AfterMaths: Manipulatives Can't Think (But Teachers Can!)

Episode 56 of The Primary Maths Podcast focuses on manipulatives in primary maths and asks a simple but important question: do manipulatives automatically lead to mathematical thinking? Jon and Becky reflect on a recent lesson about commutativity where children were building arrays with cubes but describing the task as “making it with cubes” rather than explaining the structure behind three multiplied by four being equal to four multiplied by three. This opens up a wider discussion about the CPA approach, the difference between doing and thinking, and the importance of questioning to help children notice mathematical structure rather than follow procedures.

The episode includes a listener question from Priya, a maths lead who has invested in new manipulatives but is finding that they are sitting unused or being used without clear purpose. Jon and Becky discuss how CPD can help teachers understand what each manipulative is designed to reveal, including the difference between base ten equipment and Cuisenaire rods, and how to move beyond a tick-box approach to concrete resources.

In Maths of Life, Becky explores the mathematics behind Lego, including the 0.002mm manufacturing tolerance of each brick, the 3,700 different brick shapes, the 915,103,765 possible combinations of six identical 2x4 bricks, and the approximate 1:40 scale of Lego minifigures. The conversation highlights how building blocks can be used to explore arrays, ratios, scale and structure in the classroom.

Jon also shares a research summary on maths anxiety among UK primary teachers, based on a recent cross-national study highlighted by Dr Thomas Hunt. While overall levels of maths anxiety are relatively low, UK generalist primary teachers report higher anxiety about maths and teaching maths than colleagues in some other countries, raising important questions about confidence and professional development.

The episode concludes with a short maths magic segment that demonstrates how algebraic structure sits behind a simple number trick and how manipulatives can be used to make that structure visible.

Jon also references his new Substack article responding to the Education White Paper and its implications for SEND and early numeracy, which you can read here: https://substack.com/@joncripwell.

You can join the ongoing discussion on LinkedIn at https://www.linkedin.com/in/joncripwell/.

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Next week features an interview with Hannah Allison on Storybook Maths, followed by an Aftermaths episode exploring whether teaching structures genuinely support professional judgement or risk becoming scripts.