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.

Happy half term to those who celebrate. In this slightly re-routed Aftermaths episode, Jon and Becky lean into the fact that it is Friday the 13th and explore whether the date really deserves its unlucky reputation.

From Gregorian calendar cycles to cultural superstitions across Europe and Asia, they unpack the mathematics behind how often Friday the 13th actually occurs and what the data really says about risk and coincidence.

There is also a wonderfully elegant maths problem to enjoy. If 128 players enter a knockout tennis tournament, how many matches are played? What begins as a procedural halving exercise turns into a beautiful example of structural thinking and the idea that the best mathematicians often do the simplest maths.

To round things off, Becky brings some Winter Olympics maths of life. From moguls and big air to 360s and 720s, they explore how angles, turns and even scaled scoring systems appear in freestyle snow events and what that might mean for the way we think about comparison and ranking.

There is no interview episode next week due to half term, but Aftermaths will return as usual. If you have a mathematical mystery, historical deep dive or classroom curiosity you would like explored, email primarymathspodcast@twinkl.co.uk or send a message on social media and Jon and Becky will happily fall down the rabbit hole for you.

Like and subscribe so you never miss an episode, and if you enjoyed this one, please do leave a rating or review.

What does it really mean to gamify maths, and when do games genuinely support learning rather than simply make practice feel more entertaining?

In this episode of The Primary Maths Podcast, Jon is joined by Dr Sam Parkes for a thoughtful and practical conversation about games, play and digital learning in primary mathematics. Together, they explore the difference between games that allow pupils to show how strong they already are and games that actually help them get stronger mathematically.

The discussion moves beyond surface level engagement to focus on task design, feedback, time pressure, inclusion and the role of the teacher in making games meaningful. Sam shares insights from research and classroom experience on why some games support reasoning, decision making and resilience, while others risk becoming little more than tests in disguise.

They also examine common misconceptions about play based learning, including the idea that play is only about free choice or early years provision. Instead, Sam reframes play as an attitude towards learning that involves curiosity, exploration, safe experimentation and meaningful choice, all of which have a place across the primary age range.

The conversation tackles difficult but important questions about digital maths games, including the use of speed, competition, rewards and leaderboards. Jon and Sam consider who these features benefit, who they may disadvantage, and how teachers can make more deliberate, informed choices when selecting and using games in time poor classrooms.

There is also a thoughtful discussion about inclusion, SEND and the risks of games being used as a holding activity rather than a scaffold for learning. Throughout the episode, the emphasis remains on professional judgement, clarity of purpose and the idea that games are never a replacement for good teaching, but can be a powerful tool when used well.

If you have ever wondered when maths games can help, when they might hinder, and how to evaluate them through a learning focused lens, this episode will give you plenty to think about.

As always, Jon and Becky will be back on Friday with an Aftermaths episode to reflect on the conversation and draw out key themes for classroom practice.

Dr Sam Parkes has over twenty years’ experience in mathematics education as a teacher, subject leader, school leader, lecturer and school improvement specialist. She holds a Doctorate in Education from the University of Reading and has a strong research interest in mathematics teaching and evaluation, inclusive learning cultures, communities of practice and playful pedagogy. Sam is currently working in EdTech in a Community Engagement role with NumberClub, where she continues her work to support meaningful, accessible and connected maths learning for all children and teachers.

You can find out more about NumberClub at https://numberclub.com

Sam can be contacted by email at sam@numberclub.com

In this week’s Aftermaths episode, Jon and Becky reflect on what can get lost when pace, coverage and efficiency become the main drivers of lesson planning.

The conversation begins with a light hearted look at memorable school trips, from soggy outdoor museums to luxury coaches that were wildly unsuited to Year 6 energy. From there, the discussion turns to something more serious: how tightly prescribed lesson structures and non negotiables can squeeze out curiosity, autonomy and meaningful thinking for both teachers and pupils.

Jon shares reflections on recent classroom visits and raises questions about identikit lessons, box ticking and whether every lesson really needs the same checklist of features. Becky explores how these pressures can limit opportunities to truly know pupils and respond to them as individuals.

Following last week’s episode, Jon also unpacks a lively LinkedIn discussion about engagement. He reflects on comments that challenge engagement as a proxy for learning and introduces a more nuanced view, distinguishing between behavioural, emotional and cognitive engagement. The episode explores what engagement really looks like in maths lessons, from pupils talking, noticing patterns and making connections, to experiencing those moments where ideas suddenly fall into place.

In Maths of Life, Becky explores the relationship between dance, music and number, explaining why dancers often count in eights while musicians tend to work in fours, and what this reveals about memory, chunking and structure.

The episode closes with research in 60 seconds ish, where Jon summarises a newly published meta analysis on gamification in mathematics education. The research suggests that while gamification can boost motivation, it works best when it emphasises cooperation, mastery and feedback rather than competition, points or leaderboards. Engagement, the study suggests, is often poorly defined and difficult to measure.

If you have a memorable school trip story or want to join the conversation about engagement and lesson design, you can get in touch at primarymathspodcast@twinkl.co.uk.

You can read the research discussed in this episode here:

https://link.springer.com/article/10.1007/s10648-025-10108-1

As ever, thank you for listening. If you’re enjoying the podcast, please consider subscribing, leaving a review, or sharing the episode with a colleague.

How do we decide which manipulative to use in a maths lesson, and why does that choice matter so much?

In this episode, I am joined by Jo Austen for a practical conversation about manipulatives, models, and professional judgement. Rather than treating resources as interchangeable or decorative, Jo helps us think carefully about what different manipulatives do mathematically, and what they quietly emphasise or obscure.

We explore how manipulatives fit within the CPA approach, why different models foreground different mathematical structures, and how physical properties such as loose parts, fixed parts, colour, and layout shape what pupils notice. We also discuss when virtual manipulatives can add real value, and where physical resources still play an essential role.

Along the way, Jo makes a compelling case for forward-facing maths: choosing representations not just to get through today’s lesson, but to build understanding that will support pupils later on. This is a conversation about preparation rather than performance, and about making deliberate choices that support thinking rather than replace it.

In this episode, we discuss:

1. Why CPA is not a checklist, and how manipulatives support movement between representations
2. How different manipulatives highlight different mathematical structures
3. Why physical properties such as fixed or loose parts, colour, and layout really matter
4. Common pitfalls, including choice overload and random variation
5. When virtual manipulatives can do things physical resources cannot
6. What it means to choose manipulatives with pupils future learning in mind

If you have ever wondered why a particular resource works, or does not work, in your classroom, this episode will help sharpen your thinking.

In this Aftermaths episode, Jon and Becky reflect on what it really means to do maths rather than watch it.

The conversation begins with Jon sharing an experience from a recent maths education conference, where extended time spent grappling with puzzles led to deep engagement, productive struggle and genuine mathematical thinking. Together, Jon and Becky explore why lessons that look slower on the surface can often be richer, more meaningful and more memorable for learners. They discuss the tension teachers feel between pace, coverage and allowing pupils the time they need to think, fail, notice and try again.

Becky then takes us on a fascinating whistle-stop tour through the history of the calculator. From fingers and pebbles, to abacuses, human computers and early mechanical machines, the discussion highlights how tools for calculation have always existed and how technological change challenges us to think carefully about why we teach maths at all. The conversation reinforces the idea that maths is not just about getting answers, but about developing the skills to reason, problem solve and make sense of unfamiliar situations.

The episode finishes with Jon sharing recent research into maths anxiety, focusing on age, gender and cultural differences. The discussion unpacks how anxiety can limit working memory and performance, why high attainment does not necessarily mean high confidence, and how a simple strategy such as expressive writing before tests could help pupils manage anxiety more effectively.

As always, this episode blends classroom reality, research and reflection, offering plenty of food for thought for teachers, leaders and anyone interested in how pupils experience maths.

If you enjoy the episode, please consider liking, subscribing or leaving a review, as it really helps other listeners find the podcast.