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.

In this episode of The Primary Maths Podcast, Jon Cripwell is joined by Dr Kate Quade for a thoughtful conversation about language, learning and mathematical thinking.

Language sits at the heart of mathematics, but the way pupils talk about maths often remains unnoticed or is tidied up too quickly. Together, Jon and Kate explore why mathematical thinking so often stays invisible, and how children communicate their ideas in many ways beyond written answers.

A central focus of the episode is the idea of “porridge words”. These are the imprecise, catch all or emerging terms children use when they are still forming their understanding. Kate explains where the concept comes from, how it connects to Edward de Bono’s work on thinking, and why these words are not a problem to fix but evidence of thinking in motion.

The conversation explores how pupils use language, gesture, drawings, manipulatives and symbols to express mathematical ideas, and why privileging only written or verbal explanations can limit what teachers notice. Kate shares insights from her research and teaching experience, including why rushing to correct vocabulary can shut down thinking, and how deeply listening to pupils helps teachers make better formative assessment decisions.

Jon and Kate also discuss the balance between valuing emerging language and moving pupils towards accurate mathematical terminology. They consider the importance of consistency, the risks of children disengaging when language is unclear, and how teachers can introduce precise vocabulary without undermining confidence or curiosity.

This episode is a reminder that mathematical thinking often sounds messy before it becomes precise, and that noticing how children talk about maths can tell us far more than whether an answer is right or wrong.

If you enjoyed this conversation, join Jon and Becky for the Aftermaths episode, where they reflect on the key ideas and classroom implications. You can also get in touch with the show at primarymathspodcast@twinkl.co.uk

Dr Kate Quade is a Senior Lecturer in Mathematics Education and Program Director for the Master of Teaching (Primary) at the University of Adelaide. She is a former primary teacher and maths leader, with experience as a curriculum advisor, textbook contributor and coordinator of the Questacon Maths Centre. Kate’s research focuses on mathematical thinking, language and inclusion, particularly how children make their thinking visible through talk, drawing, gesture and other multimodal forms. Her recent work on porridge words explores how imprecise or everyday language can act as a cognitive tool that supports reasoning and sense making in primary maths classrooms.

You can connect with Kate on LinkedIn at https://www.linkedin.com/in/kate-quane-7084b797/, on Bluesky at @kateqmaths.bsky.social, or by email at kate.quane@adelaide.edu.au

In this half-term Aftermaths episode, Jon and Becky take a deep dive into prime numbers and discover that they are far more than a Year 5 objective about “numbers with exactly two factors”.

The conversation begins in the classroom, exploring how we define prime numbers and why 1 and 2 are both special cases. They reflect on how primes frustrate our desire for neat patterns, how children often assume odd numbers are prime, and how the Sieve of Eratosthenes gives us a beautifully systematic way of uncovering them.

From there, the episode takes a historical journey. Jon revisits the work of Euclid, who proved over 2,000 years ago that there are infinitely many prime numbers. The discussion touches on the mind-bending nature of infinity and how powerful it is to share with pupils that maths is still unfinished.

They then explore the work of Eratosthenes, whose famous sieve remains one of the most elegant algorithms for identifying primes. Along the way, Becky shares her fondness for teaching prime factorisation and even introduces her favourite palindromic prime.

The episode moves into the 19th century and the still-unsolved Bernhard Riemann hypothesis about the distribution of primes, one of the great Millennium Prize Problems. Yes, there really is a million dollars waiting for someone who can crack it.

Finally, the discussion lands firmly in the modern world. Prime numbers underpin the encryption systems that keep online banking, shopping and government communication secure. The episode introduces RSA encryption, developed by Ron Rivest, Adi Shamir and Leonard Adleman, and explains why multiplying large primes is easy but reversing the process is extraordinarily difficult.

Key themes in this episode include:

• Why prime numbers are the “atoms” of arithmetic

• The Fundamental Theorem of Arithmetic and prime factorisation

• Infinity as a classroom conversation starter

• The beauty and mystery of unsolved problems

• How prime numbers quietly protect our digital lives

This episode is a reminder that even the most familiar Key Stage 2 content can open doors to big ideas, rich history and genuine mathematical mystery.

If you enjoyed this deep dive, leave a rating or review and let us know what topic you would like explored in a future Aftermaths episode. There are still plenty of mathematical rabbit holes to fall down.

And if you’re listening over half term, we hope you’ve had at least a little rest.