Maths involves no more factual recall than other subjects – powerful questions can help children remember key concepts
When talking to teachers, they often tell me that one of their biggest challenges is ensuring children retain the facts they learn in maths. Something is taught one day, only for it to have vanished from memory the next, be it number bonds, times tables or column subtraction. Maths is often seen as a subject that requires memorisation of abstract facts. How can we ensure that children remember all of the additions to 20, the five times table and the names of all the 3D shapes before moving on to learning formal procedures?
While there is a certain amount of factual recall required in maths, I passionately believe that it’s no more than is needed for other subjects. In fact, the relationships between numbers, calculations and concepts mean that you can learn how to use the patterns of maths to build knowledge in a way that doesn’t put much pressure on rote memorisation. Arguably, the rules of addition are easier to understand than spelling rules and simpler to explain than the correct use of a semicolon.
Academic research shows that rote memorisation and rehearsal alone are not effective in forming new memories. Through his research, Daniel Willingham suggests that memory is ‘the residue of thought… The more you think about something, the more likely it is that you’ll remember it later.’
If I think about my own memories, they are all connected to experiences that required me to be fully engaged. If we form the strongest memories when we have had to think deeply about something, the biggest challenge we face as teachers is how to inspire, surprise and challenge children to scratch beneath the surface and dig into their own conceptions and misconceptions. A curiosity and excitement for maths is instrumental in ensuring children learn deeply.
One of the most important pieces of advice I was ever given was to think carefully about the questions posed to children in maths lessons. Powerful questions have the potential to encourage children to think more deeply, and the deeper they think, the more likely they are to remember. There are questions that expose mathematical patterns:
• What do you notice?
• Can you see any similarities/ differences between … and …?
• Can you think of another example that follows this pattern? There are questions that require deeper or systematic thought:
• Is there more than one solution?
• Can you be sure you have found all the solutions?
• What is the best order to work this out?
And there are questions that encourage children to explain their reasoning and to tackle misconceptions:
• Can you show me another way?
• What would happen if…?
• Would that be true if this changed to…?
There are some excellent teaching resources that can support you with formulating the right questions, but the important thing to remember is that the best way to measure the effectiveness of a question is how deeply it prompts children to think.
Teaching for mastery promotes the use of whole-class discussion as a key strategy for developing mathematical thinking. It’s really important that all children think deeply during these sessions – not just a few. Learning partners and the use of manipulatives work well for me and ensure that all pupils have their brains engaged simultaneously.
I have seen this work really well where teachers deliver lessons which are truly accessible to all children. These often feature problems with multiple solutions, which encourage discussion and open up new avenues for conversation. Lessons which contain strong visual prompts and representations help to keep everyone engaged and challenged in their concretepictorial- abstract (CPA) journey.
A perception of the mastery approach is that it is a return to old fashioned chalk-and-talk, where the teacher explains and the children listen and copy. From my experience, this isn’t true. Instead, it provides a rich learning experience for children. Each maths lesson is like a field trip: the whole class moves forwards together, and has a meaningful conversation along the way. The best lessons are built around asking interesting questions that go deep into conceptual understanding, and are supported by a rich variety of mathematical structures and representations which support engagement and discussion for all children.
Tony Staneff is vice principal at Trinity Academy Halifax and leader of a team of mastery experts supporting schools across the UK. He is the series editor and author of Power Maths from Pearson.