Focus of the Month
March 2016
Integrating problem solving
into schemes of work
Why integrate problem-solving into schemes of work?
There is a renewed emphasis on the teaching and learning of problem solving. In the May
2012 report, Mathematics: made to measure, Ofsted stated that “Schools were more aware
than at the time of the previous survey of the need to improve pupils’ problem-solving and
investigative skills, but such activities were rarely integral to learning except in the best
schools where they were at the heart of learning mathematics. Many teachers continued to
struggle to develop skills of using and applying mathematics systematically.”
One of the three aims of the National Curriculum is to ensure that all pupils, “can solve
problems by applying their mathematics to a variety of routine and non-routine problems
with increasing sophistication, including breaking down problems into a series of simpler
steps and persevering in seeking solutions.”
At key stage 5 the new subject criteria for A level Mathematics from the Department for
Education makes many references to problem solving, including in the aims and objectives
that students, “use their mathematical skills and techniques to solve challenging problems
which require them to decide on the solution strategy”. To this end a whole overarching
theme (OT2) is given to Mathematical problem solving.
Prompts for reflection and discussion as a department.
A healthy and sustainable approach to change can require time and consideration. A
scheme of work should be viewed as a work-in-progress, a living document that is
constantly evolving and reflecting the current priorities and needs of a department. A few
prompts for thought and discussion are suggested here:
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Thinking about this difference may help you
and your colleagues clarify the progression that
students make in your school or college, and
how this comes about.
It may also be helpful to think about how you
would identify a mature student solution to a
problem in the same way as colleagues in the
English department can identify a mature
piece of written work from their students.
This is a good prompt for facilitating
discussion. Teaching is personal and
idiosyncratic, and a good team of
professionals will complement rather than
duplicate each other’s strengths. However, a
degree of commonality is important if students
are to receive a consistent experience.
MEI support
MEI produces a number of resources, and runs several professional development courses,
which help to embed the use of problem-solving in the classroom. MEI Conferences, for
example, are a rich source of resources, inspiration and discussion. See our Conference
2015 page for the latest sessions which included both financial and statistical problem
solving.
Key Stage 3/4
FRESH strategies for embedding problem solving
Professional development for experienced teachers
of secondary mathematics looking for practical
approaches for enthusing and supporting students.
The clock angles problem (right) is taken from this
course.
The Further Mathematics Support Programme
(FMSP), which is managed by MEI, has produced a
number of GCSE resources that include problems
with suitable hints and prompts for students and
group work activities. In addition, a number of GCSE
problem solving business cards are available online
or can be requested free of charge by emailing
admin@furthermaths.org.uk
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What angle is formed on this
clock face? Be careful, the
clock face has been rotated.
You may find this link helpful for
checking your answer.
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MEI produces ‘Maths Item of the Month’, a number
of which are aimed at teachers and students of
GCSE Mathematics. These problems can be used
for problem solving, enrichment, or as a way to
encourage mathematical thinking/proof.
Past problems have been mapped to the curriculum
and are available here.
A level
Teaching Advanced Mathematics (TAM)
This question from TAM shows how simply problemsolving skills can be developed at A level.
The tangent at P passes
through the origin. Find P
Cambridge Mathematics Enhancement Project
(CMEP) Problems from the project have featured in recent MEI newsletters. See February
2016, September 2015 and June 2015 editions at mei.org.uk/meinewsletters
STEP and AEA support
MEI provides real-time online tutorials and teaching sessions in STEP and AEA
Mathematics. Students can access live interactive tuition at a time and location to suit them
through an online learning platform.
The FMSP also provides regional support for students developing their problem solving
skills in the form of problem solving conferences. Year 12 conferences focus on the general
development of problem solving skills. Year 13 conferences focus on preparation for the
STEP and AEA examinations. Details can be found here.
MEI produces ‘Maths Item of the Month’, a number of which
are aimed at teachers and students of A level Mathematics.
These problems can be used for problem solving, enrichment
or as a way to encourage mathematical thinking/proof. Past
problems have been mapped to the curriculum and are
available here.
The FMSP has developed a series of My Favourite Problem
posters that can be used to brighten up your classroom.
Copies of these posters can be requested free of charge by
emailing admin@furthermaths.org.uk.
The FMSP has also produced some A level resources which,
include group work activities, year 12 problem solving
practice sheets and masterclass notes.
Integral resources offer a range of classroom-ready problem solving materials. A couple to
sample are:
• Which belongs to which - Students have to find
out which number belongs to which sequence and
also give the term number.
• Matrices in a bag - An opportunity for practice in
working with matrices, including determinants and inverses.
You can find out more information on subscribing to Integral here.
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