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Broadbent Maths - creative primary maths

Problem solving, mathematical processes and natural powers

Sunday, 5 July 2015
Mathematical problems often put children in a position where they are likely to get stuck. This may not actually be a bad thing. According to John Mason, it is 'an honourable state to be in' and should be viewed as a positive place as it is the start of the challenge to solve the problem. 

I have been heavily influenced by the work of John Mason since the 1980s, and although that was some time ago, the same message about developing children’s mathematical processes is just as important now as it was then. His book, Thinking Mathematically, has been re-published and is good reference material to dip into.

The language to describe this has altered a little over time, with processes of thinking now being referred to as 'natural powers' that learners bring to the classroom. It is then the role of the teacher to encourage and motivate children to use their natural powers in the context of mathematical thinking. This involves an atmosphere of questioning, challenging and reflecting, with children making sense of the mathematics by discovering elements of it themselves.

So how can you make this work in your classroom? 

Challenges, investigations and problems should involve thinking and working time, so encourage the children to play, explore and follow lines of enquiry, recording their thoughts and actions while working on it, rather like writing a story or transcript. They may reach brick walls and dead-ends. Rather than simply giving up, encourage children to write STUCK! as a rubric, whenever they reach an impasse in their investigation. Turn it into a positive emotional position, when the real endeavour and learning kicks in.

They may need help getting 'unstuck' so share suggestions of how they may tackle the problems facing them, perhaps putting these and others on a poster:
Read back through the problem, draw a table or picture, talk to a friend, ask a different question, look for a pattern, start again...

As soon as the children find a route ahead or discover something to explore further, they will hopefully feel that warm glow of achievement. At this point they can write AHA! on their problem to show their moment of discovery.

Aha investigation

To make the most of children's natural powers of mathematical thinking, we need to give them the opportunities to solve problems, investigate, explore and discover. These types of activities need to be planned for to become a feature of your teaching and the children's learning, so it is worth considering the balance in your maths lessons to check that you're giving time and space for this important aspect of mathematics.

Take a look at part of Joanne's investigation into patterns made by drawing borders around shapes on triangular paper. She was in my Y6 class and had a very good questioning approach - she enjoyed making discoveries and using STUCK! and AHA! 
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