feedback rating is ‘good’ or ‘excellent’.
Actual: All feedback gives average satisfaction scores between 3 (good) and 4
(excellent) with an overall average of 3.5.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Objective 6:
The FMSP makes progress towards a time when
schools and colleges will deliver FM without external
support.
FMSP Area Coordinators work to support schools/colleges to deliver FM without
external support. Where the FMSP is providing tutoring in FM for a school or
college, the FMSP Area Coordinator should discuss a strategy for developing
in-house delivery with the schools/college. There are many instances where tuition
is shared between the FMSP and a teacher within a school/college as a way of
progressing towards that goal. CPD opportunities provided by the FMSP are often
a response to particular local need where schools/colleges are planning to deliver
Further Mathematics themselves and need support with specific modules.
To help schools/colleges to offer Further Mathematics in-house, the FMSP
introduced Live Interactive Lectures for Further Mathematics in September 2011.
For a number of Further Mathematics modules, a series of online lectures has been
provided, which give an overview of the content of the module. Schools/colleges
can build in-house support for students around the lectures and are provided with
accompanying resources to do this. It is hoped that this will enable more schools/
colleges to offer FM in-house.
KPI 6a: The proportion of FM-eligible institutions* teaching FM is increasing.
Success Factor: The national target is that 58% of FM-eligible institutions offer
FM without tuition support from the FMSP in academic year 2011/12.
Actual: The number of state schools receiving tuition from the FMSP in
2011/12 was 117. Using this figure in the formula given in Note 2 of the KPIs
document gives a proportion of 57%.
This has already been discussed with DfE: the number of FM-eligible
institutions rose significantly from 2009/10 to 2010/11 (from 1,874 to 2,008),
having remained at a fairly constant level from 2006-2010 (1,900 +/- 30). For
this reason, the target in 6a has remained at 58% in the set of KPIs for the
current FMSP Agreement.
KPI 6b: The uptake of FM is increasing.
Success Factor: The national target is that 16% of A level Mathematics students
in FM-eligible institutions will also take A level FM in academic year 2011/12
Actual: Figures are not yet available for 2011/12. The latest figure available for
this is that for 2010/11. This is 13.51%.
This has already been discussed with the DfE: the last increase (from 2009-10 to
2010-11) in the number of students in state-funded institutions taking A level
Mathematics was significantly higher than in the previous year (11.5% compared
to 8.2%). For this reason, the target in 6b has remained at 16% in the set of KPIs
for the current FMSP Agreement.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FMSP Key Performance Indicators
The KPIs defined below reference the FM status of schools and colleges.
These status values are defined in the following table.
FM status
FM offered?
FM Tuition
Y
When there is demand for FM, all FM teaching is performed ‘in house’ (either by
the school/college itself, or through a consortium).
2
Y
When there is demand for FM, the school/college/consortium only teaches
some FM modules that are essential to the delivery of AS and/or A level FM;
others are taught externally. This category does not include cases where
external tuition is used to provide alternative, but non-essential module options
(e.g. high level Mechanics).
3
Y
When there is demand for FM, all teaching is provided by the FMSP.
N
The school/college does not offer FM to its students, or there is no evidence to
suggest that the subject is offered.
1
4
FMSP Key Performance Indicators
Objective
Aim
Measurement
Success factor
The FM status of 90% of
all FM-eligible
institutions* recorded by
the FMSP by 1
September 2011 has
been updated by
December 2011.
Number of such
75% of those not
1b
contacts by FMSP Area offering FM (or with
Coordinators.
unknown FM status)
have been contacted by
the FMSP between
September 2011 and
December 2011 and
100% by March 2012.
*A FM-eligible institution is a state funded school or college offering A level Mathematics
The FMSP provides
universal availability
of FM.
1a
FMSP national leadership
team and FMSP Area
Coordinators maintain
and extend their records
of the FM status of FMeligible institutions* in
each FM Area.
FMSP Area Coordinators
contact FM-eligible
institutions* not offering
FM (or with unknown FM
status) and encourage
them to offer FM.
The proportion of FMeligible institutions*
whose FM status is
recorded by the FMSP.
Evidence collection
FMSP records of the FM
status of each FM-eligible
institution* in each area.
FMSP records of contacts
with those FM-eligible
institutions* not offering
FM (or with unknown FM
status).
Objective
Aim
Measurement
Success factor
Evidence collection
The FMSP provides 1c
universal availability
of FM (cont’d).
The proportion of FMeligible institutions* with
students taking A level
FM (in-house or
externally) is increasing.
The proportion of FMeligible institutions*
with students taking A
level FM.
DFE data and FMSP
records (see note 1
below).
1d
Excluding management
and development costs,
tuition delivered by the
FMSP is self-financing.
Cost of provision of
tuition and income
received in payment.
The national target is
that 70% of FM-eligible
institutions* have
students that complete
A level FM in academic
year 2011/12.
Cost of provision is less
than income received.
FMSP records and
accounts.
*A FM-eligible institution is a state funded school or college offering A level Mathematics
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Objective
All schools and
colleges are aware
of the support
available from the
FMSP.
Aim
Measurement
Success factor
Evidence collection
2a
Up-to-date information
about the FMSP’s offer
and programmes
reaches every statefunded school or college
teaching post-16
students and every
state-funded 11-16
school.
FMSP records of direct
mailings.
All post-16 institutions
are sent an up-to-date
direct mailing by end
October 2011. All 11-16
institutions are sent an
up-to-date direct mailing
by end February 2012.
FMSP records.
2b
The FMSP collects
information about good
practice in FM and
makes it available
through the FMSP
website.
The quality and range of
information available on
the FMSP website.
Comprehensive
information on good
practice is maintained
and kept updated on the
FMSP website.
Observation of the
information provided.
Aim
Measurement
Success factor
Objective
The mechanism is
The FMSP, in agreement A mechanism is
agreed.
agreed by the end of
with the DfE, establishes
June 2011.
a mechanism for
identifying those FMeligible institutions* not
offering FM that have
students from the most
deprived backgrounds.
Data are updated on an
3b
The FMSP maintains and FMSP records of data
ongoing basis, and all
updates a register of FM- updates.
records are checked
eligible institutions* not
and updated where
offering FM that have
necessary at least once
students from the most
by March 2012.
deprived backgrounds.
By academic year
The number of these
3c
The FMSP engages with
2012/13, 40 of these
institutions that offer
FM-eligible institutions*
FM-eligible institutions*
not offering FM that have FM in academic year
offer AS FM to their
2012/13.
students from the most
students.
deprived backgrounds
and helps them to offer
FM.
*A FM-eligible institution is a state funded school or college offering A level Mathematics
3a
The FMSP targets
support to FMeligible institutions*
not offering FM that
have students from
the most deprived
backgrounds.
Objective
The FMSP
promotes the study
of FM and level 3
mathematics to
students in Key
Stage 4.
78
The mechanism is defined
and published by the
FMSP.
FMSP records.
FMSP records.
Aim
Measurement
4a
FMSP KS4 enrichment
opportunities are
available throughout
England.
The scope of the
KS4 enrichment offered
FMSP’s KS4 enrichment by the FMSP is
programme.
available in all FMSP
Areas.
FMSP promotional
materials describing the
KS4 enrichment
programme.
FMSP records of KS4
enrichment events.
4b
The FMSP Area
Coordinators run
enrichment events to
promote the study of FM
and level 3 mathematics
to students in Key Stage
4.across England,
targeted in particular at
students from 11-16
schools.
The enrichment events
are of high quality.
The number of events.
20 enrichment events
for KS4 students are run
by FMSP Area
Coordinators across
England, targeted in
particular at students
from 11-16 schools.
FMSP records.
Quantitative analysis of
feedback from
enrichment events.
The average feedback
rating is ‘good’ or
‘excellent’.
Feedback forms from
enrichment events.
4c
Success factor
Evidence collection
Evidence collection
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Objective
The FMSP provides
a CPD programme
that enhances
teachers’ skills in
teaching FM and
level 3
mathematics.
Aim
Measurement
Success factor
Evidence collection
5a
FMSP CPD opportunities
are available throughout
England.
The scope of the
FMSP’s CPD
programme.
CPD offered by the
FMSP is available in all
FMSP Areas.
FMSP website.
FMSP promotional
materials describing the
CPD programme.
FMSP records of CPD
events.
5b
The FMSP national
leadership team and
FMSP Area Coordinators
make the opportunities
for professional
development known to
teachers at FM-eligible
institutions*.
FMSP records of direct
mailings.
All FM-eligible
institutions* have
received information
concerning FMSP CPD
by Dec 2011.
FMSP records.
FMSP Area
Coordinators’ records
of contacts with
institutions concerning
CPD offered by the
FMSP.
5c
The CPD offered by the
The number of teacher
FMSP is widely taken up. days of CPD delivered
each year, excluding
the ‘Teaching
Advanced Mathematics’
(TAM) course, and the
number of teachers
completing the TAM
course.
5d
The CPD is of high
quality and meets
NCETM’s values and
emerging principles.
Quantitative analysis of
feedback from CPD
courses.
In academic year
2011/12 the FMSP
delivers at least 800
teacher days of CPD,
excluding the ‘Teaching
Advanced Mathematics’
(TAM) course, and of
the 60 teachers starting
the TAM course, at least
50 complete it.
The average feedback
rating is ‘good’ or
‘excellent’.
FMSP Area Coordinators
logs of contacts with
institutions relating to
CPD.
Promotion of CPD in
national and regional
FMSP newsletters.
FMSP records.
Feedback forms from CPD
courses.
*A FM-eligible institution is a state funded school or college offering A level Mathematics
Objective
The FMSP makes
progress towards a
time when schools
and colleges will
deliver FM without
external support.
6a
Aim
Measurement
Success factor
Evidence collection
The proportion of FMeligible institutions*
teaching FM is increasing.
The proportion of
FM-eligible
institutions* teaching
FM.
The national target is
that 58% of FM-eligible
institutions* offer FM
without tuition support
from the FMSP in
academic year 2011/12.
(See note 2)
DFE data and FMSP
records (see note 1).
The national target is
that 16% of A level
Mathematics students in
FM-eligible institutions*
will also take A level FM
in academic year
2011/12
*A FM-eligible institution is a state funded school or college offering A level Mathematics
6b
The uptake of FM is
increasing.
The proportion of
students taking AS/A
level Mathematics
and also taking AS/A
level Further
Mathematics.
DFE data.
Note 1: The DfE only provides accurate information about which institutions have
entered students for A level FM. These data alone are not an accurate measure for
the proportion of eligible institutions offering or teaching FM.
•DfE data for each academic year are not usually available until the
December following the end of the academic year.
•In the year in which an institution first teaches FM, most students will
only take AS FM. If the AS is not certificated the results will not be
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
included in the DfE data for that year. Thus there may be a delay of 28
months between when a school/college starts to teach FM and when this
is first reflected in the DfE data.
•The modal size of FM teaching group in schools and colleges is 1, and so
it will be common for an eligible institution that offers FM to its students
to have no uptake in a given year.
It is therefore essential that evidence is supplemented by FMSP records of FMeligible institutions known to be teaching FM, particularly at AS level.
Note 2: The only reliable figure for the number of FM eligible institutions offering
FM comes from the DfE data showing the number of FM eligible institutions with
students taking A level FM; there are no reliable data for AS FM. For this reason
the percentage in KPI 6a is calculated as:
number of FM eligible institutions with students taking A level FM - number
of FM eligible institutions with students receiving FM tuition from the FMSP
number of FM eligible insitutions
x 100
It is likely that some schools and colleges are able to provide AS FM tuition
themselves, but do not offer A2 FM, either themselves, or through the FMSP.
These institutions are not accounted for in this calculation.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Appendix B
Data on Student entries and achievement in A level and AS level Further
Mathematics and Mathematics in England; 2003/04 to 20010/11. (Source DfE) Table B1 GCE A level Further Mathematics entries
All student entries - percentage achieving grade
Academic year
A*
A
B
C
D
E
Pass
rate
Total
entry
Percentage
increase
2010/11
27.5
31.2
21.0
10.3
5.7
3.0
98.7
11408
5.5%
2009/10
29.3
30.1
20.2
11.4
5.4
2.8
99.3
10813
14.5%
2008/09
-
59.1
20.2
11.0
5.4
3.2
99.0
9443
11.8%
2007/08
-
58.2
20.6
11.1
5.7
2.9
98.4
8447
16.7%
2006/07
-
57.0
20.1
11.5
6.7
3.4
98.6
7241
11.1%
2005/06
-
57.8
19.4
11.7
6.5
3.5
98.9
6516
25.5%
2004/05
-
59.0
17.7
11.0
6.8
3.7
98.1
5192
1.6%
2003/04
-
59.4
16.8
10.6
6.7
4.3
97.9
5111
Table B2 GCE A level Further Mathematics entries; male entries
Male student entries - percentage achieving grade
Academic year
A*
A
B
C
D
E
Pass
rate
Total
entry
Percentage
increase
2010/11
27.9
31.0
20.7
10.3
5.8
2.9
98.7
7819
6.1%
2009/10
30.0
29.3
20.3
11.1
5.5
3.1
99.2
7369
13.5%
2008/09
-
59.4
19.7
10.4
5.8
3.6
98.9
6493
10.6%
2007/08
-
58.0
20.1
11.3
5.7
3.1
98.3
5871
15.1%
2006/07
-
57.1
19.5
11.7
6.9
3.4
98.7
5099
11.0%
2005/06
-
57.5
19.2
11.7
6.9
3.5
98.7
4595
23.2%
2004/05
-
58.0
17.7
10.8
7.6
3.8
98.0
3730
0.8%
2003/04
-
58.9
16.9
10.9
6.8
4.3
97.7
3699
Table B3 GCE A level Further Mathematics entries; female entries
Female student entries - percentage achieving grade
Academic year
82
A*
A
B
C
D
E
Pass
rate
Total
entry
Percentage
increase
2010/11
26.7
31.5
21.7
10.3
5.5
3.1
98.8
3589
4.2%
2009/10
27.7
31.9
20.1
12.0
5.3
2.3
99.3
3444
16.7%
2008/09
-
58.6
21.3
12.4
4.6
2.3
99.2
2950
14.5%
2007/08
-
58.7
21.7
10.4
5.5
2.4
98.7
2576
20.3%
2006/07
-
56.6
21.6
10.9
6.1
3.2
98.4
2142
11.5%
2005/06
-
58.3
20.1
11.9
5.5
3.6
99.3
1921
31.4%
2004/05
-
61.4
17.6
11.4
4.7
3.4
98.5
1462
3.5%
2003/04
-
61.0
16.6
10.1
6.4
4.4
98.4
1412
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table B4 GCE AS level Further Mathematics entries
All student entries - percentage achieving grade
Academic year
A
B
C
D
E
Pass
rate
Total entry
Percentage
increase
2010/11
40.7
17.8
13.9
10.1
7.5
90.0
12427
31.9%
2009/10
41.9
19.2
13.8
10.6
6.9
92.5
9421
12.2%
2008/09
41.0
19.7
14.9
10.4
7.0
93.1
8399
48.5%
2007/08
37.6
20.2
15.9
10.9
7.4
92.1
5654
15.1%
2006/07
38.5
19.2
15.7
10.4
7.3
91.0
4912
20.5%
2005/06
38.0
19.8
16.8
11.2
7.5
93.4
4078
20.4%
2004/05
39.2
18.6
14.6
12.1
7.5
92.0
3388
32.6%
2003/04
33.0
19.1
18.0
13.2
8.2
91.4
2555
Table B5 GCE AS level Further Mathematics entries; male students
Male student entries - percentage achieving grade
Academic year
A
B
C
D
E
Pass
rate
Total entry
Percentage
increase
2010/11
39.9
17.5
13.8
10.4
7.5
89.0
8199
38.7%
2009/10
40.3
18.9
13.9
10.9
7.4
91.4
5911
13.9%
2008/09
39.3
19.1
15.5
10.6
7.8
92.4
5190
45.5%
2007/08
35.8
20.0
16.2
11.4
7.8
91.1
3567
15.8%
2006/07
37.3
18.4
16.3
10.7
7.8
90.5
3079
21.4%
2005/06
35.9
19.3
17.0
12.1
8.1
92.5
2537
15.7%
2004/05
38.6
17.1
14.7
13.2
7.8
91.3
2193
31.2%
2003/04
30.7
18.5
18.0
14.4
9.3
90.9
1671
Table B6 GCE AS level Further Mathematics entries; female students
Female student entries - percentage achieving grade
Academic year
D
E
Pass
rate
Total entry
Percentage
increase
14.1
9.5
7.5
91.7
4228
20.5%
13.7
10.1
6.2
94.3
3510
9.4%
20.7
14.1
9.9
5.7
94.2
3209
53.8%
40.7
20.5
15.5
10.1
6.8
93.6
2087
13.9%
40.4
20.5
14.7
10.0
6.3
91.9
1833
18.9%
2005/06
41.3
20.6
16.5
9.8
6.5
94.7
1541
29.0%
2004/05
40.3
21.3
14.4
10.0
7.1
93.1
1195
35.2%
2003/04
37.2
20.2
17.9
11.0
6.0
92.3
884
A
B
C
2010/11
42.2
18.4
2009/10
44.6
19.7
2008/09
43.8
2007/08
2006/07
83
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Table B7 GCE A level Mathematics entries
All student entries - percentage achieving grade
Academic year
A*
A
B
C
D
E
Total
entry
Pass rate
Percentage
increase
2010/11
18.2
26.9
21.9
15.6
10.4
5.6
98.6
75547
8.2%
2009/10
17.0
27.9
22.0
15.5
10.1
6.0
98.5
69803
12.0%
2008/09
-
45.4
21.7
15.3
10.1
5.8
98.3
64517
8.0%
2007/08
-
44.2
22.2
15.4
10.2
6.0
98.0
57618
7.1%
2006/07
-
43.8
21.5
15.6
10.7
6.0
97.6
53331
8.2%
2005/06
-
43.3
21.2
15.6
10.8
6.7
97.6
49805
0.0%
2004/05
-
40.6
21.6
16.0
11.5
7.1
96.8
46034
2003/04
-
37.8
21.5
16.9
12.1
8.0
96.3
46017
Table B8 GCE AS level Mathematics entries
All student entries - percentage achieving grade
Academic year
84
A
B
C
D
E
Pass
rate
Total entry
Percentage
increase
2010/11
24.3
15.8
15.1
14.0
12.1
81.3
104586
31.6%
2009/10
23.5
16.5
15.5
14.2
12.3
81.9
79458
7.8%
2008/09
23.3
15.3
15.1
14.9
12.9
81.5
73728
11.4%
2007/08
23.6
15.7
15.4
14.4
12.5
81.6
66208
5.3%
2006/07
24.3
15.0
14.8
14.2
12.7
80.9
62896
9.1%
2005/06
25.0
15.3
15.0
13.6
12.2
81.1
57647
4.9%
2004/05
24.3
14.9
14.4
13.7
12.7
79.9
54972
7.7%
2003/04
21.0
14.1
14.5
14.4
13.4
77.4
51037
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
85
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Appendix C
Resources for teaching and learning mathematics on
the Integral website
In this evaluation the resources on the Integral mathematics are referenced as being
available to a number of users. Here clarification is given as to what access specific
users have.
Overview of Integral resources:
Over the last decade Mathematics in Education and Industry (MEI), who manage
the FMSP, has created an extensive online learning environment of mathematics
resources. The majority of the materials are aligned directly to each of the A level
specifications (AQA, Edexcel, OCR, MEI, WJEC) for Mathematics and Further
Mathematics. Each A level module contains a number of sections, with each
section containing:
•‘Before you start…’ text
•Notes and Examples document
•Crucial points document
•Additional exercise questions and solutions
•Interactive, active learning and other resources
•Links to external websites
•Section test (multiple choice automatically marked)
•‘Now you have finished…’ text
There are also forums, a calendar and messaging facilities within the site. Tens of
thousands of individual resources are available on the site and a sample of a few
sections of the materials can be seen at: http://integralmaths.org/resources/help/
info.php
FMSP Registered schools:
Any school/college who registers with the FMSP, and who updates their
contact details annually, receives a free teacher account to access A level Further
Mathematics materials (this means all A level modules excluding Core 1-4, which
are A level Mathematics modules) within Integral. This enables them to access a
substantial amount of material.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
FMSP Tutors and students:
Students who receive tuition through the FMSP, along with their tutors, have
access to the materials on the site of modules that they are studying through the
FMSP. They also get access, in the period leading up to examinations, to an area of
the site containing specific revision materials.
Tutors also have access to a separate area of the site where additional materials
appropriate for their role can be found. Included in the area is a dedicated forum
for tutors.
TAM/TFM:
In addition to access to materials on A level modules the TAM and TFM courses
gain access to separate areas of the site. The TAM areas have materials on teaching
resources, questions and problems and extension ideas, with TFM having areas on
teaching resources, links with other modules, taking ideas further and additional
resources.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
Appendix D
Full report on Access to Further Mathematics event at
York University
The standard programme for the event is as follows:
Friday 1600 – 1700 Arrival, registration
1700 – 1730 Introduction and activity
An opportunity for delegates to meet one another and the FMSP staff present
1730 – 1845
Why do Further Maths?
A presentation by FMSP making the case for offering Further Mathematics, involves
contributions from university academics and university undergraduates who took Further
Mathematics.
1915Dinner
Saturday
0915 – 1045 Resources to support students and teachers
Teachers are shown and given the chance to explore the FMSP online resources to support
the teaching and learning of Further Mathematics and given advice about how to
incorporate them into programmes of study.
1045 – 1115
Tea/Coffee
1115 – 1245 Ways to offer Further Mathematics
Advice on how to set up, promote and arrange a Further Mathematics course taking into
account timetable allocation and group size.
1245 – 1345
Lunch
1345 – 1430 Planning
A chance for delegates to consider how they incorporate what they have learnt at the event
into their own school/college provision. FMSP staff are on hand to discuss this and offer
further advice.
1430 – 1500 Making the case for Further Mathematics
A reminder about the key points to make to get support for Further Mathematics from
senior managers, other teachers, students and parents.
Access to Further Mathematics; National STEM Centre; University of
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
York 23rd-24th March 2012
Delegates arrived at the National STEM Centre on the afternoon of Friday 23rd
March, where they were greeted by the FMSP Deputy Programme Leader and the
FMSP Student Support Leader, together with some Area Coordinators from the
local regions. Suitable refreshments were available and delegates were invited to
move into their accommodation for the night which was nearby, before reconvening
at 5:00pm for the first session.
Delegates had been supplied with a delegate’s pack, which contained the
programme for the two days, a list of delegates and copies of the slides used in
the first session. According to the delegate list, there were 27 people at this event,
including 17 teachers representing 12 schools and colleges. The other delegates
were the FMSP officers, area coordinators and speakers from universities.
First session; Friday evening: At the start of the first session, everyone was
welcomed by the FMSP Deputy Programme Leader who then introduced an
activity that would act as an ‘ice-breaker’ to get delegates talking to each other and
working together. The activity was based on centre of mass. She emphasised the
importance of the concept with two contrasting examples: one about the centre
of mass of an aircraft and its location within safe limits; the other about the role
of the centre of mass of a high jumper whilst using the ‘Fosbury Flop’ and how
this led to a substantial increase in high jump records. After some discussion, she
introduced the activity with some theory on the centre of mass of a triangle and a
semi-circle, but the activity itself was practically-based. Delegates were to make a
cardboard ‘fish’ using these shapes and then decide where its balance point (centre
of mass) should be. This was a good mix of theory and practical work, as delegates
working together could test their calculations of the position of the centre of mass.
The FMSP Deputy Programme Leader gave encouragement and said she was
impressed with the results. This ‘ice-breaker’ had certainly worked well in getting
the delegates working together and sharing ideas.
The second part of this session was presented by the FMSP Student Support
Leader. In the programme there was an introduction to the session which read as
follows:
Further Mathematics has been the fastest growing AS and A levels over the past
five years, with numbers taking A level more than doubling in that time. Why
has this happened and what are the implications for students who cannot access
the subject, particularly with reference to their progression to higher education?
Representatives from universities and students who have studied Further
Mathematics will attend this session.
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
This was emphasising to delegates both the importance of Further Mathematics
itself and of the importance of providing access to it to those students who could
benefit from it.
The FMSP Student Support Leader gave a PowerPoint presentation, starting with
a brief history of the FMSP from its origins as the Further Mathematics Network
in 2005 to the present day. This included details of what the FMSP now offers in
terms of tuition for students, professional development opportunities for teachers,
resources and support for both students and teachers, and the more general
promotion of mathematics through enrichment events for Key Stage 4 students. He
also noted that the FMSP provides online resources and advice and guidance about
the Level 2 Certificate in Further Mathematics offered by the examination board
AQA, and the Free Standing Mathematics Qualification, Additional Mathematics,
offered by the examination board OCR. He noted that the FMSP gave tuition
and support for those students taking STEP (Sixth term Examination Paper)
mathematics examinations or the AEA (Advanced Extension Award) examination.
He also outlined the structure of the FMSP and how it is currently operating. This
was illustrated with some statistics; in 2011 the FMSP delivered over one thousand
teacher days of professional development; tutored over 600 students (about 25% of
which had been through online provision); and ran 30 enrichment events for Key
Stage 4 students. He also noted that the FMSP is currently working with over 30
universities. He showed some graphs illustrating the growth in numbers taking AS
and A level Mathematics and Further Mathematics and the growth in the number
of state schools and colleges that now offer Further Mathematics.
The FMSP Student Support Leader went on to note that some universities
now require Further Mathematics as an entry qualification for some courses
and many others encourage applicants to have taken it for certain courses. He
noted that if a school or college is not able to offer Further Mathematics that
may restrict the options of some students as far as choice of higher education
courses is concerned. He noted that students who have studied some Further
Mathematics generally have an increased knowledge of mathematics, have better
developed skills and are generally more confident in using mathematics. He
highlighted the need of students wanting to study the STEM (science, technology,
engineering, mathematics) subjects at university to have strength and breadth in
their mathematical skills. He noted too that schools and colleges that offer Further
Mathematics are usually able to attract and retain good teachers of mathematics.
The next two speakers reinforced what the FMSP Student Support Leader
had outlined. These speakers were admissions tutors for mathematics from the
University of York and Durham University.
Admissions tutor, University of York: He first explained why it is beneficial to
students to have studied more maths before university. He noted that ‘Further
Maths really meant more maths’. He noted that, although York does not insist
on Further Mathematics as an entry qualification for mathematics, it is certainly
an advantage to students who have studied it. He said the advantage lay in the
first year of the course, which started from an assumed knowledge of A level
Mathematics, but which includes many of the topics that students would have met
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
through studying Further Mathematics. He stressed that the mathematics course
at York was designed on the assumption that not all students taking it would have
studied Further Mathematics. Students who had met some of the topics before
were at an advantage. He reiterated that schools and colleges should work with the
FMSP to offer Further Mathematics to their students because this would clearly
benefit the students. He noted that at York some 90% of the students of STEM
subjects had done some Further Mathematics; either to AS or to the full A level.
He noted there was evidence that career prospects and earnings potential were
higher for those with mathematics qualifications at A level and beyond as logicalthinking, problem-solving ability and competence in statistical analysis were all
skills valued by employers. He finished by saying that he hoped he had convinced
delegates that taking Further Mathematics was a good thing for any student
thinking of taking a STEM subject at degree level.
Admissions tutor, Durham University : He noted first that applicants must have at
least an AS in Further Mathematics if they wish to read mathematics at Durham.
He stressed the importance of mathematics across the natural sciences. He also
noted that students who have experienced the supported self-study mode of
learning, promoted by tuition through the FMSP, were likely to have developed
good study habits which would benefit them at university. He noted also that the
department at Durham had developed a number of links with the FMSP. This
included hosting FMSP events including revision sessions and participation in the
FMSP poster competition for undergraduates. He noted that students who achieve
grade A* in A level Mathematics generally make better progress at university in
mathematics and physics than others and that, by studying Further Mathematics,
a student is more likely to achieve an A* grade in A level Mathematics. He noted
that the number of students studying the STEM subjects has increased in recent
years following a dip around ten years ago. He emphasised that at Durham 80% of
mathematics undergraduates and 60% of science undergraduates are from the state
sector. He emphasised again the advantages that studying AS Further Mathematics
can bring to maths and science undergraduates. He said that Durham feels it can
make offers requiring Further Mathematics because the opportunity to study it is
available through the FMSP for those students whose school or college do not offer
it themselves.
Undergraduate studying physics at Leeds University: He attended a school in
Northumberland where he had studied Further Mathematics with the support of a
FMSP tutor. His tutor made regular weekly visits to the school during the first year
of study. He pointed out that he also made considerable use of the Integral6 website.
For the second year of his course he mostly used the online tutorial facility. He was
able to tailor his choice of modules towards his wish to take a physics degree. He
noted how the flexibility of the FMSP tutorial support arrangements enabled him
to do this. The undergraduate noted how through taking Further Mathematics he
had got particularly interested in the topic of complex numbers and got a lot of
encouragement from his FMSP tutor. He said he has found all this to have been
very beneficial to his studies during his first year at university. He already had
some familiarity with many of the topics he met on his university course through
6 See Appendix C for details of what access to Integral provides.
91
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
studying Further Mathematics at school. He noted that he had been able to help
other students on his degree course who hadn’t studied Further Mathematics. He
also noted those who had studied Further Mathematics did considerably better in
the end of year examinations than those who hadn’t. He concluded by emphasising
that studying Further Mathematics does give great advantages to those who go on
to study STEM courses at University.
Thus these three speakers, the two university admissions tutors and an
undergraduate in a STEM subject, had made a convincing case for offering
Further Mathematics to those students wishing to pursue STEM courses in higher
education. Questions were invited from the delegates; one asked why some of the
content that used to be in the mainstream A level Mathematics had been moved
to Further Mathematics. In response it was pointed out that there had been a big
decline in the number of students taking up the STEM subject A levels towards
the end of the 1990s and following the Curriculum 2000 review. Also Curriculum
2000 which introduced the AS and A2 structure had reduced teaching time in
Year 12, thus there was a need to reduce the content of the specifications. However,
the Deputy Programme Leader emphasised that a primary aim of the FMSP
is to get more students taking mathematics after GCSE, and not particularly
preparing them for higher education courses. She noted that there is a wide spread
in mathematical ability and achievement among 16-year olds from those who are
really struggling with mathematics at any level to the gifted and talented with A*
grades at GCSE. She said that there was a large pool of students between these two
extremes, many of whom could pursue their study of mathematics beyond GCSE,
including studying at least some Further Mathematics.
The Student Support Leader also emphasised that universities are very interested in
students who have studied Further Mathematics and referred delegates to an article
about the Russell Group of universities that was in the delegate’s pack and also to
the full report by the Russell Group.
Second session, Saturday morning: This session was on the Further Mathematics
resources available to support both students and teachers. It was noted that the
slides from the PowerPoint presentation would be made available to the delegates.
The “Let Maths Take You Further” message had a large presence in the slides.
The Student Support Leader started his presentation by emphasising the teaching
and learning style of the FMSP approach. He noted that didactic lecturing was
generally not successful and that students learn more effectively through interactive
activities. He said there were many of these on the Integral website, noting this had
been under development for over ten years. It had originally been set up to support
students working in ‘self-supported study’ mode and had continued to develop in
that vein. He gave a brief overview of what is available on the website, including
study plans, notes on topics, the highlighting of critical points, exercises and
assessment through multiple choice questions and access to examination questions.
He noted that the Integral resources for Further Mathematics are available free
of charge to schools and colleges registered with the FMSP, but the resources for
92
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
the main stream A-level core modules (C1 C2 C3 C4) have to be paid for7 . The
Student Support leader pointed out that although the resources were there to
support students in their studies, they also provided a useful resource for teachers,
where they could be used to test their own knowledge of Further Mathematics and
to help refresh knowledge. He emphasised how the study plans could help teachers
organise their students’ studying arrangements. He then gave a demonstration
of some of the resources in use, showing how they can readily be linked to an
Interactive Whiteboard for classroom use.
The delegates were then shown another non-computer based type of resource.
This was a hands-on card matching exercise involving pairing questions with
answers. The delegates were invited to try the activities, with three sets of cards
on three topics from Further Mathematics. The delegates willingly took part, and
a lot of discussion ensued, supported by the FMSP officers and the three Area
Coordinators present who circulated amongst the delegates.
The Student Support Leader summed up what he hoped delegates had got from
the session. He urged them to explore the Integral site to see the range of resources
there. He emphasised the importance of discussion with and between students that
can be stimulated through the activities. He noted again the built in assessment
facilities and how teachers can keep track of their students’ progress. He also noted
the resources now available to support stretch and enrichment at Key Stage 4,
including those for the AQA Level 2 Certificate in Further Mathematics.
He gave a useful summary of how teachers could use these resources to initiate
Further Mathematics in their school or college:
•by creating programmes of study
•by supplement teaching material, such as that from a textbook
•to refresh their own knowledge
•to promote the idea of ‘supported self-study’, through student access to
the resources, particularly if teaching time is limited.
He noted too that there are lots of other (non-FMSP) resources available free
of charge, mentioning ‘NRICH’, ‘PLUS’ ‘GeoGebra’ and those available from the
National STEM Centre. He also mentioned Technology for Secondary/College
Mathematics (TSM) resources and the ‘Autograph’ software, noting that there is a
charge for the latter. He also noted that resources and tutorial support are available
through the FMSP for those aiming for the top universities who are taking STEP
and AEA mathematics papers, and invited delegates to contact the FMSP if
interested.
Third session; Saturday morning: This session, following a break for refreshments,
was on ways to offer Further Mathematics. The session was presented by the
Deputy Programme Leader, and was a comprehensive overview of how the FMSP
can support both students and teachers. She again emphasised the importance of
providing access to Further Mathematics to those students who can benefit from
7 See Appendix C for details of what access to Integral provides.
93
Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
studying it. She outlined some possible strategies:
•offering AS Further Mathematics in Year 13
•forming a consortium with other schools, to create a viable class size
•sharing teaching between school or college and FMSP tutors
•using a 5th block of teaching time and/or out of hours teaching
•using the FMSP Live Interactive Lectures facility (see below)
•making different modules available in different timetable blocks.
She emphasised that the FMSP can be flexible in how support is offered and that
it aims to meet the need and aspirations of individual students. She noted how the
Area Coordinators can help in this respect. She gave examples of this:
•helping to develop appropriate teaching and learning strategies
•providing advice on enrichment and revision opportunities
•supplying tuition, either face-to-face or through online facilities
•showing how to access less widely taken modules, such as Mechanics 4
and Statistics 4.
This was followed by two case studies. Invited teachers explained how they had
worked with the FMSP to make Further Mathematics available to their students.
The two presenters were quite contrasting in terms of the experiences they reported
but both demonstrated the flexibility of the FMSP in supporting them with tuition
and with advice about how to overcome any barriers that arose in setting up and
planning a Further Mathematics course, particularly a lack of timetabled teaching
time. The Deputy Programme Leader emphasised that the AS level in Further
Mathematics is certainly accessible to students with a good GCSE grade. She
noted that the requirements of the full A level are much more challenging, but
that support is available for students who want to take up the challenge. She noted
the role of the two online facilities offered by the FMSP in this respect; LIL (Live
Interactive Lectures) and LOT (Live Online Tuition).
The three Area Coordinators present then each gave case studies of various schools
they had worked with to set up a Further Mathematics course This brought out
how each school is quite unique in its circumstances and its needs and how the
Area Coordinators can offer advice and help devise a strategy so that Further
Mathematics is a realistic possibility in all circumstances. This showed the various
strategies outlined by the Deputy Programme Leader earlier actually being used
in practice. It was emphasised that, through working with the FMSP, teachers
experience professional development, increase their own knowledge and gain the
confidence to take on the teaching of some modules themselves. It was noted that
the aim of most of these schools was to make Further Mathematics a sustainable
option for post-16 students that they could manage and teach themselves. However,
it was clear that the FMSP was playing a crucial supportive role in bringing
this about. It was also noted however, that the FMSP can help to keep Further
Mathematics on offer if the circumstances at a school or college change, particularly
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if key specialist staff leave the school.
The Deputy Programme Leader highlighted that there were more case studies in
the delegate’s pack.
The Student Support Leader gave some information on the recently introduced
Live Interactive Lectures (LIL) facility. He noted that LIL is particularly aimed
at schools and colleges where face-to-face teaching time is limited, perhaps due
to only a small number of students wanting to study Further Mathematics. He
noted that it was different to online tuition in that students couldn’t speak to the
lecturer through a microphone, but there was interaction through the chat box
facility in Elluminate8 , through which students could ask questions. He noted that
students were expected to do some work between the fortnightly sessions under the
guidance of their teacher at school or college. He advised the cost is £50 per student
per module; it was notable that there was comment through the case studies that
LIL was good value for money. It was noted that LIL will be available in 2012/13
for modules offered by the four principal examination boards, AQA, Edexcel, MEI
and OCR, and that further details are available on the FMSP website.
The Deputy Programme Leader summed up the session. She emphasised the
important role played by the Area Coordinators. She said that teachers wanting
to offer Further Mathematics should go to them for support and advice. Area
Coordinators could also introduce teachers to their local support network, through
which they could benefit from the experiences of other teachers. It was also noted
how Area Coordinators can advise on professional development opportunities. She
highlighted some of the professional development courses offered by the FMSP,
mentioning TFM (Teaching Further Mathematics), TAM (Teaching Advanced
Mathematics) and LOPD (Live Online Professional Development). She also noted
that the FMSP will customise professional development both online and faceto-face if there is a demand. She stated that attending at FMSP revision days for
students or just sitting in at FMSP tuition sessions can provide useful professional
development for teachers as well.
Fourth session; Saturday afternoon: After lunch there was a session entitled
“Making the case for Further Mathematics”. The Deputy Programme Leader
opened this session by stating that “Further Mathematics is a good thing” and
she hoped the delegates agreed. She noted that this session was an opportunity
for discussion where delegates could think about their own school or college and
its circumstances and how the FMSP might support them in initiating Further
Mathematics. She noted that Further Mathematics needs not only to be promoted
to students who could benefit from it, but also to their parents, to other teachers at
the school or college and to the senior management team.
8 Elluminate (also known as Blackboard Collaborator) is the name of the virtual classroom software adopted by the FMSP for its
online support.
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She raised some questions to stimulate discussion:
•How, when and who should Further Mathematics be promoted to?
•How can the take up of Further Mathematics be increased?
•What support do you need from the FMSP?
•What are your staff training needs?
•How will you sustain Further Mathematics and develop it further?
The delegates were then encouraged to talk to each other and discuss the questions,
with the two FMSP officers and the three Area Coordinators circulating and
stimulating the discussion.
The Deputy Programme Leader then started to bring the session to an end. She
noted that the national picture for Further Mathematics is changing rapidly, and
that students, teachers and senior managers were now much more aware of it. She
noted the need to keep up to date with what is happening and changes in attitude
towards the type of students that can benefit from Further Mathematics. She noted
that Further Mathematics is really just more mathematics and in doing it students,
and teachers, become better mathematicians. She emphasised that taking Further
Mathematics was likely to improve a student’s grade in A level Mathematics.
She again promoted the FMSP’s online teaching facilities through LIL and LOT.
She noted that a student could receive tuition for their entire course through LOT.
She said that that LOT is fully interactive with group size being limited to six
students to encourage this interaction. In contrast, LIL is aimed at larger groups
of up to 15 students, and is appropriate when a school/college can provide only
limited time to support students themselves. Interaction during LIL sessions is via
the chat box facility in Elluminate only.
From a higher education perspective she noted that Further Mathematics “looks
good on a UCAS form” and that a qualification in Further Mathematics was
becoming essential for some universities. She noted the Institute of Physics report
‘Mind the Gap’ where the problem of lack of fluency in mathematics in some
undergraduates was highlighted. She reiterated what had been said in the first
session, that studying Further Mathematics has pay off benefits for those going
on to study STEM subjects at university. She gave as some evidence, a graph
which clearly demonstrated those students who take both A level Mathematics
and Further Mathematics, generally get a better grade in A level Mathematics
compared to those who take A level Mathematics alone.
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She ended with some recommendations about developing Further Mathematics:
•talk to all year groups about Further Mathematics
•encourage current Further Mathematics students to talk to younger ones;
they can be role models and ambassadors
•introduce younger students to what Further Mathematics involves ,
including the applications
•take students to FMSP enrichment sessions
•run taster sessions for A level Mathematics and Further Mathematics
•talk about Further Mathematics at open evenings; sixth form recruitment
evenings and parents evenings
•let other teachers know about the Integral website
•take up professional develop opportunities and encourage others to do so
•suggest to senior managers they look at the FMSP website on the
relationship between Further Mathematics and universities.
The Student Programme Leader left the delegates with the comment that the
web-search engine ‘Google’ is based on matrix algebra, and matrix algebra is a topic
in Further Mathematics; perhaps in the future some student will create something
similar and become a millionaire like the founders of ‘Google’.
After that he asked the delegates to complete and leave their exit evaluation forms.
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Appendix E
Case study interviews:
Former and current participants in Teaching Advanced
Mathematics; student interviews following the student
survey on tuition
Teacher interviews with three former TAM participants face to face at
their school
The visited school has only recently taken on a sixth form, and these three teachers
had taken the TAM course in anticipation of teaching A level Mathematics. The
three teachers were quite contrasting in the stages of their career. One was the
Head of Department, one a highly qualified, but relatively new entry to teaching,
and one who had spent most of his career at this school teaching 11-16 year olds.
They had differing reasons for taking the TAM course, particularly as regards the
Masters degree element and the assignment work associated with it. The Head of
Department wanted the refresher course on A level content and ideas for how to
teach it. She said she literally didn’t have the time to put in the work necessary for
the Masters degree. The experienced teacher also just wanted a refresher course
in the content. He did do the first of the assignments for the higher degree, but
for him, TAM gave him the opportunity to work with like-minded teachers,
and he thoroughly enjoyed and benefitted from discussion with other teachers
on how various topics might be taught. He would like opportunity to do more
of the same, having completed the course. The relatively new teacher, already
qualified to doctorate level in mathematics, wanted to complement her knowledge
of mathematics with the pedagogy of teaching it, and was enthused that TAM
gave her the opportunity to both discuss mathematics teaching and research the
theoretical aspects of it for her assignments. All three teachers were grateful for
having done the TAM course; they had clearly benefitted from it and had got what
they wanted from it. They would recommend the TAM course to others.
Telephone interviews with TAM 2010/2011 participants
The names and contact details of nine participants from each of London South
Bank University and Warwick University who had taken the TAM course in
2010/2011 were supplied to the evaluator. From these, the evaluator selected
and contacted four participants from each university with an invitation to be
interviewed. These were chosen partially at random, but also aiming for a gender
balance and a representation of different types of school and colleges at which the
participants were teaching. Five participants agreed, two who had taken the course
through Warwick University and three who had taken the course through London
South Bank University.
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Each of the participants were asked about their reasons for taking the course; their
experiences whilst on the course and the impact of the course on their teaching and
career subsequent to the course.
As each of the five responses was quite different they are reported here as five case
studies.
Participant 1; male; TAM at LSBU; currently teaching in an FE college up to
higher level GCSE
This participant has a background in civil engineering but has been teaching
mathematics in his college for the past 12 years. A threat of redundancy stimulated
him into wanting to teach A level so that he could look for opportunities elsewhere.
He had heard of the TAM course, and that it had a good reputation, so he applied
and was accepted with no problems. He funded the course himself.
He gave up participating in the Masters degree because it wasn’t really relevant to
his needs and the assignments became too demanding on his time.
Whilst on the course he attended the live online sessions when he could make
time available, and found the presentations on C1 and C2 to be very good; he
was less comfortable with C3 and C4. He noted that if he did miss a session,
he felt under pressure to catch up, but felt generally the pace of the course was
about right. He liked the university days, finding them to be well organised with a
range of activities, and good opportunities for discussion and working with other
participants. He thought it a very worthwhile experience. He was able to get some
A level teaching practice at his college and was well supported by his colleagues
there in that. He had a lot of commitments at college and did find the course
demanding in finding adequate time to devote to it, and noted his workload did
prevent him from getting on top of the C3 and C4 material, which he felt came at
him too fast in the online sessions.
On the support and resources available whilst on course, this participant noted
the rapid response from the CL to any email queries, and he also made use of the
online forum. He described the TAM resources on the website as “brilliant” noting
he uses them in his GCSE teaching and has shared them with colleagues who
teach at A level. He particularly uses the ICT graph plotting software and shares
assignments based on this with his students. On being observed, he found his first
observation to be too critical of his teaching, but the second one was much more
constructive and supportive.
He hasn’t subsequently had the opportunity for any A level teaching, but feels
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confident he can teach the AS course; rather less confident to teach the full A level.
He is however, in contact with A level students at his college and has shared some
of the resources with them; he used the power point presentation on vectors as an
example. He has purchased the CD ROM of the online sessions so that he has that
as resource when he moves, as he hopes, into A level teaching.
In summing up this participant said he was very pleased that he had taken the
course and felt very comfortable in his ability to teach the C1 and C2 material, but
would have liked more time to get to grips with the C3 and C4 material.
Participant 2. Female; TAM at LSBU; currently teaching in an 11-18 Academy
This participant has a physics degree and is in her third year as a teacher of
mathematics. She had experience of teaching C1and C2 before taking the TAM
course. She took the course to improve her teaching at this level noting she was
“dropped into it” as a replacement for an ill colleague. Her school has had two
previous participants take the TAM course and were happy to support her to
take the course as well. She noted she felt confident in her knowledge of A level
mathematics but wanted a better understanding of it, noting “I have learnt so much
through doing this course”. She opted not to take the Masters degree because she
wanted to concentrate on the teaching and learning of mathematics and thought
she had too little time to meet the requirements of the Masters course assignments.
She had no issues in enrolling on the course, and getting access to the website.
She noted that the school subscribes to the MEI website, but she was pleased
to find more was available through TAM. She was able to organise teaching of
C3 and C4 at her school, having already taught C1 and C2. She enjoyed the
university days, noting it was quite a distance to travel but she was able to stay
in London to participate. She thought the online sessions to be really good; she
got lots of ideas for teaching and appreciated where the students might have
conceptual difficulties in understanding the mathematics. She enjoyed doing the
assessments in mathematics, noting “it really made you think”. She thought there
was a good balance between content and how to teach it, saying how a deepening
understanding helped her link various topics together. She found she was able
to keep up with the workload of the course whilst managing her professional
commitments as well.
On the support available during the course she first noted the positive support
given to her by the CL when she decided to opt out of the Masters degree on
health grounds. She also appreciated his help in lesson planning. She felt the
face-to-face work at the university days was really good; noting there was lots
of interaction between participants and the tutors and sharing of approaches to
teaching topics; she is still in touch with some of her former colleagues from the
course. She made extensive use of the website whilst on the course and continues
to do so, noting how appropriate activities help students to understand the
mathematics, and how the multiple choice questions help to assess their knowledge
and understanding. On being observed, she thought it really supportive. As a recent
trainee teacher she was used to be being observed, and found the feedback on how
she could improve aspects of her teaching to be constructive. She was happy to
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share resources and ideas for teaching with her colleagues, particularly those that
she found had worked successfully for her.
As a result of taking the TAM course, this participant said she is definitely now
more confident in her A level teaching. She has taught all the core modules and
some statistics and mechanics. She noted that her school has a large sixth form
and half the students take A level mathematics, with about 100 students in year 12,
and 80 in year 13. She noted some come from a relatively weak GCSE background
and are offered extra support and she is able to make use of her experience from
TAM in contributing to that support. She has also used some of the ideas with
GCSE classes aiming for the higher grades, thinking her teaching is now giving
these students new perspectives in mathematics and making them think; she is
encouraging them to take A level. She is still in touch with the CL and will email
him for advice and references to teaching resources.
She noted in her school she now has responsibility for coordinating the raising
of achievement and team challenges, so is not really considering any further
professional development at present, but would like to take the TFM course in the
future. In summing up, she thought the best aspect of TAM was the university days
where she could “geek it out” with like minded colleagues, enjoying the challenges
that were brought up in the sessions there. She would have liked more of it. She is
very pleased to have done the course, and wanted to thank the tutors and course
organisers for a really good course.
Participant 3. Male; TAM at Warwick; currently teaching in an 11-16 high school
This participant has a background in software engineering. He has six years’
experience of teaching having trained at Manchester Metropolitan University,
where he came across the TAM course. However, he was unable to follow the
TAM course at MMU so enrolled through Warwick. He wanted to take the TAM
course so that he could prepare his Year 11 students as well as he could before some
moved on to take A level mathematics at college, noting the high reputation for
mathematics of one of the local colleges. As part of this preparation he teaches
Additional Mathematics, although this is not formerly timetabled. He chose not
to take the TAM related Masters degree as he was already involved with a similar
degree researching an area of mathematics education that was of interest to him,
through MMU.
This participant had no problems in enrolling and getting access to the website and
online sessions. He described the website resources as “fantastic”, noting he is using
them extensively both in lesson preparation and in the classroom with his students.
He attended the first few live online sessions but found lack of time prevented him
from continuing to do that, and he reverted to using the recordings. He makes use
of them to strengthen his understanding of a topic before teaching it.
He found the pace of the TAM course quite demanding; he found his mathematics
at this level was rather “rusty” but he was able to keep up. He similarly found
the university days quite demanding, but liked the way all the participants were
involved and there was a good relationship between them. He noted he did need to
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put in a lot of study time to keep on top of the mathematics, but he enjoyed doing
the mathematics assignments although he did find some of them quite challenging.
However, he was able to put challenges to his Additional Mathematics students
and give them some new perspectives on mathematics. He preferred to work on his
assignments in holiday time, so he could spend more time on them. He thought the
balance of the course between the content and the teaching of the mathematics to
be ideal.
This participant felt fully supported throughout the course and felt he would have
struggled without support. He really appreciated the resources brought to his
attention by the CL and the ideas on how to teach and explain certain topics he
obtained through the online sessions and the university days. He described his
experience of being observed as “fantastic”, clearly valuing the feedback he was
given. He thought his Additional Mathematics students were well motivated and
were making good progress, with several of them not only wanting to progress to
taking A level Mathematics but Further Mathematics as well.
This participant is now very confident in his teaching of Additional Mathematics,
but if offered any actual A level teaching he feels he would need to do some further
work in preparation. However, he feels he has developed a better understanding
of the mathematics and has become very interested in various teaching methods,
which he is pursuing in his Masters degree. In summing up the TAM course he
highlighted two aspects; the online resources and the ease of access to them and
also the opportunity to meet other teachers. He noted how the university days at
Warwick had been “very down to earth” and he was comfortable in the company of
the other participants. He would not wish to see the course altered in any way; he
said “it is a fantastic course and should be left as it is.”
Participant 4. Male; TAM at Warwick; currently teaching in an 11-18 Academy
This participant came originally from an African country from which he had
degree level qualifications in physics and chemistry. He moved to Europe to pursue
a business career, but came to the UK to retrain as a mathematics teacher. He is
now in his fourth year of teaching, teaching mostly up to GCSE, but he had some
experience of A level teaching before taking the TAM course. He enrolled on the
course with financial support from his school, with a view to gaining knowledge
and understanding of the A level curriculum in England and its assessment by the
awarding bodies. He was motivated by the idea of a post graduate degree related
to mathematics education and so the opportunity to take the Masters degree was
important to him.
He found enrolling on the course to be straightforward as was obtaining access to
the online resources. He noted he is still making regular use of the resources in his
teaching, particularly with Year 11 students where he introduces them to aspects
of C1 and C2. He took part in the live online sessions and liked the interaction
that took place. He makes use of the recordings and gets ideas from them to use
in his teaching. He had opportunity during the course to teach some A level work,
including C1 and C2 and some mechanics. He enjoyed the university days and
attended them all bar one, particularly liking the opportunity to interact with other
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participants and the tutors. He particularly highlighted being introduced to ICT
graph plotting software, which was new to him and which he is adopting into
his teaching. He noted the contrast to the traditional methods used in his home
country. He did note that he was away from school for quite a while to travel to
Warwick, so had to plan work for his students while he was away, but he wanted
to attend the Friday morning session at Warwick. He noted the Friday was rather
more intense than the Saturday, which seemed more like a refresher day on the
mathematics content.
He was able to keep on top of the demands of the course, and completed all the
mathematics assignments successfully. He embarked on a Masters dissertation on
practical work in mechanics but changed it to focus on the teaching of C1 and C2,
due to the students at school he was able to work with. In terms of the balance
of the course, he felt he knew the mathematics content, but got a lot out of the
presentations and discussions on how to teach it. He got a lot of ideas from both
the CL and the course website and he shares this with colleagues at his school.
He noted the on-going support from the CL if he had any problems with the
mathematics, and expects to make use of his tutor from Warwick as he progresses
with his Masters degree. He was very pleased with his observed lesson and having
it described as “outstanding”, but all the same appreciated the advice on how it
might be improved.
Although this participant has stayed at the school he was teaching in at the time
of taking TAM, he is aware of the limited opportunity to teach A level there and
wants to move to where there is a greater opportunity. He noted TAM has given
him the confidence to teach at A level , to plan lessons and make effective use of
the resources available to him, particularly the ICT based resources. He noted in his
school, he has had some opportunity to work with some very bright students in key
stages 3 and 4 and enjoys giving them investigative type problems and discussing
them with the students. He believes that TAM has had a large influence on his
teaching and his use of activities to enhance understanding. He plans to complete
his Masters degree, move onto a job with regular A level teaching and then move
into further mathematics and he would like to take the TFM course if funding is
available.
For him, the best thing about TAM was the university days. He noted not only
was there lots of interaction and group work and preparing lessons and materials
together but there was a good social aspect in meeting with the other participants.
He is still in touch with some of them; he would not change the TAM course in
anyway; for him “it was perfect”.
Participant 5; female; TAM at Warwick; currently teaching in an 11-18 Business
and Enterprise College.
This participant also originated from an African country where she obtained a
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mathematics degree, became a teacher and taught for 20 years. She is now in her
fifth year of teaching in the UK. She took the TAM course to boost her confidence
to teach A level Mathematics in this country. She came across TAM through a
colleague who recommended it to her. She noted there was some confusion over
the Masters degree when she went through the enrolment process at Warwick, but
she didn’t want to do it, thinking that it would be too demanding and not really
what she wanted.
She noted that getting access to the website also involved some confusion over
whether she was taking TAM or enrolling on the Masters degree at Warwick, and
it hadn’t been clear to her that there was a distinction, but it was sorted out with
help from the FMSP. She found the TAM website to be very good, once she had
access and could find her way around it. She did find the pace of the online sessions
to be too fast for her and so only attended two live sessions at the beginning of
the course. She realised she had forgotten a lot of the mathematics from her early
career and had to work hard at it but she was determined to understand it so she
could share that with her students. She was able to get some teaching practice with
A level students at her school, teaching C1 and C2. She liked the university days
and working with other teachers, and described the tutors as “super”.
As the course developed, she made more use of the TAM website and would
now describe the resources there as fantastic. She noted the support with lesson
planning is really helpful. She did find the demands of the course hard but
empathised with her students as she felt like an A level student herself. She
emphasised how different teaching in the UK now is to her early career in Africa,
but she coped with the course, making use of the recordings by dipping in and out,
rather than using a full session. She preferred to use the recordings where she could
work at her own pace. She checks to see how the CL introduced a topic before she
comes to teach it herself.
She found the support on the course to be very good, with a rapid response from
the CL about where to find certain resources. Similarly she liked the support from
colleagues when at the university days, where she lost the feeling of isolation,
because she could work with colleagues who had the same concerns as herself,
and they could share experiences and ideas for teaching. She similarly felt well
supported through lesson observation, noting she felt the sessions went well and
the feedback she received was constructive. She also got good support from her
colleagues at her school, where in particular the Head of Department was highly
experienced and would discuss what she was learning from the TAM course with
her, and how to implement the teaching and learning ideas in the classroom. She
noted how important it was to put into practice in the classroom the ideas she was
gleaning from the course. She also noted that she got good support from her own
students as well, with some positive feedback from them on her teaching.
She is currently teaching C1 and C2, and noted how her confidence to do so has
grown due to TAM. She had also done some study work on mechanics through
TAM but hasn’t had opportunity to teach it. Her approach to teaching is now to
teach for understanding, rather than just preparing students to pass examinations,
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but she noted there are time limitations and pressure for students to do well in
examinations, so she needs to balance up the use of time.
For this participant, the key to essential A level teaching is confidence, noting she
couldn’t now be teaching A level without having done TAM. She noted again the
confusion at the start of the course when enrolling, which had clearly annoyed her
greatly and she felt she had wasted a lot of time because of it, but at the end of the
course that was behind her, and she would recommend the course to others and had
already done to so to some PGCE students. She was grateful for having done the
course and in particular to “the fantastic Course Leader”.
Interviews with current TAM participants at LSBU
The names and contact details of 18 current participants from London South Bank
University were supplied to the evaluator. These participants comprised 12 females
and 6 males. From the 18 participants, 10 were selected to be invited to take part in
a telephone interview. The selection was guided by a wish to get a gender balance
and a range of different types of school or college, but was otherwise random. These
participants were then further subdivided into two groups of five; one group to be
interviewed about their views on the TAM course in general, and the other group
focussing more specifically on the online sessions and the Integral website and
resources. One of the originally chosen participants declined to be interviewed and
another made no response despite reminders. These were replaced by others and
ultimately eleven interviews took place.
Online Sessions and Resources
The interviews followed a pro-forma using questions that had been agreed with the
TAM CL.
1.
Have you taken part in any of these sessions live? If so, why did
you choose to attend the live session rather than just watch the
recording?
The participants liked to take part in the live recordings because it helped them
to keep on track with the pace of the course, but only one specifically mentioned
that she liked the opportunity to interact, whilst another said she didn’t have the
confidence to take part in the interaction. One participant felt obliged to take part
in the live sessions, as there was “pressure to be there”. However, all the participants
had missed some of the live sessions but listened to the recordings at a time
convenient to them to keep up with the course. One participant commented that he
couldn’t manage the time to attend live sessions in term time but devoted holiday
time to catching up, whilst another said due to his commitments at school, he was
rarely home in time to sit in on a live session. One participate made a decision not
to take part in the live session on C3 and C4, as she felt she wouldn’t be able to
keep up with the pace; she will watch the appropriate recording before teaching a
topic, when she can pause and replay if she wishes to.
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2. What are your thoughts on
a) the timing of the live sessions?
Whilst some felt 7:00 pm was about right, all felt it needed to be evening and
some thought 8:00 might be better for them. Another noted it was difficult for
him to commit the time on a regular basis, whilst another noted she had other
commitments most evenings. All the participants were pleased they could fall back
on the recordings if they missed a session.
b) the length of the sessions?
Most felt that 60 to 90 minutes was about right; any longer and concentration
started to wane, and two participants thought that an hour was long enough. One
participant mentioned having to leave a session to attend to her family, so missed
the examination questions at the end. Another participant, who mostly used the
recordings, noted she puts aside time so she can do the whole session in one go,
including the practice examination questions, but noted this could be up to 3
hours work for her. Another participant used the sessions in much the same way,
preferring to do the bulk of the work in holiday time, when more personal time was
available.
c) the frequency of the sessions?
Two of the participants thought a weekly session was about right, and another
commented that she liked getting the email reminders from the CL. Two of the
participants noted they preferred to use the recordings so that they could manage
their own time as to when to listen to them.
d) the ways in which the mathematical ideas are presented?
All the participants were very positive about the presentation of the mathematical
ideas with one describing it as “absolutely brilliant”. Several noted they try to
mimic the presentation style of the TAM CL in their own teaching, as they believe
through doing that they are teaching to enhance students’ understanding of a topic.
e) the opportunities for interaction in the sessions?
All the participants were pleased some colleagues were interacting even if they
chose not to, one participant mentioning a lack of confidence with the mathematics
and another with the technology. One said she appreciated the prompt response
from the CL through the chat box when a question was asked, although she found
it “scary to write on the board” herself. Another appreciated the questions posed to
the group by the CL , noting it made her have to think quickly to give her response.
One commented, particularly as regards sessions on C3 and C4, that he would have
liked some directed pre-reading to prepare for the session. Although he did take
part in the interaction, he felt the opportunity was limited due to the large group
size. He thought a “demo” of a live online session at the first university day would
have been helpful, in both anticipating any technical problems and what to expect
from a session. One participant noted, that although the CL encourages interaction,
and some does take place, the sessions do come across more as a lecture.
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3.
In what ways have you used the recordings?
As noted above, all these participants make some use of the recordings, with some
doing so extensively. One participant noted that whilst the live recording require
a lot of concentration, the recordings can be paused for a break, and a chance to
review what has been presented. Most of the participants will view a recording
about a particular topic before teaching it themselves, as an aid to lesson planning
and how they will present the topic to their students. One participant actually
shares the recordings with his students, so that they get a different perspective on
mathematics to what they get through his own teaching. He emphasises to students
how they can use these recordings to help them with their revision, and makes links
available to examination questions; he thought this a powerful revision tool for the
students.
4.
In what ways, if any, might you use the recordings in future?
One participant conveyed the general feeling when saying “I am reassured that I
have the recordings for when I need them”; meaning in revising the mathematics
topics herself and in her lesson preparation. Two participants both noted that they
had delayed using the recordings on the C3 and C4 material, but would use them
when they came to teach those topics. One was planning her assignment on C3
and C4 work and expected to make extensive use of the relevant recordings when
she came to work on her assignment. One participant intends to buy the CD
ROM, so that she will have a “brilliant resource” that will help her to teach beyond
“text books and exercises”; she would like more ideas and links to open ended
investigations. Another commented that she hopes the computer links “won’t go
away”; she depends on them a lot.
5.
Do you have any other comments about the live sessions and
recordings?
These participants generally like the live sessions and the recordings the way
they are. They think they are good and wouldn’t want to see them altered. One
emphasised how she liked the format and timing of the sessions and that she
enjoyed taking part. One participant noted that she believes “you have to teach a
topic yourself before you really understand it”, so would use a recorded session in
reviewing her own teaching. One participant commented that “the sessions are
really useful in getting my maths up to scratch and giving me ideas for teaching it.”
One participant thought it would be a good idea to have a post session forum for
discussion of any issues that arose, but appreciated that many participants would
find a lack of time prevented them from contributing.
6.
Have you attended any other online sessions NOT presented by
the CL?
If so, and if there were ways in which these were particularly more helpful or less
helpful than Bernard’s sessions, please give details.
Generally the answer to this question was no, they hadn’t attended any applications
sessions. One participant had sat in on some statistics and mechanics sessions,
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but noted the format and style were much the same as for the pure mathematics
sessions. Another commented that she had attended only the introductory sessions.
Two participants commented that they will make use of recordings; one is planning
her assignment on decision mathematics so will use the recordings for that, whilst
another is going to teach a statistics module, and will listen to recordings in her
preparation for that.
Resources
1.
For the Integral website, what are your views on :
a) Access and navigation / finding out what’s there?
Participants’ views on this were rather mixed, varying from no problems in
navigation to it is easy to get lost. A general comment was that there is a lot of
material on the site. One teacher thought the site wasn’t organised logically whilst
another said she forgets to bookmark and that the relationship between topics and
examination board questions is confusing. This contrast might well be related to
experience and frequency of use. One teacher did note that her school has been
using the site for many years through MEI and she has no problems with it. Two
teachers noted that they are only using C1 and C2 material at present and find the
navigation intuitive; they will explore further when it comes to teaching C3 and C4
and applications modules.
b) Content
One teacher again commented that there was a large amount of materials and so
a large choice of resources was on offer. Another teacher described this range as
fantastic; he highlighted his use of model answers for both himself and his students,
the schemes of work and the past papers and accompanying mark schemes. He
makes use of the interactive applets and also thought the ‘key concepts’ were
particularly helpful in preparing his students for examinations. One teacher, one
who “often gets lost” noted she does need to get better organised in the use of the
site, but did find the lesson plans particularly useful. She, like all these teachers,
had also used some of the activities. Some of the teachers said they looked for ideas
for introducing topics. Another teacher also referred to the lesson plans, noting
she thought the materials helped develop understanding by highlighting common
misconceptions. She generally thought it “brilliant” the way the materials developed
understanding rather than the rote learning of algorithms.
c) What’s good ? / Could be better.
One teacher thought it all good but can there be more of the same; more activities
and more ideas for teaching topics. However, she did qualify this by thinking
she wasn’t probably using what is there to its full potential. Another teacher just
said she thinks it’s fine as it is. One teacher picked out a particular topic from
trigonometry; she liked the way it moved from the right angle triangle to the unit
circle in introducing trigonometric functions. One teacher would like to see more
online feedback to students following assessment, with advice on which topics
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they need to work on. Another would like to see more material to support the D2
module.
The above comments and suggestions from the participants no doubt reflect their
experience and possibly that of colleagues. To get a more comprehensive overview
of teachers’ views on the site and how it might be improved, the FMSP could carry
out a survey with a much larger sample.
2. What other resources have you used, and in what ways?
All these participants mentioned card matching activities of some kind, with
the name Tarsia, being mentioned by some. They also all commented on various
aspects of ICT. One teacher commented that she made extensive use of Autograph,
rather than using the Integral resources. Other ICT packages mentioned included
Geogebra and Excel, often used in conjunction with the resources from the Integral
website. All the participants mentioned textbooks, but these are mainly seen as
a backup resource and a source of questions, particularly examination questions,
which can be used for homework, and / or to challenge students. One teacher noted
how she found some of the worked examples in textbooks to be confusing, and
another noted she wanted the students to have them for reference but there was no
dependency on the books. Another teacher commented that he thought students
learnt far more through activities and the face-to-face discussion that ensued from
them, rather than reading a book.
3.
Finally, do you have any comments about any aspect(s) of the
TAM course that you would like to pass on to the evaluation
team?
Most of the participants commented that they are enjoying the TAM course and all
felt they were benefiting from participating. One teacher commented that she did
feel under a lot of pressure from school in terms of managers wanting examination
success for the students, and she only had time to just about keep up with the TAM
mathematics based assignments; she had to give up the Masters degree. However,
this teacher did say what she wanted from TAM was the mathematical content and
how to teach it, and she was getting that. Another teacher commented that she felt
at a disadvantage, because she hadn’t taught at A level before, and was somewhat
intimidated by TAM colleagues who had. She thought the pace of the course to be
very fast, but she felt this did allow her to empathise with her students. However,
she wasn’t daunted, said she was passionate about maths and wanted to pass that on
to her students.
One teacher noted that she believed TAM had really helped her develop as a
teacher; she liked the sharing of ideas with colleagues and felt she had a lot of
support. One teacher pointed out that she was originally from the USA and was
still getting used to the English education system and that was causing her some
problems, but she thought TAM to be a really good course. She particularly liked
the collaboration at the university days, with teachers working together as equal
professionals, but with different strengths and weaknesses; she didn’t feel it was
competitive at all, just constructive.
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Although participants had generally found the university days to be very beneficial
there were two contrasting views about their duration. One participant would have
liked the sessions to have continued in to the evening with an overnight stay. She
thought an informal evening in which discussion could continue would have made
the experience even better. However, another teacher would have preferred morning
only; she said there was a lot of material being covered and that by afternoon,
she thought for her, it was becoming ineffective as she was getting tired. Another
teacher would have liked to spend more time, perhaps a whole day, on ICT and its
effective use in the classroom, mentioning Autograph, Geogebra and Sketchpad and
graphics calculators.
One teacher commented that TAM had really made her think about her teaching.
She noted some colleagues at her school had previously done TAM, and she liked
discussing ideas with them and different ways of teaching. They were getting away
from textbooks, and using and developing other resources. She again emphasised
the value she found in the recordings of the online sessions in that she could revisit
them for a refresher before introducing a new topic with her students. She hoped
to move into the teaching of Further Mathematics. Another teacher noted how
essential it is to have teaching practice as part of the course; she believed her own
understanding of the mathematics had improved through that, and through TAM
in general she was getting much more confident in her teaching.
The interviews with the six participants above focused on the online teaching
sessions and the course resources. Further interviews took place with five other
participants, but they were asked about their views on TAM in general. As these
were quite extensive interviews they are reported here as individual case studies.
The interviews were conducted using a pro-forma which covered:
•What is your professional background?
•Why are taking the TAM course?
•Your experiences whilst on the TAM course.
•Your evaluation of the TAM course.
•What was particularly good about the course / what could have been
better?
Participant 1 female, currently teaching at a FE college in the London area
This participant has a degree in statistics and a Masters degree from an overseas
country. She took her PGCE three years ago after coming to England and is in her
first year of teaching A level, taking an AS level class for 90 minutes a week. She
is taking the TAM course as she wants to teach the full A level course and develop
her career in post-16 education. She had no problems enrolling on the course.
She was initially excited at the prospect of taking the Masters degree available
through TAM, but lost confidence when she failed her first assignment. She also
noted she received a lot of negative feedback from her first teaching observation,
and found that lowered her confidence even more; she doubted her own ability in
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mathematics at this level. She was persuaded to stay with the course, and might
review the Masters degree situation, maybe taking it at a later date, but for her it
wasn’t a priority.
Her subsequent experience on the TAM course has generally been positive. She
highlighted the Integral resources; she uses them regularly with her class and said
they were the best thing about TAM. She had attended some of the live online
teaching sessions although she didn’t have the confidence to participate actively; she
finds it convenient to have the recordings available as reminders. At the university
days, she said she found it difficult to keep up with the pace and felt uncomfortable
with colleagues who were stronger mathematicians than her, but was pleased at
their willingness to help her. She noted she has struggled to keep up with the pace
of the course as a whole, but feels it has improved; she is able to devote a whole
day to her TAM work and so can take her time in answering course assignment
questions. She is continuing to do some of the Masters assignment work, and noted
she actually finds this easier than the mathematics as it involves reading papers and
doing an investigation.
She is pleased with the support she is receiving from the TAM tutors, noting in
particular the swift responses she gets from queries to the TAM CL. She noted
again the criticism she had received from her first teaching observation, and hoped
the second one would be better. She did have some doubts as to whether she was
getting out of TAM what she had hoped for, but noted things were improving and
she would reserve judgement until the end of the course. She felt her confidence is
improving, but has concerns over students asking her questions she feels unable to
answer. She noted there had been significant change in pre 16 mathematics, citing
functional skills in particular, and that it was difficult for her to keep up with all
these changes.
The best thing about TAM for this participant is the resources and access to
them. However, she added she did like the university days and going to a different
environment and sharing experience with other participants. She mentioned
the concept of the big ideas in maths, and she believes she is now seeing topics
in mathematics from different perspectives. Her major criticism was about her
pre-entry suitability for the course and should she have been better advised?
However, she felt she was learning considerably through teaching her class and
expected things to be better next year, when she has improved knowledge and ideas
for teaching. So she is generally pleased she is taking the TAM course, but has
reservations.
Participant 2 female, currently teaching in an 11-18 comprehensive school in
Buckinghamshire
This participant is qualified to degree level in mathematics. She had taken up
teaching as a second career after many years in the financial services sector. She
has been teaching for a few years and found herself struggling with A level
mathematics so wanted to improve her knowledge and get ideas for teaching topics
and get away from her dependency on textbooks; thus her participation in the
TAM course. So far she had largely taught herself from textbooks. She is currently
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teaching A level with two classes at her school and in particular wanted support
with the teaching of C3 and C4. She had embarked on the Masters degree but
wasn’t particularly concerned about the qualification and noted she might stop if
the demands get too high. She had found the enrolment process onto the course to
be very straight forward.
On the TAM course she highlighted the resources, noting there are lots of
resources within the Integral site, and it was “brilliant”. She had no problems
accessing the site and finding her way around. She had sat in on some of the live
online teaching sessions. She felt comfortable with the C1 and C2 sessions, but was
supplementing the C3 and C4 sessions with teaching herself from a textbook. She
noted she wanted to be ahead with C3 and C4 material to benefit more from the
sessions. She was making use of the recordings, and in particular mentioned those
on statistics, which she is using in preparing her lessons.
Her TAM teaching practice coincides with her normal time tabled classes. She
noted the reluctance of her students to get involved with activities; they showed a
preference for “being taught” and using the textbooks. She noted she had done all
the relevant exercises. She found she had a dilemma over being observed, wanting
to use the lesson plans and teaching styles met through the online sessions but
aware her students just “wanted to be taught so they could pass the exam”. She
does, however, use activities in class.
She has really enjoyed the university days, finding the presentations and activities
interesting, but said she is using the activity ideas lower down the school in Key
Stages 3 and 4, rather more than with her A level students. She found the balance
between topics and ideas for teaching them to be about right; she particularly liked
the way when being “taught” by the TAM CL, she felt like a 17 year old in class.
She liked the empathy but more so all the teaching ideas that were involved in
the presentations noting she has used some of them with her classes. She found
that two day sessions were fine and didn’t have a problem with travelling to and
from London, and in fact she wished the course involved more such days. On the
demands of the course, she thought generally it was about right, but found herself
preferring to do the mathematics assignments rather than essay based assignments
for the Masters degree; she said the latter tended to get left until the last moment;
she doesn’t like writing essays. She noted that she was having to do extra work for
MEI based assignments compared to the Edexcel specifications she was teaching.
On support she noted she had had little contact with the university based tutors,
but found the support from the TAM CL to be really helpful; she appreciated the
rapid and full response to any queries. She gave an example of ideas on how to
teach logarithms. She noted she got little support from colleagues at school, and the
department hadn’t done well in a recent inspection. She noted some of the head of
department duties were falling on her, and only her and a colleague were taking the
A level classes. She noted they took students with a minimum of grade B at GCSE
to keep numbers up, but it was hard work with such students as they struggled with
the A level material.
However, she felt her experiences from TAM were helping to develop her teaching
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in Key Stages 3 and 4. She had done her PGCE through the Open University, and
TAM had led her to review what she had met on the PGCE course. She said she
was copying the TAM CL’s style with these younger pupils, trying to make the
mathematics appealing to them through an activities based approach. She noted the
pupils like the way she teaches, and she noted it was different to the more didactic
approach of some of the grammar schools in the area. The evaluator noted it was
strange that younger students liked this style of teaching and learning whereas the
sixth form apparently didn’t, but things might change as the younger ones progress
to A level.
On what was best about TAM, she cited the session recordings saying she always
referred to them before planning lessons and wants to keep them as a valuable
resource. She also mentioned the resources and the quality of the presentations at
the university days. On what could be better, she noted again she didn’t like essays
and found having to give references for her work to be annoying. However, she was
finding her research topic interesting; it was on the ‘pros and cons’ of using ICT in
the classroom, and she wants to complete it. She also wondered if the timing of the
university days could be reviewed, but qualified that by saying again she coped with
the travelling involved for her.
On TAM in general, she thought the TAM course certainly worth doing and had
recommended it to a colleague. For her, it had made her into a reflective thinker.
Participant 3 male, currently teaching in a girls’ comprehensive school in the south
of England
This participant is qualified to degree level in mathematics and had taken a
mathematics orientated PGCE course. He had many years of teaching experience,
was now an Assistant Head Teacher and had formerly been a Head of Department.
He was relatively new to his current school where he has taught C1 and C2 and
Additional Mathematics. He is taking the TAM course as a refresher course in
A level mathematics and is particularly wanting to refresh his knowledge of the
content of C3 and C4 and M1. He also wants to move his teaching style from
lecturing to a more activities based teaching approach. The Masters degree wasn’t
important to him, but he had done some assignment work related to it, before
letting it lapse. He said he just wanted to be a better teacher, and that is what he
hoped to become through taking the TAM course. He noted a previous colleague
had recommended the course to him; he discussed it with his Head Teacher who
agreed he should take the course. He had no problems with the enrolment process
but he did note he was not aware of evening sessions when he enrolled, noting he
should have read the course details more closely.
On the TAM course he was making regular, weekly, use of the Integral website
based resources. He had no problems accessing them and found the resources to
be very useful. He hadn’t sat in on any online sessions saying he couldn’t manage
7:00 pm due to family commitments. However, he made use of the recordings,
and used them in his lesson planning and for ideas for teaching, citing indices
and logarithms as an area where he had found the ideas particularly useful. He is
currently teaching A level at his school so there was no need to arrange for teaching
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practice. He had been to all the university days bar one and found them particularly
helpful in helping him improve as a teacher. He likes the way the university days
are presented, both in being a student when being “taught” by the TAM CL, and
being encouraged to think reflectively about the experience by the other course
tutors. The only thing he didn’t like was the use of graphics calculators. He found
with the pace of the course he was fine with the mathematics based assignments
but the demands of the Masters course were too high and he couldn’t find the time
it required. He did find the mathematics challenging and he needed to work at the
C3 and C4 material but the support was good. He liked the way this was related
to Further Mathematics work by the TAM CL where appropriate. He generally
found the TAM course to be well balanced and liked the opportunity to both share
resources and give presentations, and seeing the student – teacher relationship from
both sides.
On support on the course he noted that he didn’t like the feedback on his first
observation and the way he had been marked, but following discussion, he was
satisfied with it. He was classified as excellent on his second observation. He noted
for the resources website, he and colleagues had been using it for several years, and
found it easy to use. He noted some of the MEI material was quite challenging
mathematics but he did make extensive use of what is on the site, including
multiple choice questions for revision with students, section reviews, and various
activities; he didn’t make any use of video. He noted at school there was a lot of
support from colleagues and they regularly discussed their teaching and sharing of
resources. He noted he had introduced colleagues to Geogebra.
So, on returning to had he got out of TAM what he had hoped for, his response
was positive. He was increasing in his confidence to teach through improving his
knowledge and teaching skills and anything else was a bonus, although he noted
again there was too much work involved in the Masters degree for him to pursue
it. He noted that students asked “difficult questions” they would discuss it in class
and resolve the problem. He noted that he still made some use of textbooks with
his students but was not dependent on them. He was developing what he called
cooperative learning both with the sixth form and with younger students.
For this participant the best thing about TAM had been meeting other like-minded
teachers. He again mentioned the student – teacher role reversal; he liked doing
the maths as a student and then reversing the role, so he was teaching a topic and
found the ensuing discussions with the participants and the tutor to be very helpful.
He would highly recommend TAM to anyone new to A level teaching.
Participant 4 male, currently teaching in an 11-18 school in Norfolk
This participant had a career change a little over ten years ago. He had previously
worked in engineering but was dissatisfied with his job, and retrained to be a
mathematics teacher. He has recently taken on A level teaching and currently
has one class. He feels that although he has always been good at maths, he is not
a natural teacher, and he wanted to move from being textbook based to using
investigative activities. Thus TAM was an appropriate course for him. He noted
the support of his school was dependent on him taking the Masters degree so he is
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doing it, and is now very glad that he is doing so.
He ultimately found the enrolment process straight forward, but that was when he
moved from Warwick to LBSU. There had been some query over the nature of his
first degree when he applied to Warwick and whether he was sufficiently qualified
to enrol on a Masters degree. His solution was to enrol at LSBU instead where
there was no such problem.
He described the resources available to the TAM course as “lovely; there is a lot
of them”, noting also that he found the Integral website easy to navigate. He had
attended a few of the online teaching sessions but noted he finds the early evening
a difficult time to be available, but he does listen to the recordings. He did say
he had enjoyed the online sessions he had been able to take part in. For teaching
practice, he noted that he is currently teaching two AS modules, C1 and S1, but has
experience of teaching C3 and C4. He assigns two evenings a week for preparation.
He has been to all the university days so far, having no problems with the distance
of his location from London; he described the days as “great and very enjoyable”.
From the university days he was getting new perspectives on topics and fresh ideas
for teaching and felt happy with the core pure mathematics up to C4. He described
himself as a reflective thinker and he is now incorporating the new ideas he has
gained from TAM into his teaching.
He is finding the pace and the course to be fine, but noted the assignments for
the Masters degree do increase the work load. He was able to manage his time,
but noted taking the TAM course does need commitment. He said he found little
need for support; he is comfortable with the maths and is able to find appropriate
resources for himself. He noted again he uses the recordings of the online sessions
for lesson preparation and ideas on how to present topics. He thought his observed
lesson went fine and was pleased with the constructive feedback he received,
including ideas for how his teaching could improve. He noted support from
colleagues at school was good; they were all experienced teachers.
When asked are you getting out of TAM what you wanted the response was
“absolutely”. He now wants to take the equivalent Further Mathematics course,
TFM, as well. He noted he now has the confidence to try new ideas in the
classroom, and noted in particular that through TAM his knowledge of statistics
has improved. He noted he still has some dependency on a statistics textbook, but
has no such need for the core pure mathematics. However, if a student asks him a
question he can’t answer immediately, he has the confidence to say so and that he
will come back to it and they will discuss it when he has done some research. He
thought TAM had had little influence on his teaching with younger students.
On what was best about TAM he cited the resources and the university days. He
thought the programme for these days was well thought out, and he particularly
liked the style of presentation of the TAM CL. He thought these days best if held
on Friday and Saturday, and would have liked them to run at his local university.
He would certainly recommend TAM to other teachers.
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Participant 5 female, currently teaching at an 11-18 Academy in Buckinghamshire
This participant is qualified to degree level in mathematics and is in her second
year of teaching following a PGCE course. She had come across TAM through
a professional development event run by the FMSP and had decided to take the
course to improve her confidence in teaching A level and also to be made aware
of the resources available and ideas for using them. She had found the enrolment
process to be very straight forward. She was interested in taking the Masters degree
but found the requirements of the assignments were too demanding on her time
and she had to stop.
She has had no problems accessing the Integral website, and is making considerable
use of the resources available there. She has only attended one live online teaching
session due to demands on her time in the early evening, but she does make use of
the recordings. She currently has students in both years 12 and 13, so has built in
teaching practice to try out ideas she has met through TAM. She has been to all
the university days so far, noting she has good support from the school in giving
her time to attend. She finds the days to be really good, and likes the opportunity
they give to meet and talk with other like-minded teachers. She said there had
been some good discussions on the “how and why” of A level mathematics. She
had no problems with the pace of the course and completing the mathematics
assignments, noting that she enjoys doing them. She thought the course had a
good balance between subject knowledge and how to teach it, and she thought
she was developing teaching strategies that would help students develop their
understanding, using the resources as appropriate. She had no problems managing
her time between school commitments and the requirements of TAM.
She thought the support available on the course was good; she noted the quick
responses from enquiries to the TAM CL, and how in particular she had been able
to discuss the issue of the Masters degree with him. She again noted her use of
the Integral website, citing several examples of her use of it including, notes and
examples on topics, activities for interactive learning and lesson plans. She also
noted the support available through the recordings of the online sessions; she says
she does watch these all the way through, but also dips into them; similarly with
the PowerPoint presentations. She thought her lesson observations had gone well,
and found the feedback very supportive; it was comprehensive with constructive
ideas for improvement. She noted that colleagues in the department at school are
mutually supporting through regular meetings.
She felt she was getting from the TAM course what she had hoped for. She is
increasing in her confidence to teach A level, is gaining a better understanding
of the mathematics and of the links between topics. On difficult questions from
a student, she said she would discuss it in class and see if they could work it out
together, or that she would look at it and come back for further discussion. She
was confident to leave textbooks aside and use the recordings for teaching ideas in
conjunction with the online resources. She noted she was using some of the ideas
from TAM lower down the school, particularly group work activities.
On what had been best about TAM for her, she praised the support available,
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describing it as “above and beyond”. She also very much appreciated the
opportunity to meet other teachers and share and discuss ideas with them. She
hoped that some sort of post course network could be established, to stay in touch
with others who were passionate about mathematics. She would make no changes
to the TAM course and would thoroughly recommend it to other teachers.
Conclusion from these five interviews
These five participants had all come to the TAM course from quite contrasting
backgrounds, but they were all clearly benefitting from taking the course. They are
getting a lot from TAM in terms of awareness of the resources available on the
Integral website and elsewhere, and ideas for using these resources in their teaching.
It was notable how they liked to copy the style of the presentations seen in the
online sessions, but somewhat regrettable that they were not able to participate
more fully in these sessions. However, having the recordings available is clearly
invaluable to these teachers. It is apparent that commitment is essential to the
successful completion of TAM, and it is a pity that some of these participants had
to give up on the Masters degree through lack of available time rather than interest
in following it. As far as teaching A level Mathematics is concerned, those teachers
all felt their knowledge of the topics had improved and their confidence to teach
them using innovative ideas was increasing. These participants like the way the
TAM course is structured, and the opportunities it brings to discuss and share ideas
with like-minded teachers and the support they get from each other and the tutors.
They would all recommend the course to others. Thus it is concluded that TAM is a
very successful course that needs no amendments, and the FMSP should continue
to offer it in its present format, including the Masters degree option.
Interviews with students who had received tuition
through FMSP tutors
Student 1
This student hadn’t heard of Further Mathematics until her Head of Department
at school discussed it with her and suggested she study it as she both liked
mathematics and was good at it. The decision was made when she was in Year 11
that she would study Further Mathematics with support from the FMSP, aiming
to take the full A level over two years. She worked with two FMSP tutors and liked
the flexibility of the tutorial arrangements, being able to negotiate the time and
venue for her face-to-face sessions. The sessions were both at her school and at the
local university and typically lasted for 90 minutes but longer as the examinations
approached. There was just her, and one other student working with the two
FMSP tutors. She had confidence in the mathematical knowledge of her tutors
and thought them to be good teachers. She took the modules FP1 2 and 3 and
Mechanics 1 2 and 3.
She said she had thoroughly enjoyed the course and had no criticism of the FMSP.
She had made extensive use of the Integral website resources, and also textbooks,
but noted her tutors were also always available for extra support if needed, and they
could both help her on all the modules she took.
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She achieved a grade B in Further Mathematics and is currently taking a
mathematics degree at her local university. She feels she is coping well with the
demands of the course, noting that having studied Further Mathematics has given
her a good start. She noted on her degree course she is experiencing a variety of
teaching styles and that lectures are sometimes difficult to follow. She reverts to
her Further Mathematics notes to help her understanding of a lecture if needs be.
She hasn’t as yet any career plans beyond her degree, but she is confident she will
pass the first year of the course, and her Further Mathematics will be a great help in
that.
She is grateful for all the support she received from the FMSP and her two tutors
in particular.
Student 2
This student had started studying Further Mathematics in the sixth form, but did
not complete his studies and left school to take a gap year. During the gap year he
decided he wanted to “keep his maths skills up to date and his brain active”. He
enrolled through the FMSP to take the AS level course, with a view to continuing
to the full A level although ultimately this wasn’t achieved; he decided he didn’t
want the pressure of taking the examination.
All his tuition was received online. He considered that some tutors were better than
others and felt that some didn’t use this medium effectively. He emphasised that he
wanted more than just “talk” and that he believed interactive activities are essential
to learning and understanding. He noted some tutors were good at providing
appropriate interaction and he enjoyed those online sessions. He felt with some
tutors, they did just talk and didn’t invite questions, and also felt at times that topics
were just glossed over and he didn’t get a good understanding. He felt with these
tutors he could have done as well just by reading a book. He hoped there would
have been more guidance on self-study. Although he did make use of textbooks, he
wanted someone to explain some of the material to him. He did make some use of
the Integral website, particularly the quizzes but described it as “not that brilliant”.
He noted the resources for Decision Maths 2 were rather lacking.
Having been quite critical, he said he none the less was pleased he had taken the
course, and also had had the opportunity to at least encounter some of the A2
topics. Ultimately he was disappointed in his examination grade, but still secured
a university place. He is currently reading computer science with mathematics,
and feels that the fact that he had done some Further Mathematics was influential
in him being made an offer. He noted that on his degree course it has been
very helpful to have met complex numbers and matrices before in the Further
Mathematics course.
He is enjoying his degree course and feels he is keeping up to date with its
requirements.
He noted in ending, that given the choice, he would have preferred to study Further
Mathematics at school, for the face-face interaction. He noted that commitment
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was needed to be successful through supported self-study with online support, as
time was short to get through the modules. He suggested the FMSP could look
at ways of improving the support, but overall his time with the FMSP was a good
experience for him and he mostly got what he wanted from it.
Student 3
This student decided he wanted to take Further Mathematics as in Year 11 he
realised he was interested in mathematics and physics and thought it would be
useful. Further Mathematics was not offered in his school, so arrangements were
made for him to study Further Mathematics through the FMSP. He was taught A
level Mathematics at school, but he was the only member of his A level class who
took Further Mathematics as well. He found it relatively straight forward to join a
FMSP tutorial group.
He started the course with some face-to-face tutorials but noted that only two
or three students turned up to them, and they moved to online provision. He
preferred the face-to-face tuition noting that online tuition was not ideal but he
had no problems with it. He felt most of the time the explanations of topics was
good, but he could seek clarification from a tutor if he found he had difficulties
understanding. He was in regular e-mail contact with his tutor but would have
preferred face-to-face discussion over points of difficulty. He noted that work was
not set regularly and that he was left to check his own work using the answers as
provided in a textbook rather than having it marked by the tutor. He considered
this to be an aspect of the FMSP that could be improved upon. He noted that he
did a lot of the required studying on his own.
However, he was successful on the course and is currently taking a degree in physics
and theoretical physics. He feels that taking Further Mathematics has given him a
good grounding for his degree course. He noted that a lot of the mathematics he is
meeting in the first year he has already met before.
So he is pleased he took Further Mathematics; he got what he wanted from it.
He particularly emphasised the revision sessions he had been to. He had attended
several of these and found them very helpful. Overall he was content with the
support he had received from the FMSP.
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Appendix F
Full report on the tutor training event at Manchester
University
The event was introduced by one of the FMSP professional officers who outlined
the purpose of the day, as above, and the programme for the day. A quick
introduction by those present indicated they were all relatively new to tutoring and
particularly had little experience of online tutoring.
The Programme Leader then gave a brief background on the FMSP and an update
on its current activities. He noted how tutors and Area Coordinators provide the
frontline interaction with students and thus the tutors have an important role in
providing students with a positive experience.
He noted that ‘in-house’ provision of Further Mathematics had increased from
about 40% in 2005 (when the former Further Mathematics Network first started)
to 60% in 2010. He showed a graph illustrating the growth in student numbers
and the number of establishments offering Further Mathematics. The emphasis
in 2011/12 would be on schools and college not offering Further Mathematics
and which are attended by students from deprived backgrounds, where the
FMSP would be offering support at Key Stage 4 as well as A level with a view to
motivating interest in Further Mathematics for some students and a belief that they
can benefit from studying it and have the ability to do so.
He emphasised the three principle strands of support offered through the FMSP
1. Student support; tutoring and involving schools.
2. Teacher support; professional development in subject knowledge and advice on
how to teach the various topics.
3. Promoting mathematics; enrichment events for Key Stage 4 students and
encouraging students to take A level Mathematics and advising on the
opportunities it brings.
The Programme Leader noted how the FMSP has developed links with many
university departments and many lecturers are now much more aware of Key
Stage 5 mathematics and give their support to the Programme. He noted many
departments now look favourably on applicants who have studied Further
Mathematics.
He informed the attendees that the FMSP had secured government funding
until March 2014, so the FMSP was now able to think in terms of a long term
programme in which tutors would play a vital part.
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In the next session the Student Support Leader gave an update on the online
resources available to students and teachers through the Integral website9 . He
noted that the navigation of the site had been improved, and that there were now
general overviews of the various modules and links to the actual examination board
specifications and past examination papers. He also noted that online test results
can be recorded to form part of a student’s record of progress. The Student Support
Leader invited questions and comments from the tutors. One tutor noted that
for a certain board he couldn’t get access to the specification and past papers; the
problem was acknowledged with a view to resolving it so that tutors would have
access to the same material as students and teachers. Some other improvements
were suggested in discussion, such as the ability to print all the study plans at the
same time, and a facility by which all resources applicable to a specific module
could be viewed at the same time.
In the next session, the Programme Leader gave some detailed input about the
role of being a tutor with the FMSP. This involved the two related aspects of the
students being tutored and the relationship with the teacher contact at the student’s
school or college. For the students, the role was essentially to manage the students’
learning, giving students feedback on their progress through assessing their work
including homework and maintaining progress and attendance records for the
school or college. On contact with the school or college, he noted the need for a
good working relationship with the mathematics department. He noted that they
need to be involved should there be a particular issue with any student regarding
progress or attendance. Also tutors need to be aware of particular schools and
colleges reporting requirements for their students and respond to them. Teachers
could also be invited to join tutoring sessions as a professional development
opportunity.
The Programme Leader also emphasised the importance of maintaining contact
with the Area Coordinator. In the first instance it was important to agree a
programme of study for the module being studied in the time available, so that
another tutor could take over the duties if required. He also noted that Area
Coordinators need to be copied into any correspondence so that they are kept
aware of contacts between the tutor and the school or college.
He noted too that all students must have enrolled, each year, with the FMSP before
joining a tutorial group so there needs to be liaison with the Area Coordinator to
check that all necessary administrative matters have been dealt with. He also noted
that all students must have the required textbook for their module, and it is the
9 See Appendix C for details of what access to the Integral website provides.
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school’s or college’s responsibility to provide it, but the Area Coordinator should
be consulted should there be problems associated with this. Similarly all students
need access to the online resources, and log in details are provided through the
Area Coordinator. The Programme Leader emphasised the importance of this
noting that students must have access as soon as possible and tutors should ensure
they do have access early in the course, and tutors should also encourage use of the
resources, with demonstrations of what is there and how to use it. He noted also
how the use of online forums can enhance communication. He also noted that
tutors should encourage students to make use of revision sessions for their module,
whether this be online or face-to-face, so tutors need to know about the availability
of these sessions.
In the subsequent discussion on the tutor role only one significant issue arose, and
that was the need for a CRB certificate to enter a school. One tutor noted it was
repetitive to keep being asked to prove who you are. This is an area that the FMSP
should address and offer guidelines to both tutors and schools.
The next session was a hands-on session using the Integral website, which took
place in a computer room in the university building. Although computers had been
reserved for the tutors near to the whiteboard, other university students were using
the room at the same time which was somewhat distracting. The Student Support
Leader introduced the session with a quick overview of what is on the site but
emphasised there is a lot of material there and it can’t all be covered in one session.
He noted the importance of tutors being familiar with the material available for
the modules they are tutoring on so as they can plan what they might use in each
session and what to draw students’ attention to. He reiterated the importance of
getting students to use the site early in their course, and making use of the selfreview process provided by online multiple choice tests and the grade book. He also
noted the forums and how they can aid communication between students, tutors
and Area Coordinators. He noted that there are several links available from the
Integral site to other related sites, such as the FMSP and MEI website and various
mathematics enrichment sites. He also showed the tutors the Tutor Area on the
Integral site and how to access resources put there by other tutors.
Following the introduction the session was exploratory with tutors invited to
pursue what interested them as opposed to being given set tasks. However, all
seemed to be engaged in what they were doing and the professional officers were on
hand to assist with any difficulties or queries.
The first session after lunch focused on online tuition and support. The Student
Support Leader talked first about Live online Tuition using the virtual classroom
software Elluminate or as it is now called Blackboard Collaborator. Some tutors
already have experience of tutoring this way and many have reported that they
like the system. Some found it strange at first being remote from the students but
grew to like it as they became familiar with the system. However, it was noted
that good internet links are essential to use the software and associated hardware
effectively. Students not having a graphics tablet and thus not being able to write
“on the board” was highlighted as a problem. However, it was noted that Live
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online Tuition offers flexibility in when the sessions are held as no travel is needed
nor access to buildings. However, there are limitations such as communication with
students is more limited than in a face-to-face tutorial, so it is recommended tutors
try to offer both types of support. It was noted that the online facility does allow
the tutor to talk students through points of common difficulty rather than writing
this out several times in written individual feedback. The similarity of this provision
to Live online Professional Development (LOPD) for teachers was noted, and
tutors were advised that they can take any of these courses, and were shown the
web page and how to sign up for the courses.
The tutors were then introduced to a new facility being introduced by the FMSP,
Live Interactive Lectures (LIL). These are a series of ten lectures that schools and
colleges can sign up to, to provide support for students who only have limited
support in their study of Further Mathematics at their school or college. Tutors
were informed the lectures would be fortnightly, starting in October, and there
would be an emphasis on mathematical content. Tutors were advised that the
number of participants would be capped at 15 students because of the limited
opportunities for communication; for example, students can only ask a question
via the chat box facility on Elluminate. However, this was contrasted with Live
online Tuition, where the cap was put at 6 students to try to facilitate greater
communication through the interactive communication facilities of Elluminate. It
was noted that the LIL sessions will also be available to mature students.
The next session was a discussion on the issues of teaching and learning in the
FMSP. The Programme Leader introduced the session highlighting several issues
which tutors would have to address in their role contrasting these with what would
be the usual case in a school or college course. These are:
1. Less time is spent with students ‘in class’.
2. Tutors will not get to know their students well.
3. Tutors will not see their students outside of lessons.
4. There is limited contact time.
5. The tutor is not a teacher from the student’s school or college.
6. Further Mathematics is a challenging subject and
7. Further Mathematics is often taken as an extra subject at A level.
How to address these issues was then discussed in two groups with a mix of
experienced and new tutors in each group. Some key points about successful
tutoring emerged from the discussion, highlighting again what had been
emphasised in the morning. That is tutor contact with the school or college is
essential in encouraging the student’s participation in attending sessions and
doing the required work outside of the sessions. It was noted again that the Area
Coordinator should be kept informed of any issues so that he/she can intervene if
necessary. Tutors were advised that they need to send a strong message to students
to begin with to ensure that they understand that this is a new way of working and
that communication with their tutor is essential. It was noted that the experience
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of most students up to GCSE and probably AS level as well was to be taught “to
the test”, and they would have to develop the study skills and the responsibility
of independent, but supported, learning if they are to be successful. It was noted
that there is no time in the sessions to practice skills, so students need to do this
outside of lessons through attempting examples and contacting their tutor if they
experience difficulties. It was noted it is important to try to resolve any student’s
misconceptions before any formal assessment, and students and tutor may agree to
an extra session to do this if required.
The day ended with a plenary session in which the attendees could make comments
or ask questions concerning their role and what is expected of them. Pace and the
time available to “get through” a module was a concern. The Programme Leader
advised that students taking Further Mathematics shouldn’t need “small steps” in
their learning of new concepts and that a pace quicker than that usually found in an
A level classroom should be found acceptable to all, with much of the consolidation
work that students would usually do in class time done in their own time. He
advised that is often preferable to cover the longer and more challenging topics
in two or three blocks of time with a gap in time between them for students to
consolidate new concepts before developing them further. He gave two examples:
(1) in the Further Pure 1 (FP1) topic of matrix algebra; matrix arithmetic and
determinants should be covered first, with the applications to transformation
geometry covered later; (2) in the Decision Mathematics topic of critical path
analysis, forward and backward passes and the critical path should be covered first
with gantt charts and resource levelling covered later. He noted it is important
for tutors to be familiar with both the specification for their module and past
examination papers that assess students’ knowledge and understanding of it, but the
primary role of the tutor is teaching; he/she is the student’s teacher and students
must be encouraged to communicate with them on any concerns or difficulties.
He emphasised that tutors do need to establish clear and strong ground rules with
their students advising what is necessary by way of individual study if students wish
ultimately to be successful in the examination. He advised further that if a student
is found to be struggling they either devise a “recovery plan” or the student should
be advised to drop the subject.
Conclusions from the Event
Tutors, in the space of 4 hours or so, had been subject to a lot of information but
had had opportunity to discuss issues arising and to ask questions about it. The
programme that was sent out in advance was not followed exactly at Manchester,
but the purpose of the event as stated at the beginning of this section, certainly
seemed to have been met.
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Appendix G
Key Stage 4 Enrichment Events Programme 2011/2012
Date of Event
Region
Venue
Title of Event
Interview
1
14/09/2011
WM
University of Keele
Maths Enrichment
Yes
2
16/09/2011
SE
University of Kent
Taking Maths Further
Yes
Taking Maths Further
Yes
3
28/09/2011
SE
Wellington College,
Crowthorne
4
11/10/2011
SW
South Wilts Grammar
School
Year 11 Maths Enrichment Day
5
21/10/2011
Y&H
University of Hull
Taking Maths Further
6
23/11/2011
NE
Teesside University
Maths in the Simpsons
7
29/11/2012
EofE
University of Essex
KS4 Enrichment Day
8
08/12/2011
EofE
University of Hertfordshire
Year 10 Maths Enrichment Day
9
13/12/2011
SW
Cornwall College, St Austell Year 10 Maths Conference
Yes
10
14/12/2011
SW
University College
Falmouth
Year 10 Maths Conference
Yes
11
08/02/2012
WM
Solihull Sixth Form College
Further Maths Conference
Yes
12
22/02/2012
NE
Teesside University
Inspirational Mathematics
13
29/02/2012
SW
University of Gloucester
Maths is for everyone
14
28/03/2012
EM
Loughborough University
Maths Rollercoaster
yes
Yes
Yes
15
28/03/2012
Y&H
Leeds University
Taking Maths Further
16
19/04/2012
SW
Plymouth University
Year 10 Maths Conference
17
20/04/2012
SW
Plymouth University
Year 10 Maths Conference
18
24/04/2012
SW
South Wilts Grammar
School
Year 10 Maths Enrichment Day
19
26/04/2012
EM
University of Nottingham
KS4 Enrichment Day
20
20/06/2012
London
University of Greenwich
KS4 Enrichment Day
21
27/06/2012
SW
Poole Grammar School
Taking Maths Further
22
02/07/2012
Y&H
University of York
Taking Maths Further
23
03/07/2012
SW
University of Bath
KS4 Enrichment Day
24
04/07/2012
London
University of London
KS4 Enrichment Day
25
06/07/2012
SW
University of Exeter
Mathematics is Your Future
26
06/07/2012
Y&H
Leeds University
Taking Maths Further
27
06/07/2012
University of
Wolverhampton
Maths Enrichment Day
28
09/07/2012
NW
University of Manchester
Manchester Mathemagic
29
10/07/2012
London
Kingston University
KS4 Enrichment Day
30
10/07/2012
NE
Dryden Centre, Gateshead
KS4 Enrichment Day
31
11/07/2012
NW
University of Liverpool
Liverpool Mathemagic
Source FMSP
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Sessions at the enrichment event at Solihull Sixth Form College
•Students were given a ‘Maths in Sports’ quiz on arrival with prizes
available for the best attempts.
•Number theory and codes.
•Which Olympic events should we compete in? Could statistics help us
win?
•Hawks and doves, adventures in evolution.
•Group theory – an introduction.
•Fun maths mini road show.
•Projectiles, how far will it go?
•The Platonic Solids, modelling with balloons.
•Plenary session titled “From Lampard to the Olympics”.
The evaluator could only visit two of these sessions due to the way the programme
had been structured. For the same reason, the students with their teachers were only
able to attend two sessions. The evaluator chose to visit the session ‘Number theory
and codes’ and the session ‘Hawks and doves, adventures in evolution’.
Number theory and codes:
The room was a little small and extra seating was needed for some of the 20 or so
students attending. The presenter soon settled them all down with his introductory
challenge to break a code which he had put on the whiteboard.
The students mostly worked in pairs, with school colleagues, and most had broken
this code within 5 minutes or so. A discussion followed based on asking students
how they did it and what clues they found about how to do it. The speaker was
establishing a good rapport with the students which he developed further with
his second activity, based on mobile phones. Several students made suggestions as
to how these “text codes” could be deciphered and the speaker then gave them a
text code to break. Students were quietly engaged in the activity with many again
solving it within a few minutes.
The presenter moved the session on to a more mathematics based code, which
was based on factors of numbers. He gave an example and invited the students to
explain how the code had been formed, which led to some constructive discussion,
before he again gave them a challenge of more codes to decipher. Students readily
engaged with the problem and there was a lot of discussion, with the speaker
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circulating amongst the students checking on progress and making suggestions.
Many students also completed this challenge successfully, indicating the speaker
had got the difficulty level of his “challenges” about right.
The speaker’s final code was based on binary numbers; although he explained the
concept well, students who had not met it before did struggle a little to begin with.
The teachers present willingly helped those who were in difficulties. The speaker
congratulated the students who had managed to complete all the challenges. His
final coded message “computers do everything in ones and zeroes” was appropriate
and the speaker stressed to the students the importance of binary based coding. He
ended with a brief history of the use of mathematics in coding, noting how the use
of sophisticated mathematics could make information “safe”. The students certainly
seemed to have enjoyed this session, and all had been involved throughout.
In the changeover between sessions students seemed to have no problems finding
their next room; maps had been supplied and all was well signposted. However on
arrival at his next session, the evaluator again found the room to be a little short of
chairs.
Hawks and doves – an adventure in evolution:
The speaker introduced himself and his topic. He started by outlining the idea
of a mathematical model and he stated that they were going to create one for an
aspect of evolution. He illustrated the problem with a computer generated video
on conflict aggression, which featured a lion versus a crocodile. He explained how
animals of different species will fight each other for food, but not for space. He
went on to explain that fights for space tended to happen between members of
the same species who will also fight for mates. He showed another video clip of
some elephant seals fighting, with a group of penguins just ignoring them. He was
certainly engaging the students’ interest. Just as the evaluator was wondering when
the mathematics was going to come in, the speaker went into more detail of the
modelling cycle.
He left the animals examples, to move on to a three-way face off based on the three
principal characters from the film The Good, the Bad and the Ugly. He asked for
student volunteers to be each character and many were keen to participate. He gave
some data on the probability of a hit and the time it took to draw a gun for each
character. He then asked for a strategy - who should aim at who? He invited the
participating students to “shoot”. Two picked on the characters with the quickest
draw and highest hit rate. Acknowledging that this was a reasonable strategy, but
asking whether it was the best strategy, he altered the problem. He asked what if
they were all three were perfect shots and had unlimited ammunition but could
only shoot in turn? What was the best strategy now? The speaker had quietly told
the participating students to deliberately not shoot at each other, which led to some
discussion on why this was the best strategy.
The students all seemed to be enjoying this immensely, but the evaluator did think
again that the connection to mathematics was getting rather tenuous. The speaker
came back to the animals problem and modelling. He noted that animals don’t fight
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to the death but rather their behaviour as individuals is geared towards the good of
the gene pool of the species. He said that in a first model, we assume all individuals
are equal, that no one is stronger or weaker than any another.
The speaker didn’t develop that any further, but went on to introduce the students
to evolutionary stable strategy and its relationship to an aspect of game theory
through ‘hawks and doves’, the title of his session. He introduced a pay-off matrix
in which the results of simulated conflict between hawks and doves both between
and within species would be recorded. He explained the simulation which was
one that all the students could participate in and the scoring system as a result of
the ‘conflict’. He explained that ‘scissors, paper, stone’ would be used to decide the
winner in each ‘conflict’. The students all willingly took part, clearly enjoying it, and
it gave them opportunity to interact with students from other schools. The speaker
then settled the students down to review the scores, and asked how the results
could be as they are, before telling them only one student had been a hawk, the rest
were doves.
The speaker then invited the students to have a second round of the game, and
again distributed hawks and doves cards. The scores came out completely differently
this time, as the speaker explained in the review; they had been all hawks except for
the one dove. This led to a discussion of why, in terms of the gene points, the single
dove actually did better than all the hawks.
The evaluator was again thinking the connection to mathematics was a bit
tenuous or the session was progressing at too great a pace for the students to really
understand, but the presenter reinterpreted the problem with some algebra and a
probability tree that Key Stage 4students would be much more familiar with. He
used the probabilities to find the expected score for a dove and a hawk, showing
that when these were equal the ratio of hawks to doves was 7:5 and this was a
stable population, referring back to evolutionary stable strategies.
The speaker invited the students to be critical of the model assumptions and
solicited several suggestions. He noted there were other models and strategies
and gave a few examples. He noted in conclusion that hawk-type animals intrude
on others’ space, whereas dove-type animals “own the resource”. The students
certainly seemed to have enjoyed this session, but just how much of the associated
mathematics they had understood was difficult to gauge. Perhaps too much was
attempted in the 40 minutes available, but the students went away with plenty to
think about.
Plenary Session – From Lampard to the Olympics:
The final session was scheduled to last about an hour. The speaker explained
that he intended to give the students a new perspective on a range of sports
and also give them a flavour of some of the mathematics they would meet in A
level Mathematics. While he went through his wide range of sports, the speaker
interacted with the students and invited contributions by posing questions.
He made use of a variety of visual aids and brought in some mathematics as
appropriate. He started with cricket, describing a bowler spinning the ball which he
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
demonstrated with a cricket ball. He asked whether it was cheating to spin the ball
in a certain way.
He then brought in his Olympics theme, asking what is meant by a distance on
an oval running track. He asked the students how far the winning athlete actually
ran in races like the 800m or 1500m. He related the question to Kelly Holmes
winning these events at the 2004 Olympics. It seemed that most of the students
identified with this. He had a video clip of her winning and asked the student how
far she actually ran. Some mathematics based on the width of a lane on the track
and the semi-circular ends followed, which was readily accessible to Key Stage 4
students. The result was quite surprising; in winning she had run about an extra 10
metres. He noted athletes have to make a decision, which can be analysed using
mathematics, about where to run on the track as opposed to the total distance they
run, to optimise their chance of winning.
He moved onto shot put asking what the best angle of projection is. A student
responded that it is 45 degrees. The speaker then used the formula for the range
of a projectile to explain why that was the right answer. He asked what else would
affect the path of a ball in flight. There were several responses including how fast
the ball is thrown and how heavy it is. The speaker used the last example to explain
how gravity affected results in shot put. The difference in the high altitude at
Mexico City compared to Helsinki, made a difference of about 30 cm on a throw.
He moved on to goal-kicking in rugby, noting that when a try is scored the kicker
may place the ball anywhere in line with where the try was scored. He asked about
where is it best to place the ball so that the likelihood of success is highest. He drew
a diagram to explain the optimum position, which seemed to be well within the
mathematical experience of the students. He moved this on to what he described as
“the best try ever” (Barbarians v The All Blacks 1973). He showed a video clip from
the game and noted that it appeared a forward pass was made during the move
shown. He then went into the vector based mathematics of how a ball that looks
to have gone backwards, might well have gone forwards. The students were all very
attentive, and it was notable how good this speaker was at balancing entertainment
and relating his topic to the relevant mathematics.
He moved on with the question ‘why are there 11 players in a football team’. No
one knew why, but he claimed it came from cricket towards the end of the 19th
century, and the importance of the number 22. The pitch is 22 yards long, the
stumps are 22 inches high and the game is played between 22 players. He asked
about the significance of 22, mentioning the old imperial unit of a chain being 22
yards and left the students to think about that.
The speaker developed the football theme and brought up the disallowed goal
between England and Germany in the Football World Cup of 2010. He noted
that if the referee had known the appropriate mathematics he must allow the goal,
and then demonstrated that mathematics shows the path of the ball as seen on a
video clip can only happen if the ball went beyond the goal line! He continued with
the football theme asking the students about the shape of a football. He queried
the obvious answer of ‘a sphere’ asking why many club logos show a football made
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Evaluation of the Further Mathematics Support Programme 2009-2012 – Summary Report: August 2012
out of hexagons, when it is actually impossible to make a ball out of hexagons.
He noted that such a shape is in fact an icosahedron with 20 sides, not a sphere.
He noted that it can become a sphere if some of the hexagons are replaced with
pentagons, thus forming a truncated icosahedron, but that such a shape is very
difficult to draw. So, footballs on club logos are not in fact spheres, which gave any
football fans present something to think about.
Next he discussed darts and asked for volunteers to come and throw three darts at
a board. He had no problems recruiting volunteers. He asked for suggestions as to
where you should aim to try to maximise your score, and particularly where to aim
if you are not a good shot! The mathematics here was a mix of the geometry of the
dartboard and the probability of hitting the various scores. The speaker showed
how this suggested that you should aim for 19 if you are a good shot and14 or 16
otherwise, unless you are a very poor shot when you should aim for the bulls-eye.
He showed some data which suggested boys aim for the treble 20 and score 35
on average with three darts, whereas girls aim for the bulls-eye and score 45 on
average.
In bringing his session to an end, the speaker showed some video clips of snooker
shots and raised the question of what geometry is involved. He asked the question
‘does it matter who serves first in tennis?’. He noted that one of the longest matches
on record was won by the man who served first. He also asked about the probability
that Manchester United could draw Manchester City in the 3rd round of the FA
cup. He noted that the probability is 1/127 and it is not that small. Staying with
football and his title, he noted that Frank Lampard earns £5 million a year and
pointed out that if you earned £20 a week it would take 5000 years for you to
earn to £5 million! He contrasted this with a particular hedge fund manager, who
last year earned £400 million, noting that the man concerned is a mathematician.
That certainly gave the students food for thought about continuing their study of
mathematics post-16.
The event was brought to a close by the organiser. She asked for the feedback forms
to be completed. She said that she hoped that the event had served its purpose in
raising interest in mathematics and that students would consider continuing their
study of mathematics at AS level and beyond. She noted how most Key Stage 4
students had now heard of Further Mathematics and so might consider studying
it, and the organiser noted that some university courses were now requiring or
encouraging students to take Further Mathematics. Lastly she asked the plenary
speaker to present the prizes for the sports quiz. There were prizes for the three best
performing schools and the three best individuals.
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