Meaningful Mathematical Recording

With problem solving and reasoning at the core of the mathematics curriculum, we recognise an increased emphasis on developing teaching styles where children are encouraged to think for themselves, explore strategies, communicate their thinking and discuss and debate with their peers. This can be in conflict with a belief that all learning in mathematics has to be evidenced, and that it should be recorded in a particular way. But mathematical recording and evidence of learning do not have to be in conflict.

Some schools are moving towards a more child-centred approach to recording mathematics which allows teachers to evidence and access learning.

Making tighter links with English learning

English skills are directly transferable to mathematics. In English, children are taught to communicate in writing for a purpose, for example: to organise thinking, writing a report, keeping track of events, articulating ideas. In reading lessons, children learn to evidence their responses, draw inferences, make predictions, etc.

We can use the same terminology and have similar expectations for children’s written mathematics. If we give children ownership in what they record and explicitly teach them how to build better explanations, children’s learning in mathematics can be more focused on the mathematical thinking, rather than remembering how to record within a modelled frame.

Here children were asked to find which digit had been turned over in the addition shown. They were asked to record their first thoughts when faced with the problem.  This child is beginning to explain their thinking, and ‘thinking ahead’ about a strategy. They were asked to reflect on how they could convince someone that their answer was correct.

Reigning in free recording

Children’s mathematical thinking is often more visible when they record on individual whiteboards or large sheets of paper. Whiteboard work is quickly lost, and storage is a problem with large sheets of paper or the work is not considered neat enough to be used as evidence.

Children need to be taught how to record in a way that is free, makes sense to others, communicates their thoughts and is acceptable as evidence. A Year 4 class recently made that changeover in a week:

  • Day 1: Children recorded in pairs on large sheets of paper.
  • Day 2: Three examples of work were shared with the class. The children analysed whether the recording made sense to others (was it annotations, writing things in sequence, numbering the development of ideas, acceptable handwriting). Children recorded in pairs on blank A3 paper.
  • Day 3: The children reflected on the previous day’s work against the criteria they had set themselves, agreeing that a clear conclusion is also helpful. Children recorded on blank A4 paper. They reviewed and commented on each others’ recording.
  • Day 4: The children worked individually on blank A4 paper, the teacher commented on their work and suggested improvements.
  • Day 5: The children worked in their books.

By enabling children to record their own way, they are not only given ownership of the learning, they are also creating evidence of their thinking, including learning that we would categorise as greater depth. Children had a document to ‘talk to’ when they entered into a dialogue with peers or adults about their thought process. Adults and children both explain with greater confidence with the support of their own notes.

Say it before you write it

Some schools are successfully using iPads as a vehicle to enable children to rehearse and improve their explanations. For example, given the task ‘Explain how to add these two fractions with the same denominator’, children were asked to add 3/5 and 3/5. This was the first time they had encountered the addition of fractions, where the answer was greater than 1.  Children worked in pairs using an iPad. They solved the problem, and then set about preparing a visual explanation, with pictures, to present to the class. They were given time to re-record if they needed to.  Without exception, the children in the class were focused on understanding the mathematics in order to articulate it to others. They then reviewed each other’s film clips. At the end of the lesson the children wrote a paragraph summarising what they knew. 

For the future

Danny Brown and Mike Ollerton ran a brilliant session at the 2019 Joint ATM/MA Conference in April this year entitled ‘Mathematics Live’.  Delegates solved problems using their preferred note-taking method, then tweeted their solutions live to the audience. A great deal of thought was put into how to communicate and justify the tweeted outcomes. Our children are moving into a future, where written and visual communication of mathematics is often live and always purposeful. It is not a reproduction of learned structures, and we should, at least, be heading in the same direction!

Janine Blinko is an independent consultant in primary mathematics. She works in primary schools, leads training and works alongside teachers and leaders, authors books and writes assessment materials. Janine is an author of our new digitally-led primary maths programme, MathsBeat