Widening Participation in Mathematics
Project report
Version 3
22 November 2010
www.ncetm.org.uk
Contents
Executive summary .............................................................................................................................................................................. 2
National trends ...................................................................................................................................................................................... 6
Case study schools and colleges...................................................................................................................................................... 8
Project initiation and support ........................................................................................................................................................ 11
Patterns of intervention ................................................................................................................................................................... 14
Measures of success .......................................................................................................................................................................... 15
Recommendations ............................................................................................................................................................................ 16
References ............................................................................................................................................................................................ 18
Appendix .............................................................................................................................................................................................. 19
Bishop Challoner Catholic College ............................................................................................................................................... 19
Bridlington School ............................................................................................................................................................................. 21
Chesterton Community College ................................................................................................................................................... 24
Childwall Sports College .................................................................................................................................................................. 27
Long Road Sixth Form College ...................................................................................................................................................... 30
Marshland High School .................................................................................................................................................................... 34
Plymstock School ............................................................................................................................................................................... 37
West Anglia, College of .................................................................................................................................................................... 42
Harris Academies, London .............................................................................................................................................................. 44
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Widening Participation in Mathematics
Executive summary
This report describes the outcomes of a set of case studies in which participants sought to increase the
number of learners progressing to mathematics at AS or A2 level post 16, having achieved at most a grade B
at GCSE. These case studies were commissioned by the National Centre for Excellence in the Teaching of
Mathematics (NCETM) as part of an exploration of how schools and colleges might contribute to the
improvement of these transition rates nationally.
Context
The context of the case studies is a series of papers published in the last decade that focussed on the
relatively poor participation rate in mathematics at Advanced Level (References, page 18). These
documents identified a number of contributory factors, of which the low participation rates of girls and of
young people achieving a grade B or less at GCSE were particularly significant.
The report produced for the then DCSF by the NCETM Factors influencing progression to A Level mathematics
(2008) identified a range of strategies used by schools with the highest transfer rates nationally in
mathematics from GCSE to A Level. The common thread identified by the report was the way in which these
schools sought to attend to the important aspects of managing the teaching of mathematics and to do
them all well. They were:
•
high quality teaching throughout the secondary phase
•
clearly demonstrated enthusiasm and passion for mathematics
•
professional planning and managing of the several elements that between them make for effective
teaching and learning of mathematics
•
high expectations of pupils’ learning of mathematics
•
effective pupil monitoring and assessment regimes
•
a positive whole-school attitude towards mathematics as a subject
•
good inter-personal teacher-pupil relationships.
In particular, it is clear from the evidence that pursuing single strategies in isolation is unlikely to have a
significant impact on participation rates.
Ten case study schools and colleges were selected to provide a small but varied selection of educational
establishments that between them offer a set of very different experiences of providing mathematical
education.
Interventions
A number of potential interventions were suggested to case study participants as part of the project’s
initiation phase. These interventions had previously been documented in, for example, Robinson (2007) and
NCETM (2008). Each of the case study schools and colleges chose one or more interventions that they
believed would have an impact on progression rates, based on perceived similarities between their own
circumstances and those in the previously researched schools. The most common interventions or change
programmes that case study schools and colleges sought to make were:
•
interviewing and surveying students to gain an insight into their attitudes to mathematics and
their reasons for choosing or not choosing the subject at A Level
•
professional development for teachers of mathematics on active learning approaches such as
those promoted by the NCETM;
•
taster or interest-raising sessions for potential students, with an emphasis on the accessibility of
the subject
•
using Year 12 and 13 students as positive role models, as speakers or in a formal mentoring scheme
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•
awareness and interest-raising through special activities such as visits to mathematics events and
venues with mathematical significance
•
mathematics clubs and drop-in sessions designed or re-designed to attract a broader range of
students and not just the most able
•
working with local universities to provide enrichment and encouragement.
Learning experiences from the project
Having emphasised the differences between the case study schools and colleges and their chosen change
programmes and interventions, there were nevertheless some common characteristics in the kinds of
learning experiences that participants reported as a result of their participation in this project.
Chief amongst these were the confirmations of previous research; in particular:
No single solution
There is no single “magic bullet” that can be used to address the issue of low rates of transition for B-grade
learners. Many case study participants were aware of how the different interventions they were making
tended to support each other – or to be weak in their implementation because other improvement
measures were not in place to help embed the outcomes.
Attitudes matter
The school’s attitudes to mathematics – its cultural norms and assumptions about the subject and about
how it should be discussed and presented – have an important impact on progression. Several of the case
studies sought to develop ways of raising the status of the subject in the eyes of pupils, either as a career
choice or as an important and valued intellectual discipline.
The options trap
In all schools mathematics is an automatic choice at the selecting options stage, typically in Year 9. Because
it is a non-negotiable choice, mathematics is rarely given any profile at this stage and an important
opportunity to raise its significance for young people’s futures is lost.
Lack of learning continuity
As well as the selection of options in Year 9, there are other critical stages in young people’s lives,
depending on the particular system of schooling they find themselves in. The transfers into secondary,
typically into Year 7, as well as the move to a college, if there is one at the end of Year 11, are very important
stages. Several case study schools and colleges experienced a loss of information about pupils at moments
of transition, especially from school to college. One of the case studies involved a college seeking to
establish a strong and early relationship with pupils at feeder schools in advance of transfer. This should
have been unexceptional, but was actually significant because of how rarely this appears to happen in
practice.
National issues
In addition, two issues emerged that have national significance. Even though the case studies represent a
very small sample, the two emerging themes described below nevertheless ring true, and the case studies
direct our attention to them because of the consistency with which these issues were present across the
majority of participant establishments.
Maintaining quality before and after transition
There are big differences between schools, sixth form colleges and colleges of further education. These
establishments still effectively operate under different funding regimes and the power to effect change
within them continues to be located in different parts of the education system. The recent launch of the
Young People’s Learning Agency (YLPA 1 ) presents an opportunity to improve the ways in which
1
http://www.ypla.gov.uk/
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mathematics teaching is monitored and supported before and after transition across these three different
kinds of educational institution.
Whilst it is not the whole story, the consistency of the quality of teaching and learning of mathematics
across both sides of the transition at age 16 was identified as an important factor. It was seen as significant
both in students opting to continue the study of mathematics after 16 and in the successful completion of
AS or A2 courses of study. Several of the case study schools and colleges recognised that they needed to
improve the overall quality of teaching in general and in post-16 in particular. They identified gaps in their
teachers’ knowledge of recent developments in the pedagogy of mathematics and sought to deal with this
by providing continuing professional development designed to bring teachers up to date.
This, of course, supports what is already known about the need to continue to raise standards of
mathematics teaching. However, it also points to the importance of ensuring that if pupils experience good
quality teaching at GCSE they must also experience good quality teaching at A Level if they are to remain
positive about the subject and speak well of it to their younger peers. These issues are particularly
important where students change institutions on completion of KS4.
Maintaining quality is also about ensuring there is an appropriate relationship between GCSE and AS/A
Level curricula. In some of the case studies, older students would report to their younger peers that they
had difficulties with the transition. The schools or colleges involved could do little if anything about the
curriculum and sought instead to address these messages. Long Road Sixth Form College, however, actually
changed the curriculum by piloting Use of Mathematics AS/A Level.
Collecting data
One of the weaknesses identified by the project was the limited availability of hard data. Despite
participating schools and colleges being asked to ensure they had reliable initial benchmark data on pupil
progression, hardly any such data had been routinely collected. In the case of 11-16 schools and colleges
data on progression was difficult to garner, both locally and nationally. Attempts were made to collect the
data through National Data Services. However, even in the 11-18 schools such data was not forthcoming.
The simple reason appears to be that the schools in the sample did routinely collect and analyse data to
shape selection processes for entry to post-16 study, but they did not track learner performance in GCE,
after transition, in relation to previous GCSE performance. Anecdotal evidence suggests this is a general
problem rather than a mathematics-specific one.
In the case of partner establishments with pupils transferring at age 16, there is considerable collaboration
effort needed if progression data is to be captured reliably. In 11-18 schools there is clearly a need for a
strategic focus by mathematics teams on capturing and using progression data.
Implications
There are clear implications from these case studies and from previous work on transfer to A Level.
More than anything else, schools and colleges need to become aware that in order to achieve the kind of
transfer rates that are appropriate for a leading OECD country, they need to focus on seeking to do well all
those key activities (such as those listed on page 2 above) that make up the daily, weekly, termly and annual
work of a mathematics team. This will, of course, bring with it all kinds of positive outcomes and benefits.
Additionally, along with those will also come an increasing self-confidence in young people in their own
ability to take mathematics further.
In order to be able to do things well, mathematics teams need reliable and timely data and information
about the progression profiles of their pupils, about their attitudes to mathematics and how these affect
their decision to progress with the subject. Some of these data should be collected routinely by the school
or college, but more affective data such as pupil attitudes may need building in to teaching and learning.
In order to support the mathematics team, the school or college needs to take a strategic approach to the
ways in which it speaks about, promotes and makes visible its commitment to mathematics, not just as a
subject but as a life-long learning habit.
It is not enough that the teaching of mathematics to GCSE or the teaching at A Level should promote high
quality learning. This quality must also be a golden thread that connects the pre- and post-16 experience of
the subject. In addition, therefore, to continuing professional development (CPD) that promotes good
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teaching and learning, there is also a need for CPD targeted both at mathematics teachers and at school
and college managers about what makes for effective transition and how to manage this.
The establishment of the YPLA creates an opportunity to really tackle the relationship between providers of
GCSE and A Level mathematics.
The goal, whether from school to college or within an 11-18 school, is to establish a symbiotic relationship
that makes for an almost seamless transition between pre-and post-16, with young people getting the
same positive messages about mathematics, the same high quality of provision and the same expectations
that they can and will succeed at this subject which is an essential life skill for the citizens of a modern
developed economy.
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National trends
Whilst there have been some significant swings in engagement over the last 20 years, the national trend in
recent years has been for the number of students who are studying A Level mathematics to increase.
Despite this, the number of pupils progressing to A Level has not reached the peaks achieved in earlier
years:
Year
Mathematics
Entries
Percentage
change
2005
46,034
+0%
2006
49,805
+8.2%
2007
53,331
+7.1%
2008
59,105
+10.8%
2009**
66,552
+12.6%
** data not available for 2010 until November.
(Source: Rises in A Level mathematics – Some Preliminary Thoughts by ACME, October 2009)
The previous government set a target of 80,000 entries to A Level mathematics to be achieved by 2014.
How realistic this target is depends on the number of students achieving GCSE at the appropriate level. The
most recent data available shows that 224,712 students achieved GCSE A*-C in the year 2006-7 and of these
152,571 achieved A*, A or B. The target of 80,000 therefore seems achievable. However, of these students
only 41,299 were entered for A Level. The number of students who achieved grades A and A* totalled
74,360, so even if all these students progressed to A Level the target would not be achieved.
This underlines the importance of encouraging the 78,211 students who achieved a grade B GCSE
mathematics to consider progressing to A Level.
To meet the proposed target on present numbers, a large proportion of the grade B students need to take
up A Level mathematics as well as a greater proportion of students achieving a grade A* and A . The current
position based on exam entries for 2008 and 2009 is shown in the table below:
Year
2009
2008
Progressed from mathematics GCSE Grade B to mathematics AS Level
1,669
1,673
Progressed from mathematics GCSE Grade B to mathematics A Level
4,815
4,724
Total number of students who progressed to AS or A Level
6,484
6,397
Total number of students who progressed to AS or A Level
6,484
6,397
It became clear at the national workshop for this project, that some schools and colleges would have
difficulties in gathering historical GCSE data linked to transfers to A Level. This was particularly difficult for
the 11-16 schools present, who seemed to have limited access to data about progression. It was agreed in
these cases, to use the resources of National Data Services (NDS) to find relevant data.
The NDS data for the 11-16 schools were not generally available to classroom teachers but were compiled
for those who took part in this project. The data were compiled by using GCSE results and relating them to
AS and A Level entry. The data were therefore historical and related the GCSE grades of students who had
been entered for AS and A Level a year ago and whose GCSE grade was achieved one or two years earlier. In
practice, the picture was complicated by the fact that the AS entries are not made in some circumstances
until the summer term of the first year or, in some circumstances, December of the following year or not at
all. (In the science area there is some evidence that up to one third of centres may not certificate AS
qualifications.)
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This provided some help in tracking progression and the data were the best available through NDS. In the
future, changes to examination processes will require post-16 providers to register all AS students during
the first term, so this should improve the system and data should in future include those students who are
currently never accredited with completing AS studies – usually those with less than C grades.
If the data tables had been generally available then they could have been used in a number of ways. For
example, the tables show that 152,571 students achieved a grade A*-B in 2006-7 and can therefore give an
indication of the number of potential students who might progress to A Level. The fact that 41,299 students
were entered for A Level in 2009 indicates a progression rate of 27%. The comparable progression rate
when A Level and AS Level entries are combined is 30%.
Using the same measure of eligibility, one of the schools who took part in the project, Chesterton
Community College, achieved a progression rate to A Level of 36% and to AS and A Level combined of 47%,
both of which are considerably above the national percentage.
The teachers were unaware of their positive achievement until they took part in the project.
Similarly, Marshland High School, another 11-16 school that took part in the project, had 31 students who
achieved a grade B or above at GCSE. Of these students, ten went on to complete an A Level course. This
indicates a progression rate of 32%, which again is above the national rate. This could be welcome news for
a National Challenge school.
A number of schools and colleges are asking for grade B or above at GCSE in order to enter AS Level
mathematics. However, the data tables from the NDS and the case study reports indicate that there are a
number of grade C students and grade D students who progress. Making these data available may have an
impact on these requirements for admission.
An analysis of the data available for science seems to coincide with the findings for mathematics. In
compiling the science data the explanations and idiosyncrasies of schools and colleges reflected those in
the mathematics case studies. For example, there are students in one of the case study schools who take
Additional Mathematics and get better grades than in their GCSE. The same issue was identified with
science students taking Additional Science. However, further work is needed to see if either of these affects
progression.
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Case study schools and colleges
Selection of case studies
Ten schools and colleges were selected for the case studies. The main criterion for selection was to get a
wide range of institutions with very different characters of mathematics provision and covering the majority
of phase or sector structures common in England. While a small number had particularly good transfer rates
from GCSE to A Level, others did not. Some of the establishments were selected because of particularly
interesting individual features that were felt might offer some useful insights. For example, the proportion
of pupils who previously took GCSE mathematics and achieved Grade B at Childwall Sports College was
56% but only 8% of pupils gaining a B grade at GCSE in 2007/8 took A Level mathematics. Another school,
Chesterton Community College, was selected because it illustrates the challenges associated with
mathematical pathways from 11-16 phase schools, where the local progression route is to a sixth form
college.
Some of the schools were identified nationally by DCSF(now DfE) as having high numbers of students
achieving grade B in mathematics but with less than 25% of these progressing to A Level. Of the 18 schools
identified in this way, four volunteered to take part in the project. However, these were all 11-18 schools
and while this made identification of transition data easier it did not provide a focus on 11-16 schools and
colleges. A selection of colleges and 11-16 schools were included for comparison purposes.
The College of West Anglia was selected as an FE College to see if this was the route that students used who
gained grade B or grade C and wanted to progress to AS Level. Marshland High School was used as an
example of an 11-16 school whose students did not have a single route for progression: students from this
school could choose to study AS mathematics at any of one of four 11-18 schools in the area or the local FE
College (College of West Anglia). They were included to provide an example of the data generally available
to an 11-16 school and to examine the efforts of such a school in encouraging progression amongst their
students.
Chesterton Community College was chosen as an example of an 11-16 school whose students’ had
relatively few progression routes. The majority of students transfer to one of two local sixth form colleges,
one of which is Long Road Sixth Form College. They were intended to be a contrast with Marshland to
examine the different experiences of 11-16 schools. Long Road was included to provide evidence about the
role of sixth form colleges in recruitment of students on to AS mathematics. Subsequently, they also
became a case study in the role of the Use of Mathematics A Level pilot.
Harris Academy was included as an 11-16 school that was hoping to establish a sixth form and thus provide
an additional option for their pupils..
The circumstances of each case study, then, are sufficiently different from each other to provide a marked
variety of experience. This is a particular strength of this study.
Bishop Challoner Catholic College, Birmingham
Bishop Challoner is a Voluntary Aided 11-19 comprehensive school in the Kings Heath area of Birmingham.
Their intervention was focussed primarily on increasing the number of girls progressing to A Level in the
belief that this would also increase the number of students with B grades progressing. They used a
combination of university visits and additional mathematics sessions to increase interest in mathematics.
They also used girls who were studying mathematics in Years 12 and 13 as role models for the students
lower down the school.
In 2009, the school had 55 students studying A Level, 32 studying AS and 23 studying A2; in 2010 they have
66 students studying A Level, 41 in Year 12 and 25 in A2.
Bridlington School, Bridlington
Bridlington School Sports College is an 11-18 comprehensive in West Yorkshire with a little under 1,000
students.
The DCSF data showed that 51% of students achieved a grade B at GCSE and that of those students eligible
at KS5 only 15% chose to study A Level mathematics. There seemed to be a large group of students with the
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potential to continue to study mathematics. In the initial plan, the school had intended to invite outside
speakers to talk to potential mathematics students and arrange trips for students to universities to increase
motivation to progress. In fact, the results of an early survey disclosed important barriers to progression in
the attitude of learners. The mathematics team addressed these problems first and made changes to
teaching and learning. Once these changes had taken place invited speakers were used to increase
motivation to progress. In 2009, 39% students who gained GCSE Grades A*- B progressed, which was an
improvement on previous years; but in 2010, after the changes described in the case study, 52% of students
who gained grades A* - B progressed.
Chesterton Community College, Cambridgeshire
Chesterton Community College is an 11-16 school in the centre of Cambridge. The head of mathematics is a
shared post between two women teachers. Girls and boys are taught in separate groups for some sets for
Years 10 and 11. The school has well-documented evidence to show that this approach works for them and
has increased their success rates at GCSE.
The school conducted a survey and focus group discussion with students about what motivated them to
want to progress to AS Level. Their choice of career and degree aspirations were important motivators so
the school introduced the students to career websites and created a careers notice board. Former students
returned to the school to help to motivate students to progress.
Using statistics compiled for this project, Chesterton had the highest rate of progression of all the schools
that took part. The historical data showed that 47% of students who gained grades A*-B progressed,
compared with a national proportion of 30%. The result of taking part in the project suggested an
improvement of this figure for the school to 65%, with 52 from 80 students progressing to study
mathematics.
Childwall School, Liverpool
Childwall Sports College is a large inner city 11-19 secondary school with a comprehensive intake and has
approximately 1,300 students.
This school focused its intervention on using the time between the end of GCSEs and the start of the
summer break to introduce the students to topics they would encounter at AS Level. The activities they
used were based on those in Improving Learning in Mathematics. In the first year, the introductory
programme lasted for two days in each of two weeks. The recruitment rate to AS in this school was 48% for
2010, which was above the rate of recruitment for A*-B that had been achieved previously. However, the
key measure of success for this centre was the increase in the number of students who progressed to AS,
which during the life of the project went from three to 22.
Long Road Sixth Form College, Cambridge
Long Road Sixth Form College in Cambridge is one of two sixth form colleges in the area. It has an intake of
over 2,000 students per year. Students in the area generally compare well against the national average for
five GCSE A* to C.
The college has introduced a series of taster days to introduce potential students to the courses that are on
offer there. This is particularly important because the college now offers Use of Mathematics, which had
increased the number of students studying mathematics, perhaps because it had a wider appeal. It is worth
noting, however, that the introduction of Use of Mathematics has had no impact on the numbers taking A
Level. The majority of students gaining a grade B GCSE now appear to take this option.
Marshland High School
Marshland High School is an 11-16 comprehensive in Norfolk. Students may progress from this school to
the college of West Anglia (an FE college) or one of eight 11-18 schools in the area. The school gained
specialist status for science in September 2005, but prior to the beginning of this project, it was designated
a National Challenge school. At the school’s inspection in May 2009 it was given a Notice to Improve. The
school used a combination of a mathematics club and entry into Additional Mathematics as a way of
boosting students’ self-esteem in relation to mathematics. Although it was possible to calculate a
progression rate for this school based on 2009 entries, it was more difficult to calculate a rate for the current
year due to the number of possible routes that students could take. There is a need for more work to be
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completed with schools in this situation to give feedback about the effect of their encouragement of
students to progress.
Plymstock School, Devon
Plymstock School is a comprehensive 11-18 school with 1,700 students. It is a specialist sports college.
They used differentiated learning for the taster sessions they staged for Year 11 and catered for the needs of
grade B students to bridge into AS Level. They also used real world applications of mathematics within the
Year 11 and AS mathematics schemes of work to relate mathematics to a career pathway. As a result of the
changes made at the school the recruitment to AS Level mathematics had increased from 39 to 58, and the
number of students who progressed with a grade B had increased from 12 to 23. The students with grade B
GCSE now accounted for 40% of the AS mathematics intake.
College of West Anglia, Kings Lynn
College of West Anglia is a post-16 FE college in Norfolk. There are a number of 11-19 schools in the
immediate area but the college continues to offer and recruit to A Level mathematics and Further
Mathematics. Twenty-six schools provide students for the college.
The college concentrated on raising interest in and enjoyment of mathematics with a specific focus on its
“Launch Pad” website and event sponsored by Norfolk LEA. The event featured LA advisers, teachers from
the college, invited presenters and teachers from local schools. The recruitment for 2010 showed that there
had been an increase in the number of students with grade B or grade C at GCSE who were studying at AS
Level.
Harris Academy London
There are a number of schools in this consortium who are just beginning to offer A Level mathematics.
The academy planned to contact former pupils to offer role models of students who had progressed with
mathematics. They also planned to complete a questionnaire survey of the whole consortium to find out
what would motivate students to progress.
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Project initiation and support
Throughout the project the case study schools and clusters were supported by an NCETM regional
coordinator. On 15 July 2010 the project participants were invited to a national workshop in London. More
than half of the case study schools and colleges were able to send representatives and this enabled
participants to compare activities and hear progress reports from each other.
It became clear at the national workshop that schools and colleges would have some difficulty in gathering
historical GCSE data linked to transfers to A Level. This would be the case especially for schools that take
pupils up to age 16 and therefore have limited access to transfer data. It was agreed that in these cases
Julian Clark, senior adviser to the Secondary National Strategy, would use the resources of NDS to find
relevant data.
Suggestions for identifying interventions
All case study participants were encouraged to read the NCETM report participation to DCSF on widening
Factors influencing progression to A Level mathematics (2008). They were also provided with suggestions for
the ways in which they might identify appropriate interventions. These suggestions are summarised below.
Gathering data about progression
Analysing data about progression to A Level mathematics:
•
highlights issues about recruitment
•
sets the scene for the discussions that follow
•
sets a baseline for measuring success of any intervention
•
brings the issue of progression of students with grade B in GCSE mathematics to the attention of
staff and encourages debate
•
highlights the points where data is missing e.g. with progression data for staff in 11-16 schools
there is possibly a need to establish informal means to get data on progression.
Discussion of progression amongst mathematics staff
Discussion of progression issues within the mathematics team is as an opportunity to raise awareness,
especially about the recruitment of GCSE mathematics grade B students on to A Level mathematics
programmes. In particular, it is worth considering what factors teachers think are influencing student choice
of subject at A Level.
Interviewing students
Interview Year 12/13 students to discuss the factors that influenced their choice of A Level subjects. Share
the interview results with the mathematics team in order to:
•
make them aware of the reasons students give for rejecting or selecting mathematics as an option
at level 3
•
Identify significant factors in the students’ choice of A Level subjects to inform a strategy of making
mathematics more attractive to future students, especially those with target grade B at GCSE.
Interview Year 11 students to discuss the factors that influence their choice of A Level subjects. Share the
interview results with the mathematics team to raise awareness and identify selection factors, and how
approaches to teaching and learning might be influenced.
The interview can also be an opportunity to present the advantages of studying mathematics.
Interview Year 10 students to discuss the factors that are currently influencing their choice of A Level
subjects. Again, share the interview results with mathematics team.
The interview can also be used as an opportunity to counter the negative images of mathematics and
accentuate the positive value of studying the subject.
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Student survey conducted for the project
A small-scale survey was conducted for the project. 165 students of AS Level mathematics were asked to
give their reasons for choosing the subject. They were also asked to prioritise those reasons. The graph
below shows the percentage of all students and those who achieved grades B or C at GCSE that gave the
highest priorities to the reasons offered in the survey.
This was provided to participants as a suggested starting point for discussions of the reasons students
choose A Level mathematics and to encourage them to consider conducting a similar survey in their school
or college.
Suggested interventions in relation to career choice
Case study schools and colleges were also invited to consider a number of careers-related interventions
they might make:
•
Teachers of mathematics could use the opportunities during their lessons to emphasise the careers
that an AS- or A Level qualification leads to. Surveys of students such as the one described briefly
above have shown that teachers are more significant than parents for influencing progression into
mathematics.
•
Set up a mathematics careers notice board and website.
•
Highlight the career pathways for a specialist mathematician to make the subject relevant to career
choice. Posters that advertise careers not normally associated with mathematics are also useful.
Images from FutureMorph and Mathscareers can be used to advertise these websites. These
highlight the importance of mathematics as a general qualification that supports many career
pathways.
•
Use invited speakers to emphasise the value and usefulness of mathematics in the workplace.
•
Visit the local university to emphasise the usefulness of mathematics in degree studies. Not
necessarily degrees in mathematics.
Other suggested interventions
Further suggestions to case study schools included:
•
Use existing students to report their experiences of AS mathematics to Year 11 students.
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•
Prepare bridging work for grade B students to complete, perhaps over the summer, to support
fluency in algebra in preparation for AS mathematics.
•
Hold taster sessions after GCSEs are complete but before the summer holidays begin, to encourage
an image of mathematics as an enjoyable subject to study.
•
Have other appropriate pathways available for students with grade B, e.g. Use of Mathematics as
well as A Level mathematics.
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Patterns of intervention
The schools and colleges participating in this project were given a free hand to develop interventions that
they believed would work in their specific context. They had, however, been given a steer through the
project initiation process and most of them chose one or more of the suggested interventions.
The interventions used by case study participants fell into the following categories:
•
Interviewing and surveying students to gain an insight into their attitudes to mathematics and
their reasons for choosing or not choosing the subject at A Level (five cases)
•
Professional development for mathematics teachers on active learning approaches to teaching
mathematics, such as those promoted by the NCETM (three cases)
•
Taster or interest-raising sessions for potential students with an emphasis on the accessibility of
the subject (three cases)
•
Using Year 12 and 13 students as positive role models as speakers or in a formal mentoring scheme
(three cases)
•
Awareness and interest-raising through special events and activities such as visits to mathematicsrelevant venues (two cases)
•
Mathematics clubs and drop-in sessions designed or re-designed to attract a broader range of
students and not just the most able (two cases)
•
Working with local universities to provide enrichment and encouragement (two cases)
•
Entering students for Additional Mathematics GCSE, including those predicted grades below A in
mathematics GCE (one case)
•
Including more material on real-world applications of mathematics into GCE teaching (one case)
•
Creating positive messages about mathematics through such things as posters, displays of work
and assembly input (one case)
•
Identifying a specific target group for progression to A Level mathematics that includes students
likely to get a grade B at GCSE and working with them specifically (one case).
These are described in more detail in the appendices.
All case study participants used more than one intervention. As a research project this made it difficult to
disentangle the benefits of specific interventions. However, as examples of action research these case
studies exemplified the creative nature of the process and in most cases engaged the whole mathematics
team. In many cases, this was a journey of discovery that led to some challenging realisations for the
teachers involved, especially about what informs students’ decision-making about progression.
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Measures of success
It proved remarkably difficult for project schools to collect the kind of hard evidence about progression that
would support the proposition that their intervention had been successful. However, there was good deal
of soft evidence in the form of improved student attitudes and a greater focus of interest by the schools in
their grade B students.
The table below indicates the evidence that was available:
Participant
Nature of evidence
Bishop Challoner Catholic
College, Birmingham
In 2009 the school had 55 students studying A Level – 32 studying AS and
23 studying A2; in 2010 they have 66 students studying A Level, 41 in Year
12 and 25 in A2.
Bridlington School,
Bridlington
12 out of 31 students with grade B going on to A Level (of which seven out
of 16 are girls).
Three students with grade B at GCSE were studying A Level in one year so
that they could take up Further Mathematics next year.
Chesterton Community
College, Cambridgeshire
No hard data but a decision to focus on students with grade B at GCSE by
the 16+ establishment to which students from the school progressed.
Childwall School, Liverpool
12 out of 33 students with grade B progressing to A Level (nine out of 19
were girls).
Long Road Sixth Form
College, Cambridge
Large increase in Use of Mathematics AS (mostly grade B at GCSE) with no
corresponding fall off in numbers of AS mathematics students.
Marshland High School
Increasing number of students with grade B at GCSE with corresponding
increase of those going on to A Level.
Plymstock School, Devon
50% of boys and 11% of girls with grade B at GCSE opting to progress to A
Level.
West Anglia, College of,
Kings Lynn
Increase from nine out of 22 students with grade B or C at GCSE
mathematics taking A Level, to 13 out of 22
Wisbech School
[No report received]
Harris Academy
Identification of student attitudes and its impact on planning the
development of sixth form mathematics provision.
The schools and colleges in these case studies appear to have a significant poverty of information about
their students’ progression profiles in mathematics. If the situation evidenced here is a common
phenomenon across all schools and colleges this would be a matter of significant concern. It is also clear
that many mathematics teachers within these establishments need more opportunities for professional
development in such areas as the active learning approaches to mathematics promoted by the National
Centre.
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Recommendations
This study has confirmed a number of promising interventions and change programmes that have the
potential to make a difference to the numbers of young people with grade B in mathematics progressing to
A Level.
Recommendations to schools
In the light of the NCETM report to DCSF on widening participation, Factors influencing progression to A Level
mathematics (2008), it is important that schools and colleges seek to make a number of interventions and
do not rely on just one to improve progression rates to A Level.
All of the interventions suggested to and used by the case study participants appear to have had at least
some measure of success and there is evidence from the 2008 report that they are more likely to be
effective in combination. In particular, the gathering of students’ views on mathematics and their reasons
for choosing or not choosing to progress in the subject has been especially illuminating for case study
participants.
However, it is clear that schools and colleges have relatively poor information about the progression
profiles of their students in mathematics. It is also clear that many teachers of mathematics still have little
knowledge of current developments in mathematics teaching.
It is therefore recommended that schools and colleges:
•
place a priority on collecting, analysing and acting upon data about the grade profile of student
progression in mathematics
•
ensure that all teachers of mathematics are up to date with current developments in teaching and
learning by, for example, active engagement with the NCETM
•
develop ways of regularly collecting students’ views about mathematics and especially about their
reasons for choosing or not choosing to progress to A Level
•
seek to work collaboratively to manage effective transition to A Level
•
consider at least two of the interventions listed in the “Patterns of Intervention” section above
(page 14), if they are not already doing them.
Issues for consideration by the National Mathematics CPD Committee or by
other infrastructure organisations supporting increased transition to A Level
It is clear from these case studies that more needs to be done to engage teachers in the quality of teaching
and learning of mathematics that is promoted by the National Centre and other organisations and
professional development providers who have similar roles.
The solution to the problem of promoting transition is multi-faceted with no one approach offering a high
degree of success by itself. The most important elements of the solution appear to be:
•
high quality teaching throughout the secondary phase leading up to GCSE
•
enthusiasm and passion for mathematics
•
professional planning and managing of the several elements that between them make for effective
teaching and learning of mathematics
•
aspirations and ethos demonstrated by the school or college
•
a whole school attitude to recognising the learning of mathematics as a lifelong journey.
One other critical factor in successful outcomes following transition is that the nature and quality of the
teaching and learning must be maintained during the programme of A Level study following transfer. The
implication for the FE sector is the need to recruit, retain and develop mathematics teachers of the highest
calibre.
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Therefore, the key issue is managing the transition to A Level both through effective teaching and learning
and through collaborative CPD between teachers pre- and post-16. Key to the ability to effect change is the
availability and timeliness of the data and its usefulness. A great deal of work is being done in this area at
present. It is particularly important that where the transition at 16 involves a change of learning centre –
such as from an 11-16 school to a sixth form centre or an FE college – there must be effective and
transparent ways for the two establishments to have dialogue about the most effective ways to manage
successful mathematical journeys leading to good mathematics outcomes for students. Making data
available to 11-16 schools in a form that they can use to gauge their success at progression is particularly
important. This is an area currently being explored by the Department for Business, Innovation and Skills.
The list below contains relatively easy interventions identified by the case study schools and colleges. They
promote good engagement with mathematics and when applied at or near the transition period can be
very powerful in persuading students about future pathways. They are:
•
running taster sessions that incorporate active learning approaches to mathematics as a way to
increase GCSE to A Level conversion
•
emphasising the importance of mathematics as a progression route to higher education and
employment outside mathematics, thus giving a relevance to the need to progress
•
emphasising the relevance of mathematics to many careers is a great “pull” for progression; use of
a mathematics careers notice board and the web sites helps but the best ambassador appears to
be the mathematics teacher.
•
surveying students and responding to their opinions, leading to a positive atmosphere and hence
a negotiated progression
•
staff taking part in any intervention, making them question the progression factors, canvass
student opinion and challenge their received opinions
•
having a number of appropriate pathways for progression available in order to enhance
progression e.g. AS Level and AS Use of Mathematics allows more students to access the subject
•
tackling the gender issue – the gender issue and mathematics grade B is very complex but we
found that this can open up the debate about progression and then motivate change for the good.
Whilst the project has focused on grade B and above, there are students who achieve grade C who wish to
progress to A Level, and other studies (notably the pilot for Improving Learning in Mathematics) have shown
that more active approaches are inclusive of all students. However, there is pressure on teachers to achieve
high success rates and this can lead to rigid entry criteria which exclude students below grade B.
The issue to be addressed is not whether these are good or worthwhile activities, but how to disseminate
with clarity this guidance and information to schools and to colleges, and to ensure that the messages are
embedded and then sustained over many years, The National Centre has a key role to play in this and
indeed has been very successful in promoting appropriate help and guidance. This has been made difficult
in the past by the different funding streams and regulatory regimes that were in place for providers of 16-19
education. The creation of YPLA creates an opportunity to seek to develop a symbiotic relationship
between pre- and post-16 providers. In the area of mathematics, a key common goal would be to establish
effective and high quality teaching of the subject.
In support of this goal, there is a need for some specialist professional development provision that will
address the challenges of educating teachers in the skill of ensuring effective transition at 16. Careful
thought needs to be given as to who should take responsibility for ensuring that such a programme exists
and that it is coordinated nationally, is of high quality and is effective.
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References
Kowszun, J. (2004) “This Innumerate Isle” Times Educational Supplement 17 Sept 2004
Nardi, E. and Steward, S. (2003) “Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary
Mathematics Classroom” British Educational Research Journal June, vol. 29, no. 3, pp. 345 366
NCETM (2008) Factors influencing progression to A Level mathematics
[https://www.ncetm.org.uk/enquiry/10114]
Ofsted (2006) Evaluating mathematics provision for 14-19-year-olds [HMI 2611]
QCA (2007) Evaluation of participation in GCE mathematics [QCA/07/3388]
Robinson, D. (2007) Post 16 participation in mathematics Specialist Schools and Academies Trust
Smith, A. (2004) “Making mathematics count. The report of Professor Adrian Smith’s inquiry into post-14
mathematics education” London: DFES
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Appendix
This appendix provides detailed reports from nine of the ten case study schools and colleges.
Bishop Challoner Catholic College
Bishop Challoner is a Voluntary Aided 11-19 comprehensive school in the Kings Heath area of Birmingham
and describes itself as “an integral part of the Catholic Community”. Its pass rate at GCSE mathematics A* C, was 75% in 2009 and 77% in 2010. The school was inspected by Ofsted in March 2009 when it was
described as providing “an outstanding education built upon high expectations, the desire to provide
young people with an enriching range of opportunities and the readiness to adopt improvements, which
address the needs and talents of individual students. ... students feel challenged, confident in their teachers’
expectations of them and secure in taking the risks necessary to make outstanding progress.”
In looking for means to increase the uptake of AS mathematics at the school, the mathematics department
decided to look at two inter-related themes. Across the A Level programme they looked at ways to increase
the number of girls who were studying mathematics, in the belief that this would also increase the number
of students with grade B who were studying the subject. This meant that one of the targets they set
themselves was that of “increasing the number of female students opting for A Level mathematics study at
the end of the 2009/2010 academic year.” This would address the “loss” of girls from mathematics, which
happened when those with very good GCSE results had to make a choice at AS Level and, particularly those
who wanted to study medicine, did not choose mathematics. There was also a perceived need to make
mathematics more attractive to girls generally and so draw into the subject area students from across the
acceptable ability range.
The mathematics department also set itself “less measurable success criteria”, namely, “a better idea of the
importance of mathematics within chosen career paths, a greater awareness of what is involved in further
mathematics study and improved confidence and self-belief within the chosen cohort.”
The project had very strong management backing, with the head of mathematics, the deputy head of
department and a member of the senior management team supporting the project.
Interviewing staff and students
The project began with the deputy head of department interviewing staff and students to canvass opinion
about the potential barriers to the uptake of mathematics at AS Level. This identified that there was a need
for more female role models studying mathematics and the need to raise awareness of the uses of
mathematics beyond GCSE and AS Level.
Perception of mathematics
As part of raising awareness, the school established contact with Birmingham University and arranged for
students to attend an event that consisted of master classes and lectures in mathematics, physics and
engineering. The aim was to create and sustain an interest in mathematics amongst the students so that
they would want to continue with their studies. As part of this event, there was a session about the careers
to which a mathematics qualification could lead. This was particularly well received by the students and the
staff thought that this was one of the most important parts of the day.
As part of the same theme of developing awareness, a second trip was organised for a small group of
students to visit Bletchley Park. The visit demonstrated the importance of mathematics in the past, but was
also related to the importance of encryption systems for modern internet communication. The success of
the event has meant that it is planned to be a recurrent visit in future years.
The school also organised a visit to the “Take Mathematics Further” event at University of Warwick.
The aim of these visits was to change the perception of mathematics as a “dry” subject, to one that was
vibrant and had many exciting developments taking place, with connections to many career pathways.
Targeting specific students with the potential to progress
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The head of mathematics used indices that had been compiled earlier in students’ school career, (MABLE
and JESSON) along with predicted GCSE grades, to identify a target group of students for progression. The
students were encouraged to attend further mathematics sessions which ran after school and were wellattended. Students were encouraged to explore mathematics interactively and the sessions received
positive feedback. This has become the mathematics Drop-in Centre which, in 2010, is now part of the
enrichment activity programme that takes place after school.
Providing positive role models
To establish more positive role models, the mathematics department ensured large numbers of female
mathematicians in Years 12 and 13 attended the sixth form open evening, to encourage younger students
to consider the benefits of taking A Level mathematics
The department also created a mentoring scheme using Year 12 mathematics students. The emphasis was
on recruiting girls from Year 12, to provide support for Year 10 and 11 students, to act as positive role
models. This was included as part of the Year 12’s enrichment programme and the mentors were
incorporated into the work of the department by supporting students during lessons. The same students
helped the department to select display materials that would emphasise a positive image of women
mathematicians. The students who took part in this exercise were often those who were thinking of taking
up teaching as a career.
Measure of success
In 2009, the school had 55 students studying A Level, 32 studying AS and 23 studying A2; in 2010 they have
66 students studying A Level, 41 in Year 12 and 25 in A2.
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Bridlington School
Background
Bridlington Sports College is a slightly larger than average 11-18 comprehensive in the East Riding of
Yorkshire. The proportion of students with learning difficulties and/or disabilities is well above average and
the proportion with statements of special educational need is more than double the national average.
Students enter the school with standards which are below, and sometimes well below, the national average
but make progress through their school career so that the pass rate for five GCSEs is about the national
average. The school offers a traditional sixth form curriculum including mathematics. There were 150 in the
Year 11 cohort for 2010 and the GCSE results for the school have been steadily improving.
Generally, the teachers were aware that students’ perception of mathematics was that it was not much fun;
the department cared about the success of the students but they also expected hard work. As students
progressed towards the Year 11 GCSE exams, teachers were aware that the students were less optimistic
about their chances of progression. The head of mathematics pointed out at the beginning of the project
that the GCSE grade was not always a good indicator for A Level success and good grades at GCSE were no
guarantee that students were going to do well. Attitude and approach were as important as ability.
At the beginning of the project, 20 students were studying AS mathematics and 15 were expected to
complete, most of whom would gain a pass. Ten students were expected to continue to A2. Generally, very
few students gain a higher grade in other subjects than their mathematics grade.
The head of mathematics found it difficult to identify consistent trends in gender differences for
achievement at Key Stage 3 and GCSE in mathematics. However, fewer girls than boys chose AS
mathematics. For those that did choose mathematics, there were no marked differences between the
achievements of male and female at AS and A Level. The focus of the project was therefore “to encourage
more girls and pupils with grade B at GCSE to progress on to A Level mathematics”.
The project
A series of visits to outside venues and by invited speakers were written into the action plan, because it was
assumed that the main issue would be portraying a positive role model for girls. The action plan started
with a questionnaire and focus group discussion, with mathematics students in Year 11 and those studying
AS Level. The intention was to find out student attitudes and then plan interventions to change them.
The questionnaire for both Year 11 and Year 12 included a question about how much the students enjoyed
mathematics. The focus group was asked the same question.
This simple question created a major change for the project. The staff were shocked at the level of
disenchantment shown by the survey, particularly amongst girls. The focus group interview was lead by
someone outside the department, who was a woman, and this revealed that the girls in the group
displayed low self-esteem where mathematics was concerned.
The 26 Year 11 students who were present were asked about their intentions to progress in mathematics
with the following results:
Number present
Number choosing AS
mathematics
Girls
11
1
Boys
15
6
Total
26
7
This showed that a disappointing number of students were going to progress, only 27%. The department
realised that what they had found out here was more significant than the items on their original action plan,
so they re-wrote the plan in response to the student’s feedback.
As the head of mathematics said, “The survey made us change our practices.” It also had an impact on the
class teachers of the Year 11 group and the AS group. They decided that they had to respond to the survey
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and adopt more varied activities in lessons. The department realised that simply arranging for visits from
outside speakers was not going to be enough, so, although they kept these within the action plan, they
added professional development activities as well.
One of the problems was that traditional teaching approaches were used to deliver A Level lessons, even by
teachers who used much more varied styles in Key Stage 3 and 4. Teachers were encouraged to use a
greater variety of activity in GCSE classes as well as AS classes. An outside consultant came into the
department and ran professional development sessions to make staff aware of active learning approaches
to teaching mathematics.
The students were surveyed again
The outcomes of the new survey suggested that many students now had a positive attitude towards
mathematics. Most were enjoying the subject more and there was a “shift” in the student’s perception of
how good they were at mathematics. The survey of Year 11 students showed the following:
Number present
Number choosing AS
mathematics
Girls
13
4
Boys
14
12
Total
27
16
Four girls and two boys recognised that they had changed their minds about studying AS mathematics. The
table of results suggests that more students changed their minds than were willing to admit in public. The
key issue for the project was that the staff had responded to the perceived needs of the students and the
students had appreciated this. The head of mathematics thought that this perceived response to student
need was probably more important than the activities that were used.
Although not reflected in the survey, five students were now thinking of tackling Further Mathematics.
The changes introduced by the teachers meant that activities were being used more in their mathematics
lessons, consequently the staff decided to devote one of their professional development days for training in
the use of activities taken from Improving Learning in Mathematics.
Videos from the “mathematics in work” series were also used as “starters” at the beginning of some
mathematics lessons, to relate the mathematics to real applications.
Whilst this was taking place, some of the original action plan was implemented. Outside speakers were
invited into the school to talk to students about mathematics. These talks took place in girl-only sessions
and the speakers were women who were mathematicians: two were primary school teachers, one was an
engineer and a fourth was a lecturer with the Further Mathematics Support Programme. The intention was
to give girls confidence and foster the belief that they could be successful at mathematics beyond GCSE. By
its very nature, organising the sessions conveyed the message that girls were important to the department.
The sessions were not restricted to the top set but included set two as well. The head of mathematics noted
that, “Including the girls from set two definitely raised expectations and gave the girls confidence. Three
girls in set two got grade As and a fourth was one mark short. This level of success in set two is
unparalleled.” As the same person noted, “It was clear from the final survey that attitudes to continuing
mathematics had changed during the year.”
To continue the theme of encouraging girls to adopt a positive attitude to mathematics, an all girls team
was entered for a local mathematics competition.
These changes produced the following results and illustrate the improved progression that had taken place
within this group:
Grade
Gender
A*
Boys
Fraction of students getting this grade
going on to study AS Level
Percentage of students getting this
grade going on to study AS Level
1 out of 1
100%
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A
B
Girls
No passes at A*
Boys
5 out of 5
100%
Girls
4 out of 5 **
80% **
Boys
7 out of 16
44%
Girls
5 out of 15
33%
** The girl who is not studying A Level, wanted to but could not because of a clash with other subjects. In
order to do some mathematics she is doing AS FSMQ over two years.
More students are now opting for A Level mathematics; the particularly important point is that the whole of
the A and A* grades opted for mathematics.
Another indication of renewed motivation was shown by the fact that three grade B students, were
studying A Level in a year, so that they could take up Further Mathematics next year.
The school intends to continue to organise outside speakers for the top two sets. They will probably be
mixed in future rather than single sex and will start in Year 10.
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Chesterton Community College
Chesterton Community College is an 11-16 school in the centre of Cambridge. Its recent GCSE results show
that 34% of pupils achieve at least 1 A or A* and that 77% achieve 5 A*-C . The head of mathematics is a
shared post between two women teachers and girls and boys are taught in separate groups for some sets
for Years 10 and 11. The school has well-documented evidence to show that this approach works for them
and has increased their success rates.
As an 11-16 school, Chesterton does not have a sixth form, but the majority of pupils who want to study AS
mathematics go on to two local sixth form colleges. A local school offers the International Baccalaureate
(where one or two students go each year, and so study mathematics beyond GCSE), but as the local FE
college no longer offers A Levels, the two sixth form colleges account for practically all progression
pathways on to AS mathematics.
The project at this school had two separate strands. One was to interview Year 10 and 11 pupils to find out
what their main motivations were for choosing or not choosing mathematics as an option after GCSE. When
this was known the issues could be addressed and progression encouraged. The other strand concerned
the data available to the average classroom teacher in an 11-16 school who wanted to encourage their
students to progress. How easy was it for them to get access to progression data and so give good advice to
their pupils?
Two focus groups of students were interviewed, one in Year 10 and one in Year 11. The results of these
interviews showed that pupils were thinking of choosing AS mathematics because they saw themselves as
good at the subject, but those that lacked confidence, even if they were in the higher sets, did not seek to
progress. In some cases parental encouragement was a factor, but the most important driver was the
perceived use of the subject to aid a future career. Mathematics was seen as a good “holding” subject for
those who had not made a definite choice of career and essential for those that had chosen careers like
engineering. Where the choice of career definitely involved mathematics, then this was a strong pull
towards the subject, even if the student’s predicted grade was not encouraging. As one student said, “I
want to do engineering but my predicted grade in mathematics is a C, I know I will find it difficult but I still
want to do it [AS mathematics].” Where students wanted to do a degree, then they were more likely to want
to study mathematics, sometimes to increase their chances to get into a “good” university.
The findings are broadly in line with the results of a survey that was conducted with a group of 165 AS
students as part of the project. The survey showed that students had chosen to study mathematics because
they enjoyed the subject, thought that they were good at it and because it was going to be useful for them
in their career or degree. The survey also showed that teachers were a greater influence than parents in
encouraging students to choose AS mathematics.
The focus group interviews and the survey lead to the use of a mathematics careers notice board. The
notice board displayed posters to show that mathematics was useful for a fashion designer, landscape
architect, pharmacist, civil engineer and solar physicist. It also advertised the Mathscareers website and
Future Morph, a STEM careers website. Staff directed potential mathematics students to look on the
websites and at the notice board so that they were aware of the opportunities available to successful
mathematicians.
The other major factor was enjoyment of and confidence with the subject. One of the sixth form colleges
encouraged former pupils to return to their school to give an insight into AS mathematics at the college.
The school took advantage of this opportunity when three former students returned to the school to talk
about the choices they had made to accompany AS mathematics. One had chosen to study mathematics,
further mathematics and physics, another had chosen music, a classical language, a modern language and
English and the third was studying the three sciences and mathematics. The importance of the event was
underlined by the fact that the whole of Year 11 was invited.
Whether or not these measures were successful formed the second part of the project. The difficulty for 1116 schools is that the classroom teacher does not have information on progression readily available. In fact,
Chesterton did have an indication of intended destination but did not have the complete picture of who
had gone where. There was no formal requirement to analyse the data on progression and consequently it
was not routinely completed. What was readily to hand was the data on predicted GCSE grades and the
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data on intended destination, and from this the head of mathematics could produce a prediction of likely
progression.
This showed the following picture:
Predicted grades
Female
Number
Male
Number
A*
3
A*
19.0
A
15
A
14.0
B
15
B
16.0
C
27
C
25.0
total grade B+
33
49
82
Total
60
74
134
The two local sixth form colleges required students to have a grade B to take AS Level, so this table shows
that there were 82 students with a grade B or better.
This table shows those students who had expressed an interest with continuing their mathematics:
Want to continue with mathematics
Female
Male
A*
3
A*
14
A
6
A
12
B
3
B
2
C
1
C
1
total grade B+
12
Total
13
total
28
40
29
42
Hence, 40 students of the 82 who were predicted a grade B or above at GCSE had expressed an interest in
continuing – a progression rate of 49%.
The sixth form college that encouraged former students to return to their school to promote AS
mathematics also supplied Chesterton with information about their students. This was part of the
established relationship between the two organisations. The college prided itself on being a high achieving
college, with 56.2% of its annual intake studying AS mathematics, representing 550 students. The college
was therefore seen as a magnet for able mathematics students. It had also established a procedure that
asked the “feeder” schools for a thumb-nail sketch of applicants to the college. These sketches were used to
indicate students who might find the AS course difficult or who could be described as “gifted and talented”.
This helped to form a close relationship between the school teachers and the college, as did the release
from timetabled duties for a member of the mathematics staff to act as a liaison person with the schools.
The college did not run taster events but instead relied heavily on this liaison work and the reputation of
the college to attract students. A member of staff had produced a set of question sheets that prepared
students for AS mathematics and these were distributed to applicants on the understanding that they
would be completed before the beginning of the academic year. The revision sheets formed the basis of the
induction programme.
The feedback from the college showed that 35 students were studying mathematics there. The liason work
between the sixth form college and the 11-16 schools seemed to encourage the staff from Chesterton to
assume that the route to this particular college was the main one for their mathematics students. However,
this college only had 26 students with GCSE grade B, out of a total of 550 studying the subject, so their
intake of students was biased towards the higher grades, but the school did not know this. The teachers in
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Chesterton therefore tended only to receive information about the achievements of their more talented
mathematicians.
An NCETM Associate worked with the school and the two colleges it fed into, to try to provide data. In fact,
17 students were studying AS mathematics at the other sixth form college, of which eight had a grade B.
The majority of the grade Bs, that is five out of the eight, were studying Use of Mathematics.
This meant that Chesterton had 52 students studying AS mathematics at one or other of sixth form colleges,
which was more than they had estimated. Their progression rate was 52 students out of 80, which was 65%.
This analysis suggests that a number of students may have changed their minds about studying AS
mathematics and, perhaps in the light of better-than-expected GCSE results, had opted to study the
subject. It is also possible that the predicted grades may have under-represented the number of students
who achieved grade B or higher, and consequently there was a larger number of students who could
potentially study AS Level. For whatever reason, this second channel of mathematics recruitment came as a
surprise to the Chesterton teachers.
The example illustrates the way that the 11-16 school relied on the receiving organisations to supply data
on progression so that they could give good advice and encourage progression.
The school is now in touch with both sixth form colleges and in the future ought to receive information on
progression from both. The school needed to know the number of students progressing to both colleges so
that they knew the importance of each to the progression of their students.
In fact, using statistics compiled for this project, Chesterton had the highest rate of progression of all the
schools that took part. The historical data showed that 47% of students who gained grades A*-B
progressed, compared with a national proportion of 30%. The result of taking part in the project suggested
an improvement of this figure for the school to 65%, with 52 from 80 students progressing to study
mathematics.
However, there were additional factors that may have enhanced the rate of progression in this case. The
college that received the students who achieved a high grade had a very high take-up of mathematics;
Chesterton Students who went to this college were therefore very likely to progress. The other college that
received students with a wider spread of GCSE grades had introduced a curriculum change that may have
encouraged more students to take up mathematics.
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Widening Participation in Mathematics
Childwall Sports College
Childwall Sports College is a large inner city 11-19 secondary school with a comprehensive intake. There are
approximately 1300 pupils including 300 in Years 12 and 13. The school population consists of 58% males
and 42% females.
In the first year of the project, the mathematics department provided a specific route through GCSE for
pupils with the potential to study the subject beyond GCSE. At the end of KS4, following the terminal paper,
they ran two courses for pupils that opted for A Level mathematics. They both ran until the end of the term.
Refreshments were provided to foster a more relaxed environment for pupils. Graphical calculators were
purchased to encourage deeper thinking when investigating graphs.
One of the ‘bridging courses’ was aimed at B-grade pupils. It was designed to ensure that the learners had
experience of using A* techniques that are utilised in Core 1. The course covered: surds; completing the
square; algebraic fractions and co-ordinate geometry. No assumptions were made about the pupils’ ability
to access the content, simply that they had not yet accessed the topics.
An ‘enrichment course’ was aimed at A/A* grade pupils. It used practical activities based around extending
GCSE knowledge to encourage deeper thinking. The topics were drawn together to form a ‘bigger picture’
of how mathematics fits together. The course covered: exploring circles; investigating quadratics;
understanding trigonometry; rates of change.
The outcomes of the end of term course in the first year were:
•
momentum was maintained following completion of GCSE
•
the activities demonstrated to the B-grade pupils that they are able to achieve success at A Level
•
greater communication was developed between pupils because the practical activities gave them
more opportunities to express their ideas to each other
•
the girls involved in the course agreed that, “girls are better at finding different ways of getting the
answer, it was good to be given opportunities to investigate instead of being told how to do
something”.
The head of mathematics at the time wrote, “The curricular route that we provide through GCSE has
resulted in our A Level pupils being able to undertake both Core 1 and Core 2 examinations at the same
time in January. This is having a direct impact upon their results and confidence.”
Learning conversations show that pupils felt very confident in undertaking the A Level course – pupils
reported that they had sampled some of the content without feeling pressured. There are a growing
number of girls undertaking A Level mathematics, 45% (nine out of 20) of the cohort are female, in
comparison to 18% the previous year. Amy Bersantie, Year 13, said, “I found that I could relate much easier
to my female mathematics teacher, this made me feel that I could do it,” she added that, “I am proud to be
studying mathematics it makes me feel very intelligent. I know that studying mathematics will give me
more opportunities.” Thirty-five per cent of the cohort that year achieved B grades at GCSE, 17 of the 20
students continued to A2, one student failed and the rest achieved grade E and above.
Whereas the school had recruited relatively low numbers to its A Level mathematics in previous years –
sometimes only three made this option choice – the result of using the taster course was that, their
recruitment went up to 20.
Two changes then took place in the school. The head of mathematics left to take up a promoted post and
the school adopted the idea of a set of taster events across the sixth form. The new head of mathematics
was male, very committed to the promotion of students from GCSE to AS Level and adapted the original
plan to match his own priorities. The expansion of the taster programme meant that this was now a
timetabled event that took place over a two-week period with each subject having four two-hour slots. The
previous programme was adapted to keep the topics the same, but there was no distinction between a
‘bridging group’ and an ‘enrichment group’.
An Associate visited one of the induction sessions which dealt with manipulating surds. The head of
mathematics ran the session, set the scene for the topic in relation to the GCSE and A Level syllabus,
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emphasising that they were going to tackle some AS questions at the end of the session, hopefully with
some degree of success. The teacher had attended some training sessions run by Susan Wall and so was
familiar with the Standards Unit materials and the principles of effective teaching and learning summarised
in Mathematics Matters. The group therefore tried a quiz, where they had to identify whether or not
statements about surds were true or false and an “always equal” or “never equal” exercise where the
learners had to insert the correct symbol between two statements. Both exercises explored common
misconceptions about surds and learners in pairs or threes engaged in discussion to come to an agreed
answer. They used mini-whiteboards to try out ideas.
The group then had a look at some exam questions on the topic that had been extracted from past papers.
The learners tackled the questions as a small group exercise. The same questions and more were available
on the school’s website and the teacher set the challenge to try as many as possible of these questions over
the summer break.
The session ended with an emphasis that the group had tackled what was probably going to be their first
topic on the AS course, and they had all made some progress – the subject was therefore accessible to them
at AS Level.
Fourteen potential students attended, three were predicted a grade A*, seven had predicted grade A and
four had predicted grade B; there was one girl. Five were thinking of studying mathematics because they
were good at the subject, 13 thought that it would be a useful qualification to have, six chose mathematics
because they wanted to work in the construction industry, possibly as civil engineers or architects, two were
thinking of becoming mathematics teachers.
Recruitment to the AS mathematics course continued to increase in September 2010. This was helped by an
increased GCSE pass rate at grade C and above in mathematics, which went from 43% to 56%. The head of
mathematics was particularly pleased with an increase in the number of A* and A grades, which he thought
had resulted from an increase in the number of students taking A Level mathematics acting as a “pull” to
encourage students to achieve higher grades at GCSE. The school had recruited 22 students in 2010, which
were taught in two groups, three students had A*, nine had grade A, nine had grade B and one had grade C.
The number of grade Bs had increased from seven to nine over the previous year. Four of the AS students
were girls. All the pupils who took part in the taster days had progressed, in particular, the A* pupils had
continued their studies at the school at AS Level and were now taking part in a further mathematics group
supported by one of the local universities. One student had joined the AS group from another school.
Using the “down time” at the end of the GCSE exam period had been so productive that the mathematics
department had tried this at the end of the AS exam period. They had brought the AS students into school
after they had finished their AS exams and started to teach the next pure mathematics module. This had
meant that the syllabus knowledge had been covered relatively early in the new academic year and allowed
more time for revision and consolidation.
The emphasis that learners placed on the value of mathematics to open up career pathways had become
apparent during the project with the result that the head of mathematics was hoping to run a school trip to
Salford University to explore this careers angle further. The mathematics department had produced a
pamphlet “Why study A Level?” which also emphasised this angle.
Clearly the tasters had increased recruitment to AS mathematics. There had been a dramatic, sustained
increase in the number of pupils studying AS Level and the number of grade B students studying the
subject had increased.
The table below shows how many students started taking A Level mathematics in Year 12, broken down by
gender and their GCSE mathematics grade. The proportion is shown in each case.
Students starting A Level mathematics in September 2010 from Childwall
School
(Of the 22 starters, 21 were from the school and one from outside. The cohort for the school was 89 boys
and 80 girls)
Grade
Gender
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Fraction of those with
Percentage of those with
A*
A
B
C
the grade who went on
to A Level
the grade who went on
to A Level
Boys
3/3
100%
Girls
None achieved this
grade
Boys
4/4
100%
Girls
1/4
25%
Boys
9/19
47%
Girls
3/14
21%
Boys
1/23
4%
Girls
0/27
0%
The table shows that 21 students from 94 progressed, which is a progression rate of 22%.
The project used the proportion of students who gained A*-B as a measure of progression. The historical
data showed that in the recent past Childwall had a progression rate of 41%, but they now had a
progression rate of 48%. The earlier figures had been based on relatively low numbers, so the success of the
changes introduced at this school ought to be measured in terms of the increased numbers of students
who were now opting to take mathematics. This number had increased from three to 22.
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Widening Participation in Mathematics
Long Road Sixth Form College
Long Road Sixth Form College is located in Cambridge, one of two sixth form colleges in the area. It has an
intake of over 2,000 students per year. Students in the area generally compare well against the national
average for five GCSE A* to C. According to Long Road’s last inspection, 61% achieve five GCSEs at grades
A* to C in 2006/7.
The college visits the local feeder schools for post-16 progression events, but unlike the neighbouring sixth
form college, does not have a system in place to encourage students at the college to visit their former
school. Until recently, students applied to the college via the Cambridge Education Partnership, were
interviewed and then, if they achieved the required the GCSE grades, would start the course in September.
However, for the last two years the college has run a taster event. In the first year, the college contacted the
students via their applications but had a poor response, so the head of mathematics repeated the invitation
via the student’s parents and the response improved significantly. In the second year, the response from the
initial invitation was sufficient to not warrant a second invite and the take-up on all three taster days was
substantial, with 155 potential students attending.
The feedback from the events was an opportunity for the staff at Long Road to canvas the opinions of
students about what they thought was in store for them on the AS mathematics course. Ninety-eight per
cent of those who attended thought that the event had helped them to understand what the AS course
would entail. Some of the other statements explored other aspects of studying mathematics at AS Level.
To the statement: “I feel that GCSE mathematics has prepared me effectively for the AS course” the
students’ responses were:
Total
Percentage
108
70
Disagree
27
17
Strongly Agree
19
12
1
1
155
100
Agree
Strongly Disagree
Total
The responses indicate that there were a number of students (17%) who did not think that GCSE was
adequate preparation for AS Level, which echoed the comments from some of the teachers who took part
in the project.
To the statement: “I am studying AS mathematics because I have enjoyed the subject at GCSE level” the
students’ responses were:
Total
Percentage
Agree
79
51
Disagree
32
21
Strongly Agree
40
26
4
3
155
100
Strongly Disagree
Total
In the survey of 165 students taking AS mathematics completed for the project, enjoyment of mathematics
was a significant reason for studying the subject. This is borne out by these results, but in this sample 36
students actively disagreed with the statement.
To the statement: “I think that I will enjoy the subject at AS Level” the students’ responses were:
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Widening Participation in Mathematics
Total
Percentage
108
70
Disagree
19
12
Strongly Agree
24
15
4
3
155
100
Agree
Strongly Disagree
Total
This showed that the number of students who were expecting not to like AS mathematics was fewer than
those who did not like GCSE, which indicates that the sessions had a positive effect on attitude to the
subject at a higher level.
However, the survey also indicated that the students were expecting to find the subject difficult.
To the statement: “I expect to find AS Level mathematics very difficult” the students’ responses were:
Total
Percentage
Agree
76
49
Disagree
32
21
Strongly Agree
41
27
5
3
155
100
Strongly Disagree
Total
The tables indicate that that there were a sizeable number of students who expected to enjoy the subject
but knew it would be challenging.
An Associate interviewed students during one of the sessions and found that although the students did
expect the subject to be challenging they wanted to study it because they thought that it would increase
their chances of getting on a good degree course. The presentation given at the taster session emphasised
the importance of four key A Levels, of which mathematics was one (the others being English literature,
chemistry and history). None of the students interviewed wanted to do a mathematics degree but business
studies, psychology and architecture were popular choices.
The sessions used mathematical activities that were intended to enhance the student’s algebra skills and
encouraged discussion in small groups. The activities were like ones in the Improving Learning in
Mathematics pack and concentrated on solving quadratic equations and completing the square. At the end
of the session, the students attempted some AS-style questions and then tried some online work that could
be accessed over the summer holiday. The same topic sheets were used during the course as a means to
increase fluency with a particular subject.
Use of Mathematics
One important reason for the taster sessions taking place was because the college offered Use of
Mathematics alongside A Level mathematics, and the taster session was to help students to make up their
minds about which AS was appropriate for them. The opening presentation set the scene by describing AS
mathematics as placing algebra in a pure mathematics context while Use of Mathematics tested algebra
skills in a more practical context. This introduction was to set the scene for more detailed discussion during
an interview or during induction.
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The importance for this option for the department was that the senior management team at the college
had just given its approval for the department to enter the Use of Mathematics Pilot for the full A Level. The
head of mathematics saw this as a positive decision that would allow more students to be successful at AS
Level. He thought that this was particularly important for students who gained a grade B or grade C at
GCSE. He thought that they were more likely to be successful at Use of Mathematics than the more
“traditional” AS Level mathematics.
The decision about increasing the AS offer had been informed by the experiences of Colchester sixth form
college, with whom Long Road had connections as part of a consortium of sixth form colleges that shared
professional development days. The sixth form college in Colchester was taking part in the A Level Use of
Mathematics pilot and had presented their findings at a consortium event.
The following table demonstrated the growth in numbers that they had sustained from using the Use of
Mathematics qualification.
Year
Use of Maths
Maths AS
Maths
(Mechanics)
Further
Maths
Statistics
Total
2005
39
244
41
20
35
379
2006
34
223
32
25
31
345
2007
46
290
47
38
48
469
2008
81
271
45
37
54
488
2009
159
286
38
42
60
585
What was apparent was that Use of Mathematics had demonstrated a growth that had not affected
significantly the numbers on the “traditional” mathematics course. Colchester also presented an analysis of
their AS results related to GCSE grades. This was similar to the chances chart produced for the “traditional”
AS Level mathematics and showed that students with grades B and C at GCSE had good chances of gaining
an AS in Use of Mathematics.
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It was by using this evidence that the head of mathematics at Long Road had persuaded the SMT to
approve the college to enter the pilot for A Level. However, the qualification was largely unknown to the
college’s feeder schools and so the taster days were an important vehicle for the students to understand
the AS offer in mathematics.
The result has been that in 2010 the Use of Mathematics recruited 67 students, AS mechanics recruited 72
and AS statistics recruited 127. Of the grade Bs recruited by the college on to AS mathematics courses, 18
are studying mechanics, 32 are studying statistics and 54 are studying Use of Mathematics.
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Widening Participation in Mathematics
Marshland High School
Marshland High School is an 11-16 comprehensive in Norfolk. It is smaller than the national average, with
830 pupils, and students enter the school with levels of attainment that are broadly average or just below.
The school gained specialist status for science in September 2005, but prior to the beginning of this project,
it was designated a National Challenge school. At the school’s inspection in May 2009 it was given a Notice
to Improve. The outcome of the Inspection and the National Challenge status, meant that the focus of
attention of the head of mathematics was on supporting students with a predicted GCSE grade D to
achieve a grade C. From the inspection report, the school and the head of mathematics recognised that the
school needed to increase the number of students gaining the highest grades. However, the subject leader
was also keen to encourage her students to progress and to continue to study mathematics even if they did
not achieve A and A*.
Marshland is therefore a school in challenging circumstances that chose, much to their credit, to take part in
the project.
What happened
The head of mathematics conducted an attitude survey about progression amongst Year 11 students. The
survey showed that students thought of themselves as “not good enough” to get on to an AS mathematics
course and that the work would be too hard for them. She felt that this highlighted a low level of aspiration,
so she aimed at getting the pupils to believe they could get a grade B in mathematics, to view themselves
as successes and so continue to study the subject. This followed up a point that was apparent from the
survey of 165 students conducted for the project, which showed that the belief in being “good at
mathematics” was the largest single factor in influencing AS students for choosing the subject.
As part of the strategy the head of mathematics ran a mathematics club after school as well as increasing
the number of students being entered for Additional Mathematics. The mathematics club provided
opportunities to show students how the subject could be extended beyond GCSE. It also provided extra
support for students who were on the boundary of a GCSE grade, which was particularly important where
the boundary was between a grade D and a grade C. The club therefore served a dual purpose.
The GCSE mathematics results for the period 2008 to 2010 were as follows:
GCSE Grade
Number
achieving the
grade 2008
Number
achieving the
grade 2009
Number
achieving the
grade 2010
A*
5
1
1
A
5
4
7
B
9
12
23
C
38
62
60
The significance of these results for progression, was that the schools and colleges in the immediate area
preferred a GCSE grade B or above in order to continue. Using this criterion, the potential number of
students to progress was 19 in 2008, 17 in 2009 and 31 in 2010.
What was also apparent was an increasing number of students gaining grade B. This was important because
it increased the pool of students who could potentially progress.
However, the attitude survey showed a general lack of confidence, which suggested using a further
qualification would show that progression was possible; this was the role for Additional Mathematics.
In 2008 the school entered 36 students for Additional Mathematics but this was increased in 2009 to 61 and
107 in 2010. One idea was to increase aspirations by opening up the qualification to a wider range of ability.
The questions the students encountered were more open-ended problems than those in the GCSE, so they
could get a wider experience of mathematics, gain in confidence and hopefully feel that they could tackle
AS mathematics.
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The results for Additional Mathematics over the period 2008 -2010 are shown below for those that achieved
a grade A*-C:
Results 2008
Results 2009
Results 2010
A*
4
A*
1
A*
2
A
4
A
10
A
9
B
15
B
15
B
24
C
12
C
19
C
41
Total entries
36
61
107
Each year there were students who gained a better grade at Additional Mathematics than in their GCSE.
Analysing this in terms of grade improvement, showed that in 2008, 12 students improved their grades in
this way, eight going from grade C at GCSE to grade B at Additional Mathematics, but none going from
grade B to grade A. The table below shows an increasing number of students improving their grade,
particularly for those going from grade B GCSE to grade A at Additional Mathematics. You would expect
such students to progress on to AS mathematics with some degree of success.
2008
2009
2010
12
22
24
Improving from grade C at GCSE to grade B Additional Mathematics
8
8
7
Improving from grade C and B at GCSE to grade A and A* Additional
Mathematics
0
8
14
Number getting a higher grade on Additional Mathematics than GCSE
Also, if a minimum of grade C at GCSE is required to study AS Mathematics, then the grade B for Additional
Mathematics may indicate that these students had the potential to continue. In which case, there were
eight potential AS students in 2008, to add to the 23 in 2008 who gained a grade B and above, giving a
possible 31 students who might progress. Using the same criteria would indicate a possible 25 to progress
in 2009 and 38 in 2010. This pattern of increasing numbers of potential students to progress accompanied
an increasing pass rate at GCSE mathematics at the school, which went from 38% in 2008 to 56% in 2009
and 63% in 2010.
To accompany this attempt to foster a positive attitude to progression in mathematics, the mathematics
department placed posters all around school, cross referencing mathematics in different subjects. The head
of mathematics talked to student about different career pathways and how mathematics was useful for
them all. Notice boards were also used to display career pathways for mathematics.
At the beginning of the academic year 2010-11, the school was re-inspected. The inspection report noted
that “Marshland High is a satisfactory school that is improving. A culture of high aspirations is being
embedded successfully by the head teacher, the senior management team and by staff and students alike ...
standards, particularly in English and mathematics, are rising rapidly... Attainment of both genders
improved in 2009/10 with a notable increase in the standards reached by boys.” Within the report there
was, then, some recognition of a measure of success in raising aspirations.
The problems arise in tracing what has happened to the students. The head of mathematics’ commented in
October 2010 about the destinations of students into mathematics: “No clues where they went, we may find
out at prize-giving next half term.”
The problem for the school is that their former pupils have previously gone to an FE college and two 11-19
schools in the nearest large town, travelled further afield to an 11-19 school in rural Norfolk, or gone to an
11-19 school in Cambridgeshire. An Associate has tried to help with tracing former students but with
limited success.
When asked about whether encouraging progression has had a positive effect on success in mathematics,
the subject leader said, “Progression discussions have been too recent to have had an effect. [We may see
confirmation] possibly in the 2011 GCSE results.”
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Data produced by the project suggested that the progression rate for Marshland, based on entries for 2009,
was 35% compare to the national rate of 30%, which suggests that Marshland’s approach is having some
success. However, whether the changes introduced recently in mathematics have made a difference is
difficult to evaluate statistically because data on individual progression was not available to the project.
There is a need for more work to be completed with schools like this one to give some indication about
whether or not their strategies for progression are successful.
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Plymstock School
Key aim:
“To improve the number of students going on to study A Level mathematics with a particular focus on girls
and students gaining grade B at GCSE mathematics.”
To help the school to understand where they were in terms of students opting to take AS Level
mathematics, they started the project by determining the proportion of students opting to take AS Level
mathematics in September 2009:
Students starting AS Level mathematics in September 2009
A*
A
B
Boys
2/3
67 %
Girls
3/4
75 %
Boys
16/27
59 %
Girls
6/15
40 %
Boys
5/20
25 %
Girls
7/35
20 %
This showed that of the 104 students who gained a grade A* - B, 39 progressed, indicating a progression
rate of 38%. Data compiled from the national statistics for the 2009 entries indicated a progression rate of
40%, which gives some indication of how representative these figures for Plymstock.
The department compared data from previous years, which are illustrated below. This analysis indicated an
issue for recruitment because it appears that the proportion of A* and A students from the whole cohort,
both male and female, that are taking A Level Mathematics has fallen, when the actual number of students
taking A Level mathematics at Plymstock School has remained fairly constant with 35 students in 2007 and
39 students in 2008 and 2009. Although the low numbers in the A* category means that small changes have
been a significant influence on the final percentage, nevertheless a trend is apparent. At the same time, the
number of grade B students taking the subject has increased, particularly for girls.
Grade
A*
A
B
Sex
2007
2008
2009
Boys
100 %
91 %
67 %
Girls
100 %
83 %
75 %
Boys
79 %
74 %
59 %
Girls
48 %
45 %
40 %
Boys
16 %
19 %
25 %
Girls
0%
0%
20 %
As part of the project, Plymstock used two main interventions. These were:
•
Increased differentiation at AS and A2 level. This included setting one AS mathematics group,
increasing the resources to incorporate different learning styles, and increasing students’ selfassessment skills.
•
Increased reference to ‘real world’ applications for A Level topics, which included informing
students of real world applications of the mathematics they were learning, ways that these can be
researched further by students and relating mathematics to career choices. In particular, they
introduced this to a number of students in Year 11, to encourage A Level uptake of mathematics.
The mathematics department implemented this strategy in a number of ways. The January report showed
that they had completed the following actions:
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•
In the summer of 2009, once they had completed their GCSEs, work was set for students to help
them to prepare in depth for the start of the AS mathematics course. In particular, this included
many of the algebra tasks that are covered early in the C1 module. This helped students at the
lower end of the ability range to develop their skills further and practise more of the basic algebra
that would be involved in AS Level. This meant that students started the course with a similar skill
set.
•
Teachers and students have spoken positively about this, although there needs to be more work
on closing the gap between GCSE and AS Level, as students still see this gap as significant. One
teacher is now considering developing a bridging project for students to complete at the start of
the AS Level course.
•
Self-assessment sheets have been produced for all chapters for the core modules. These need to be
used more and discussed in class. Self-assessment at KS3 and KS4 has also been discussed within
the whole mathematics department to make sure we are starting to implement these skills as soon
as we can for as long as we can!
•
Members of staff have identified particular students for progression on to AS Level, with particular
reference to grade B girls. Many discussions have taken place with students during class time, but
particularly during parents’ evening and KS5 options evening. We also asked students currently
taking A Level mathematics, both in Years 12 and 13, to speak to students at the options evening.
We had many students turn up to help who talked very positively about the subject, but also very
truthfully especially when talking about the level of difficulty. The Year 11 students and their
parents have said how useful this was and the students were in much more demand for
discussions than staff!
•
Discussions about the project have taken place within the mathematics department, increasing all
members’ awareness of AS Level mathematics issues. This has lead to the production of further
ideas and work to help towards the project.
•
A number of posters, relating STEM subjects and mathematics to the real world and careers, have
been laminated and are now on permanent display in the mathematics corridor. The intention is to
increase the application value of the subject to real life problems. From discussion with the whole
mathematics department it is clear that this is something that still needs to be increased for the
subject.
•
A Year 10 mathematics conference at the University of Plymouth has been arranged for our top set
Year 10 (grades A*, A and B) to highlight their mathematics work and support taking mathematics
beyond GCSE. This will take place in March.
The January 2010 update report indicated that, although the number of students taking AS Level
mathematics at Plymstock School has remained fairly constant, with 35 students in 2007 and 39 students in
2008 and 2009, initial numbers of students choosing A Level mathematics in 2010 seems to be significantly
higher.
In the final report the project leader at the school made the following
observations:
Students’ thoughts
“As part of the study we spoke to the Year 11s (after they had made their post-16 choices) and the Year 12s
about what had influenced their choices at AS Level. By far the main reasons students chose specific
subjects at AS Level, was for their future career or their enjoyment of the subject. (This echoed the results of
a survey of 165 students that was completed as part of the project and asked them for the main influences
on them choosing mathematics.)”
Increased differentiation
“After questioning the Year 12 students in 2009, a large proportion of the students thought that the jump
from GCSE mathematics to the start of the AS Level mathematics course was very large; significantly larger
than in other subjects. To try to decrease this gap, and therefore improve the new Year 12’s confidence and
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retention rate, the mathematics department set work for students to complete over the summer. This
highlighted to the students with a lower predicted GCSE grade, some of the areas that they needed to
practice to become fluent. Opportunities were given to students to come in to school and receive help from
AS Level mathematics teachers with this work. Students have spoken highly about this as they felt more
prepared to start their AS Level work. Teachers have also spoken highly about this and feel that students are
more prepared now than in previous years.
“In September 2009, one of the groups that had chosen to do AS Level mathematics (approximately 25
students) was set according to their GCSE results. This has helped staff to differentiate the subjects taught,
allowing less confident students more time with the teacher and also allowing for more extension activities
for students who are fluent with the work. We also set a Year 13 class according to AS results, which has had
very positive effects for both students at both ends of the ability range.”
Resources
“We have produced a number of resources to aid the teaching of mathematics at A Level using different
teaching approaches rather than relying on traditional “textbook and exercise” lessons. A number of
jigsaw/domino activities have been produced for the core mathematics modules using the TARSIA software.
These resources are referenced in the schemes of work, and are available already printed within the
department. This has promoted discussion between groups of students.”
Self-assessment
“We have also produced new self-assessment documents for students to use for each of the modules at A
Level (both core and applied). The importance of self-assessment has been discussed in class between staff
and students. As staff we have also discussed self assessment across the whole school, particularly at KS3
and KS4 so that we can start building these skills at an earlier age.
“A couple of the Year 13 students have also talked to the current Year 12s about what they can do to make
sure they achieve their full potential in the subject and to make the course go as smoothly as possible for
them.”
Real world applications
“To increase student’s awareness of the real world applications of mathematics a number of posters have
been produced and displayed around the mathematics area. They have also been posted in other areas of
the school, showing possible careers that mathematics can lead to as well as the use of mathematics in
other subjects. Some of the posters were produced using information from the Mathscareers website
(www.mathscareers.org.uk) and some were from the STEM network.
“Representatives from a company called ‘Intelligent Counting Limited’ came into the school to speak to a
number of students from Years 10 to 13 about how they use mathematics in their company and how other
companies use the mathematical data they produce as well. This allowed almost 100 students to think
about how mathematics is used in one area of business and produced some positive and high-level
thinking from some of the students. This was a successful day and we are looking at continuing this in the
future with the possibility of an optician coming to the school to speak to some of the students.
“A group of high achieving Year 10 students attended the University of Plymouth to take part in a
mathematics conference with other students from around Plymouth. This showed a number of applications
of mathematics in the real world looking at Mathematical Modelling in Mechanics, some statistics work with
the Royal Statistical Society and a lecture on ‘Bubbles!’. Students were enthused by the day and a number
have talked about modules studied at A Level. The day was very positive.
Some Year 13 students who have studied mathematics at A Level are going to speak to some of the Year 10
students (aimed at Year 10 girls with predicted grade B) about why they chose mathematics at A Level and
how they are planning to use it in the future.
All A Level schemes of work now have a column entitled ‘real life’ in them with a number of real life
applications of specific topics being given. The new textbooks that the school have bought for S1 and C3
also show in them a number of real world applications and we are working at highlighting these to
students.”
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[Extracts from the final report compiled by the teachers who took part in the project.]
September 2010 Cohort
Students were targeted in a number of different ways this year to encourage continued study of
mathematics at A Level. Staff held discussions with classes during the year about the course, encouraging
students to opt for A Level. Mathematics staff spoke to students and parents at parents’ evening to
encourage uptake of the subject. Students currently taking A Level mathematics both in Years 12 and 13
talked to students at the options evening with the intention of encouraging take-up of mathematics. Many
students turned up to help who all talked very positively about the subject, but also truthfully, especially
about the level of difficulty. Both students and parents commented about how useful this was to answer
their questions and aid their choices.
This resulted in an increased level of interest in A Level mathematics this year. The Year 11s made their
choices and it indicated that 57students were thinking of studying A Level mathematics starting in
September 2010.
A*
A
B
Boys
7/7
100 %
Girls
3/3
100 %
Boys
17/30
57 %
Girls
14/29
48 %
Boys
13/26
50 %
Girls
3/28
11 %
Three other students who had a predicted grade of C, had also opted to study the subject. At the time the
head of mathematics noted that, “It is difficult to analyses these numbers properly as these are only taken
on current predicted grades. There are a number of students who will achieve differently from their
predicted grade as of January 2010. There has been a large increase in the number of students choosing to
take further mathematics A Level (currently 10 students compared to last year’s one).” The take-up of
mathematics amongst girls with a target grade B was 11%. The head of mathematics’ comment on this was
that, “We feel 11% is still a good uptake at this level but could still improve.”
The final results of the interventions at the school, shown in the table below, are that the number of
students recruited had increased to 58, much as the staff predicted. The table shows that 58 out of the
students who gained a grade B or above for GCSE mathematics had progressed. This indicated a
progression rate of 47% compared with the previous figure of 38%. There had been a significant increase in
the number of grade Bs studying AS mathematics, this had increased from 15 to 23. The proportion of girls
studying mathematics had remained static at 40%, however, as the table below shows, the growth in
numbers had come from the increased recruitment in students who gained a grade B:
GCSE Grade
Number in 2009
Fraction of AS
group with this
grade
Number in 2010
Fraction of AS
group with this
grade
A*
5
13%
9
16%
A
22
56%
26
45%
B
12
31%
23
40%
The project leader at the school thought that the success of the project resulted from having “more
discussion with students earlier in the year as to them taking up A Level” and “involving current students
taking the A Level mathematics course in the recruitment evenings”. She goes on to echo comments from
other teachers who have taken part in the project: “We have had more discussion in class with the students
targeted grade B to encourage them to uptake mathematics, teachers of A Level have been teaching these
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Widening Participation in Mathematics
classes to increase the awareness of A Level and also comment on the suitability of students for an A Level
course.”
Grade
A*
A
B
Fraction of students getting this
grade going on to study AS Level
Percentage of students getting this
grade going on to study AS Level
Boys
6/6
100 %
Girls
3/3
100 %
Boys
18/28
64 %
Girls
8/19
42 %
Boys
11/29
38 %
Girls
12/39
31 %
Gender
In terms of the permanent change that the project has made to the school, she also says that, “We are going
to continue to use current students to talk about their experiences and the use of A Level mathematics
when promoting the course. We have increased the awareness of the use of mathematics in other areas of
the school and are going to continue this, as well as the real life mathematics uses in the KS3 curriculum. We
are looking at increasing the career aspects of mathematics through speakers and posters this year.”
Although the mathematics staff are planning to emphasise the importance of mathematics for career
progression, not many of their students will continue on to degrees in mathematics, no more than two or
three. Those that are interested in progressing to a degree, are aiming at science and engineering, for which
mathematics is directly relevant, or more generally see mathematics as a well-respected subject that will
lead on to a variety of degree pathways.
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Widening Participation in Mathematics
West Anglia, College of
College of West Anglia (CoWA) is a post-16 FE college in Kings Lynn, Norfolk. There are a number of 11-19
schools in the immediate area but the college continues to offer and recruit to A Level mathematics and
further mathematics. Twenty six schools feed into the college, the majority of them in Norfolk.
Pupils in the immediate area transfer to post-16 education in a smaller proportion than the regional or
national average, with 69.3% moving to full-time post-16 education, compared with the national average of
71.3%. As the schools in the area are a mixture of 11-16 and 11-18 comprehensives, this means that the
college is in competition with local 11-19 schools to attract students.
The college began the project by surveying the AS students to find out what motivated them to take up the
course. The results were incorporated into the survey of 165 students conducted for the project and
showed that students had chosen mathematics because they liked the subject, saw themselves as good at
it, and needed it for their chosen career or degree. Staff had the opportunity to emphasise these messages
when potential students came in to the college for open days, but the bulk of the recruitment in the local
schools was conducted by the marketing department who did not promote specific subjects, more the
college as a whole. There was therefore limited opportunity to use the results of the survey.
One of the key results, however, demonstrated the importance of enjoyment of the subject and this
became a theme for an event that took place during the summer months, when the Year 11 students from
the “feeder” schools had completed their GCSEs. The aim was to encourage progression in mathematics
and Norfolk County Council, in response to the below average progression rates in the area, sponsored the
event for which the college played host. A similar event, to motivate students to study mathematics, was
held at the University of East Anglia, in Norwich, but, perhaps because it was held in a university, it attracted
a different spread of predicted grades, the majority being A and A*, with 14% predicted a grade B, no grade
C students attended. The CoWA event attracted a wider audience, with 44% predicted a grade B or C.
Despite the competitive environment and because it was sponsored by the local authority, the event did
not market the college courses specifically. The students enrolled on the course via a website called
“Launch Pad”, which was hosted by the local authority and the students were expected to make their own
arrangements to travel to the event and make their own catering arrangements. The local authority paid for
the speakers, if this was necessary, and for the teachers who supported the workshops that took place.
The Launch Pad event lasted for five days and the ethos was to motivate students and introduce them to
new ways of thinking and working in preparation for their new course. The teachers emphasised to learners
that mathematics was an enjoyable subject and could be fun, as well as introducing some of the topics that
they would meet at AS Level. The students tackled activities similar to those found in Improving Learning in
Mathematics and teachers used the principles of effective teaching outlined in Mathematics Matters, both of
which were familiar to staff through the subject learning coach programme.
Throughout the week the students worked on open-ended tasks using small group work and discussion,
which culminated in each group presenting a possible solution to one of the problems they had tackled.
This problem solving approach was used to develop some of the skills that they would need for the AS
mathematics course.
Some of the fun activities involved the mathematics of juggling, the use of students as co-ordinate points
who formed shapes according to the dictates of a formula, and analysing the outcomes of successful and
unsuccessful bungy jumps using conservation of energy. On another occasion, after learning about the
centre of gravity of a system of bodies, the learners then worked in teams to construct these frameworks as
a set of “impossible” (which meant in this context surprisingly possible) sets of objects that could be
balanced on top of each other.
The feedback from the evaluations completed by the students was extremely positive. One of the
associates for the project attended both the Launch Pad events and found that the event had generated
real enthusiasm for mathematics, regardless of the student’s predicted grades.
The nature of the event meant that its success could not be measured by CoWA’s recruitment alone.
In 2009 the profile of the group studying AS mathematics was as follows:
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Widening Participation in Mathematics
Grade
A*
A
B
C
Fraction of students getting this
grade studying AS Level
Percentage of students getting this
grade studying AS Level
Boys
0
0
Girls
4/22
18
Boys
6/22
27
Girls
3/22
13.6
Boys
4/22
18
Girls
4/22
18
Boys
0
0
Girls
1/22
4.5
Gender
Of the 22 students, eight had achieved grade B. At this time, the entry requirement for the AS mathematics
course was a grade C, and this year Launch Pad did not take place.
The equivalent statistics for this year are as follows:
Grade
A*
A
B
C
Fraction of students getting this
grade studying AS Level
Percentage of students getting this
grade studying AS Level
Boys
1/22
4.5
Girls
1/22
4.5
Boys
6/22
27
Girls
1/22
4.5
Boys
6/22
27
Girls
4/22
18
Boys
0
0
Girls
3/22
13.6
Gender
This shows an increase in the number of grade Bs and grade Cs that have opted for the subject.
However, for a variety of reasons, the college increased its entry criteria from grade C to grade B at GCSE in
order to continue at AS Level. The table shows that girls with grade C have been persistent in wanting to
study mathematics and teachers have been sympathetic to that request, which may have been due to
participating in the project and staging Launch Pad.
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Widening Participation in Mathematics
Harris Academies, London
The Harris Girls’ Academy, East Dulwich, is an 11-18 school for 900 girls which opened as an academy in
September 2006. It is one of nine schools in the South London Harris Federation. The academy has been
judged by Ofsted to be making ‘Good Progress’ with student progress in the top 25% nationally. It offers a
co-educational post-16 curriculum with Harris Boys’ and together they have a capacity for 400 sixth formers.
Although they now described themselves as an 11-18 academy, their sixth form was in its infancy and they
had just had their first student go through the A Level mathematics course. In the federation many of the
schools offered A Levels mathematics so they planned to take advantage of this expertise to grow their
mathematics qualifications. Grade B progression would be important for their future growth.
The plan that the head of mathematics developed had five key points:
•
Identify the factors that influence students’ choice of subjects at A Level by interviewing a focus
group of Year 12 students from across the Harris Academies.
•
Use the focus group to formulate a questionnaire asking students to identify reasons for choosing
to study mathematics to be distributed across the Harris Academies.
•
Conduct a similar interview and survey with Year 11 students.
•
Interview a selection of Year 11 students to identify the reasons for not choosing to study
mathematics, in particular for those students who have the ability to study the subject at AS Level.
•
Raise awareness of the different career choices available to those who have studied the subject.
As part of the promotion of the sixth form in an area where progression into the sixth form was not the
norm, the school held an open evening. The head of mathematics used the opportunity to highlight
“mathematics in real life” and was pleased with the response from students and parents who were surprised
to see the applications of mathematics that were shown. In many cases, she found that parents showed an
interest first and then brought the students to along to look at mathematics as an option.
The interviews with Year 12 in the other academies produced a questionnaire which was distributed within
the academy schools. The distribution of the questionnaire also gave the teacher and opportunity to ask
the other centres if they had received students from the Dulwich Girls Academy.
Introducing a similar procedure with the Year 11 students, of interviewing a focus group and formulating a
questionnaire raised the profile of the new A Level offer. The interviews in particular were a time when the
teacher could learn about the challenges that potential students saw with continuing to study AS Level
mathematics.
The students who were predicted to get an A*, A or B were quite confident with their choice of
mathematics but the grade C students were no more than “maybe” for progressing to AS. After further
interviews the main issue revolved around lack of self-confidence, summed up by the comment “If I got a
grade C and went on to A Level, there’s no way I could cope with the course.”
This highlighted a problem with the students’ attitude to progression and showed the need for adult
support. In these circumstances the teacher’s role was vital. The survey that was conducted for the project
of 165 students showed that teachers’ opinions had greater influence than parents’ and this encouraged
the head of mathematics to make greater efforts to give a positive message during her lessons.
Seventy per cent of those students with a predicted grade A*-B said that they wanted to do A Level
mathematics but did not give a reason. The results of these interventions need to be confirmed by 2010
results.
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Widening Participation in Mathematics