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BOWLAND MATHS –
THE CPD MODULES
Alice Onion introduces new resources launched in autumn
2010 with a focus on mathematical processes.
I imagine you have heard of Bowland maths and
will know something of the ‘case studies’ that were
published in 2008. These are substantial mathematics projects, taking five hours, or more, to
complete. Most are set in real or realistic contexts,
like designing a smoothy – Product Wars, or devising
plans to improve road safety – Reducing Road
Accidents, although the most popular case study is
set in the fanciful context of an alien invasion.
The launch in autumn 2008 was timed to
coincide with implementation of the then new
national curriculum which places an even greater
emphasis on mathematical processes than previous
versions of the curriculum. It was, and still is,
recognised by Ofsted and others that Using and
applying mathematics is the least well taught aspect
of the mathematics curriculum. Teachers themselves
said they were not confident when they moved
away from lessons based solely on content, using a
transmission method. Many teachers were wanting
support with planning, and delivering, the sort of
lessons where students are able to make mathematical choices, to pursue their own lines of reasoning,
and to communicate mathematically. So not only
did Bowland provide eighteen of these case studies,
we also released five CPD modules to support
teachers with their own development in teaching
‘key’ processes. Both the case studies and CPD
modules are available free: download from the
Bowland website – www.bowlandmaths.org.uk. The
materials were also made available to schools in
England on DVD. Each school was entitled to five
copies of the DVD, so if you are new to school and
do not have a Bowland DVD to hand, it is quite
likely that there is at least one in the maths stock
cupboard.
We recently commissioned a survey about the
2008 materials and found that the vast majority of
people have heard of Bowland maths – 88%. Some
62% had used the materials at least once, 46% had
used it more than 2-3 times in the year, and 42%
had used at least one of the cases more than once.
These seem to us fairly encouraging figures.
However, only 19% had made any use of the CPD
modules. You can predict the reason given for this
– lack of time. Almost all respondents who had
looked at the CPD materials thought they were of
high quality, and most respondents to the survey
said they would welcome more training in this area.
So, Bowland has partially met its aim. There is a
feeling though that we have provided materials for
those teachers who were already teaching mathematical processes though group work, who were
already enabling learners to progress through the
use of ICT, and through discussion. But we have
not done enough to help those teachers who want
to work in this way, but feel they lack the necessary
skills to do so.
Alongside the survey, we were also hearing from
teachers that some found the prospect of a full case
study rather daunting, and they would prefer to
start with something shorter, a single lesson at most.
In fact, this is exactly what the CPD modules
provide along with the development activities for
teachers and video footage from classrooms.
For example, in Module 1 ‘The Case Studies and
Mathematics: Where is the maths in these Case
Studies?’, as well as the real example from Honduras
of building a school from plastic bottles, which you
maybe familiar with, there is also a set of mathematical photographs with associated questions to
stimulate discussion. Teachers who are not used to
extracting mathematics from real contexts can use
the photographs as a ‘toe in the water’ to this type
of work, spending as little as ten minutes to start
with, where students discuss the questions in groups.
One such photograph shows row of Russian
dolls in descending order of size. These are the
kind of dolls that can be packed sequentially inside
one another. The following questions are posed in
Module 1, to support classroom exploration using
the photograph.
MATHEMATICS TEACHING 221 / MARCH 2011
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41
© ATM 2011 • No reproduction (including Internet) except for legitimate academic purposes
copyright@atm.org.uk for permissions
•
•
•
•
•
Do the tops of the heads lie on a straight line?
What does this tell you?
If you divide each doll’s height by its width,
what do you get?
What does this tell you?
If you were to make some bigger dolls in this
set – how big would they have to be?
Other photographs in the handbook for
Module 1 include a tricycle with square wheels and
an interesting pavement formed of tessellated irregular pentagons. There are six photographs
altogether and for each there is a list of specific
questions like the ones above.
In Module 2, ‘Tackling unstructured problems: Do
are curriculum, teacher skill, and, of course,
assessment.
The support for curriculum is provided though
the case studies, and for teachers’ development
through the CPD modules. Much thinking has gone
into the support for assessment during the past
three years. During that time statutory end of key
stage 3 tests have ceased, although the requirement
to report teacher assessment results remains. As
with curriculum and CPD, we made the judgement
that the assessment need is greatest in mathematical processes, rather than in content. So we have
now produced 35 short assessment tasks.
For example:
I just stand back and watch or intervene and tell them
what to do?’ there are three unstructured problems
given as examples for teachers to try out in the
classroom as part of the development of their
understanding and practice. These are:
• Organising a table-tennis tournament
• Designing a box for 18 sweets
• Calculating Body Mass Index
Each unstructured problem is presented on one
side of paper with full instructions for students.
These are more ‘scaffolded’ for learners than the
case studies. For example, in Organising a table
tennis tournament, students are told:
• how to code the players (A, B, C ... etc)
• to list all the matches that need to be played
• how to organise these matches systematically
• how to tabulate the order of play
• to remember that players cannot play on two
tables at once.
As part of their own development teachers are
invited to compare structured and unstructured
problems. These more structured problems give
teachers something to start with if they are less
familiar with this way of working.
Module 3 focuses on group work and as with
the first two modules there are specific mathematical problems provided for teachers to use in the
classroom to develop their range of teaching strategies when students are working together in groups.
Teachers are also invited to take part in a mathematical discussion with colleagues and then to
reflect on the discussion process. One suggested
mathematical question to use for this discussion is
‘How many people can stand comfortably on a football
pitch?’
Bowland’s aspiration from the start was to
provide support for secondary mathematics in
three ways, which between them are intended to
enable a transformation. The original analysis of the
status quo before Bowland made any decisions, led
to a view that the three key influences on practice
42
To help solve this problem students are given
these two facts:
At the beginning of the
20th century, the average
number of children per
family was 3.5
In 1900, life expectancy of
new born children was 45
years for boys and 49
years for girls.
By the end of the century
this number had fallen to
1.7
By the end of the century
it was 75 years for boys
and 80 years for girls.
Each of these tasks comes with full teachers’
notes, including suggestions on how to introduce
the tasks – there are Powerpoint slides for each one
and, more importantly, guidance on progression
through mathematical processes. As a reminder the
mathematical processes are:
MATHEMATICS TEACHING 221 / MARCH 2011
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© ATM 2011 • No reproduction (including Internet) except for legitimate academic purposes
copyright@atm.org.uk for permissions
The task ‘110 years on’ focuses on three of
these. Here is the chart showing progress through
these processes in the context of this task.
Of course, bringing in assessment makes new
demands on teachers. The original five CPD
modules dealt with the topics needed to teach key
processes. Alongside the 35 new shorter assessment
tasks we have also published two new CPD
modules. So the full set of CPD modules now looks
like this:
The Secondary National Strategy has collaborated with Bowland on letting schools know about
these new materials, as they did with the original
publications in 2008. So we hope that at
least those who lead a department and/or
work closely with a local authority, will at
least have some familiarity with this.
We are confident that there will be
extensive use made of these new shorter
tasks, but we also hope that teachers will be
able to use the CPD modules. As a reminder
each module takes the form of a ‘sandwich’:
And a final reminder of what is available
within the CPD modules. Each one follows
the structure above and can be used in a
variety of ways, from an individual teacher
working alone, to whole departments
working together, or as materials for training
sessions led by an experienced facilitator.
Alice Onion is a Visiting Senior Research
Fellow, Kings College London and Bowland
mathematics adviser. alice.onion@kcl.ac.uk
MATHEMATICS TEACHING 221 / MARCH 2011
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Thanks to Malcolm Swan
for use of his slides,
which he prepared for
BCME 2010.
43
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