How does children’s
understanding of subtraction
help engage and motivate
them when tackling
mathematical problems?
The Ryde School Context
DATA Trends show that the school achieves highly
in mathematics.
• In 2011 93% achieved level 4+ at the end of
Key Stage 2 and 43% level 5+.
• This was in line with the performance over the
last 3 years. The value added score was 101.1
in both maths and English. 93.1% of pupils
made 2 levels progress in mathematics.
• During this academic year maths has not been
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identified as a whole school priority but in the
school development plan the following targets
were set for mathematics:
To develop mathematics within the creative
curriculum,
To plan an enrichment focus that linked
mathematics, technology and literacy
To build up resources to teach the more and less
able in mathematics.
• Much of the work for these targets had already been
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carried out before the details of the project were
revealed therefore we decided to look at the analysis of
data and see where the weaknesses were.
The analysis revealed that children were finding
questions that involved applying their knowledge of the
4 operations particularly difficult.
Subtraction and division were weaknesses in all Key
Stage 2 classes.. It was recognised that if the findings
were positive the strategies and approaches could be
used in the teaching of problem solving with the other
operations.
The Elephant in the Classroom
• Jo Boaler in her book “The Elephant in the
Classroom” writes, “Students are forced into a
passive relationship with their knowledge-they
are taught to follow rules and not to engage in
sense-making, reasoning, or thought, acts that
are critical to an effective use of mathematics.
This passive approach, that characterizes maths
teaching in many schools, is highly ineffective.”
• “When students try to memorize hundreds of
methods, as students do in classes that use a
passive approach, they find it extremely hard to
use the methods in any new situations, often
resulting in failure in exams as well as in life.
The secret that good mathematics users know is
that only a few methods need to be memorized
and that most mathematics problems can be
tackled through the understanding of
mathematical concepts and active problem
solving.”
Staff Meeting
• We looked at the progression of teaching in counting back and
finding the difference by counting on. This gave staff the
opportunity to look at the different methods involved in teaching the
key areas of subtraction. There was a lot of discussion about which
methods to introduce and when to use them rather than which
method to use in the given context.
• A sorting activity was carried out which involved staff considering
the context and whether this meant that the problem was more
naturally a counting back or counting on problem.
• By the end there was a growing understanding that the choice of
method needed to be context driven and that in many cases a
variety of methods could be successful in solving the problems.
Year 3
• A sequence of work was planned for Year 3 which
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involved some method teaching but lots of opportunities
to apply their knowledge.
Developing an understanding of the key vocabulary as
well as consolidating understanding of different
strategies became a key focus Teaching time was spent
in unpicking the language of word problems. The stepby-step approach to word problems was introduced and
used as a framework to help children.
As children’s ability to unpick problems grew so did their
motivation and engagement in the work.
• They enthused when trying to solve problems
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about hippos and children.
The children who fed back their findings
described their maths lesson as “fascinating”
and “the best ever”.
Starting with an interesting stimulus and then
generating their own questions motivated this
group to use mathematics to find out interesting
answers to real life questions.
Year 5
• The Year 5 cohort’s initial test examined their application of
subtraction in problem solving contexts. They found the test
particularly difficult and after analyzing the data I was unsure
whether they had any real understanding of subtraction.
• A sequence of work was planned that focused on problem solving
strategies. Time was used as a stimulus as children would naturally
be able to use number lines and informal strategies to complete
tasks rather than methods that were inappropriate in the context.
• After a series of sessions where work was modelled and then
scaffolds were offered, children soon became confident in using a
range of strategies to tackle problems.
• Their talk about the maths showed that they were much more
engaged and motivated in the work. They began to develop their
own questions and problems around time.
• This approach has subsequently been used in work around
multiplication.
• Children have greater confidence in generating appropriate
problems. Over 30 viable questions around their reading books were
generated. They wanted to find out how many words are in a book,
how many letters, how many started with vowels – the list was
endless.
• Children became highly motivated to use multiplication strategies to
solve the problems and to compare their answers with their
partners.
The Findings
• When both groups were re-tested they showed
a big improvement in their understanding of the
problem solving questions. They had greater
confidence in making sense of the language and
then using appropriate number sentences to
help solve the problem. The opportunities to talk
through class tasks and then the use of scaffolds
to support learning has certainly helped further
engage and motivate both cohorts of children.
Future Work
• This work will be fed back to all staff with a focus on the need for
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teaching problem solving strategies along side calculation strategies.
The messages that we hope to be able to convey are that:
Children’s motivation and engagement in all areas of mathematics
comes when they really understand the language of the tasks being
presented to them.
It takes time to embed language in children’s minds and then to get
children to talk mathematically.
Work needs to be modelled and scaffolds need to be offered to
children to help them succeed.
Real understanding comes when children are motivated and
engaged in solving problems that they have generated and that
have meaningful contexts.