# How does children’s understanding of subtraction help engage and motivate them when tackling mathematical problems?

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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+. 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. 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 identified as a whole school priority but in the school development plan the following targets were set for mathematics: During this academic year maths has not been 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 develop mathematics within the creative curriculum, To plan an enrichment focus that linked mathematics, technology and literacy To plan an enrichment focus that linked mathematics, technology and literacy To build up resources to teach the more and less able in mathematics. To build up resources to teach the more and less able in mathematics.

Much of the work for these targets had already been 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. Much of the work for these targets had already been 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. 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. 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.” 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.” “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. 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. 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. 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 involved some method teaching but lots of opportunities to apply their knowledge. A sequence of work was planned for Year 3 which 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 step- by-step approach to word problems was introduced and used as a framework to help children. 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 step- by-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. As children’s ability to unpick problems grew so did their motivation and engagement in the work.

They enthused when trying to solve problems about hippos and children. They enthused when trying to solve problems about hippos and children. The children who fed back their findings described their maths lesson as “fascinating” and “the best ever”. 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. 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. 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. 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. 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. 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. 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 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. 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. 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 teaching problem solving strategies along side calculation strategies. The messages that we hope to be able to convey are that: This work will be fed back to all staff with a focus on the need for 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. 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. 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. 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. Real understanding comes when children are motivated and engaged in solving problems that they have generated and that have meaningful contexts.

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