In this episode of The Primary Maths Podcast, Jon speaks with Lucy Cragg, Professor of Developmental Psychology at the University of Nottingham, about what cognitive science reveals about how children learn multiplication facts.

Lucy’s research explores executive function skills such as working memory, inhibitory control and cognitive flexibility, and how these shape children’s mathematical learning. The conversation dives into how multiplication facts are stored and retrieved, why certain errors (like 6 × 7 = 42) are so common, and what this tells us about the structure of memory.

Together, Jon and Lucy explore the distinction between fluency and understanding. While more pupils are improving their scores on England’s Multiplication Tables Check, Lucy explains why improved recall does not automatically translate into stronger applied mathematical reasoning. Drawing on findings from the ESRC-funded SUM Project, she discusses how children can improve fact recall without a corresponding gain in multiplicative understanding.

The episode also tackles maths anxiety, the impact of timed practice, and why speed may matter for testing but not necessarily for learning. Lucy shares practical insights for teachers, including the benefits of varied practice, careful use of multiple-choice formats, and ensuring that multiplication facts are connected to meaningful mathematical structures rather than learned in isolation.

This is a thoughtful and research-informed conversation for teachers and leaders who want to understand not just how to help children remember their times tables, but how to help them truly understand multiplication.

SUM Project website:

https://www.sumproject.org.uk/

Further reading and related articles:

Nine-year-olds in England sit a timed multiplication test – but using times tables is about more than quick recall:

https://theconversation.com/nine-year-olds-in-england-sit-timed-multiplication-test-but-using-times-tables-is-about-more-than-quick-recall-258320

Learning, using and applying multiplication facts – insights from research:

https://my.chartered.college/impact_article/learning-using-and-applying-multiplication-facts-insights-from-research/

Connect with Lucy Cragg on LinkedIn:

https://www.linkedin.com/in/lucy-cragg-b22b0a386/

Contact Lucy via email:

lucy.cragg@nottingham.ac.uk

Connect with Jon Cripwell on LinkedIn:

https://www.linkedin.com/in/joncripwell/

Subscribe to Jon’s Substack, The Primary Maths Podcast:

https://theprimarymathspodcast.substack.com/

Professor Lucy Cragg is a developmental psychologist based in the School of Psychology at the University of Nottingham. Her research focuses on the development of executive function skills in children and the role these skills play in learning mathematics.

She led a recent ESRC-funded project investigating the cognitive factors involved in multiplication fact learning, examining both multiplication fact retrieval and its contribution to broader multiplicative understanding. Her work bridges cognitive science and classroom practice, helping educators better understand how memory, attention and inhibition influence mathematical learning.

She is passionate about making research accessible to teachers and welcomes contact from practitioners interested in applying cognitive science insights in the classroom.

The Primary Maths Podcast is for teachers and leaders who believe primary maths can be thoughtful, ambitious and inclusive. Hosted by Jon Cripwell, the show explores lesson design, mathematical habits, maths anxiety, problem solving, curriculum thinking and the research that shapes great teaching.

In this episode of The Primary Maths Podcast, Jon Cripwell speaks with Tom Oakley about one of the most important — and often overlooked — aspects of mathematics education: belonging.

Why do some pupils decide that maths “isn’t for them”? Why do confident learners sometimes disengage from mathematics? And what can teachers do to help every child feel like they belong in the maths classroom?

Tom draws on research around motivation, self-perception and classroom culture to explore how children develop their identity as mathematicians. The conversation looks at how pupils’ beliefs about themselves are shaped over time through small classroom experiences — and how teachers can design lessons that help pupils feel successful, valued and able to contribute.

The discussion also explores the difference between behavioural engagement and cognitive engagement, why success and motivation reinforce each other, and how carefully designed routines and questioning can help pupils build confidence in mathematics.

Along the way, Tom shares practical strategies teachers can use straight away, including partner discussion routines, improving the use of mini whiteboards, and structuring lessons so that pupils experience meaningful success before encountering challenge.

If you want to create maths lessons where every child feels like they matter — and where thinking is valued as much as answers — this episode is packed with ideas you can take straight back to the classroom.

Tom Oakley is a Deputy Headteacher at a primary school in Suffolk, England. Previously, Tom worked as a lead teacher for mathematics in south-west London and later as a Local Authority Maths Adviser in Cambridge for six years. In between those roles, Tom taught at an international school on Koh Samui in Thailand. Since 2010, Tom has supported colleagues’ professional learning in a range of roles and settings. He is an enthusiastic reader of education blogs and an occasional writer, with particular interests in professional development, primary mathematics and curriculum design.

Follow Tom Oakley on LinkedIn

https://www.linkedin.com/in/tom-e-oakley/

Follow Jon Cripwell on LinkedIn

https://www.linkedin.com/in/joncripwell/

Subscribe to The Primary Maths Podcast Substack

https://primarymathspodcast.substack.com/

Contact the podcast

primarymathspodcast@twinkl.co.uk

Explore Twinkl’s maths resources

https://www.twinkl.co.uk/resources/ks2-maths

If you enjoyed this episode, make sure you follow or subscribe to The Primary Maths Podcast so you never miss an interview or Aftermaths episode.

New episodes are released every week, featuring conversations with researchers, teachers and school leaders about what really works in primary mathematics.

Episode 60 of The Primary Maths Podcast is an Aftermaths episode where Jon Cripwell and Becky Brown reflect on mathematical thinking in the classroom, the hidden cost of passive maths, and why pupils’ mathematical identity matters as much as their test scores.

The episode begins with a lighter moment as Jon points out that it is Friday the 13th again, one of three Friday the 13ths in 2026, the maximum possible in a single year. The conversation then moves to this week’s interview episode with secondary maths teacher Will McLoughlin, which explored direct instruction, conceptual understanding and mathematical thinking.

Jon reflects on a moment from a recent school visit where a Year 5 pupil casually said, “I’m not really a maths person.” That comment becomes the starting point for the main discussion: what passive maths can cost learners over time. When pupils spend too much time watching maths rather than doing maths, they may complete work and pass tests, but gradually lose confidence, identity and a sense of belonging in mathematics. The challenge for teachers is that these losses are often invisible in data. Schools can measure answers on a page, but it is much harder to measure what pupils have quietly stopped believing about themselves as mathematicians.

Jon and Becky discuss how lesson design and task choice can make a difference. Starting lessons with accessible entry points, encouraging pupils to explain their thinking, and creating collaborative mathematical environments can all help build confidence and participation. While accountability measures such as the KS2 SATs arithmetic paper or the Year 4 Multiplication Tables Check prioritise speed and procedural accuracy, great maths teaching also develops curiosity, reasoning and identity as a mathematician.

The episode also includes Becky’s History of Maths segment in honour of Pi Day on 14 March. Becky explains the origins of the number π, how ancient Babylonians and Egyptians approximated it thousands of years ago, and how Archimedes later developed more precise methods for calculating it. The Greek letter π was first used to represent the number by Welsh mathematician William Jones in the early eighteenth century. Becky also explores some fun facts about π, including the world record for memorising its digits.

Jon highlights that even though π is not formally taught in the primary curriculum, sharing mathematical curiosities like this can help create a sense of wonder and show pupils that mathematics extends far beyond the classroom.

Towards the end of the episode Jon announces that Twinkl’s PlanIt Maths scheme of work is being completely refreshed, with every lesson rewritten to reflect current research and pedagogy. The new scheme builds problem solving, scaffolding and greater depth thinking throughout lessons rather than adding them as optional extras. A free taster pack is now available for teachers who would like to explore the new materials.

If you enjoy the podcast, remember to subscribe so you never miss an episode. Jon also invites listeners to continue the discussion on LinkedIn and through the podcast Substack.

Listen to the previous interview episode with Will McLoughlin (Episode 59)

https://primarymathspodcast.substack.com/

Download the free PlanIt Maths taster pack

https://www.twinkl.co.uk/resource/free-planit-maths-taster-pack-t-m-1691485779

Follow Jon Cripwell on LinkedIn

https://www.linkedin.com/in/joncripwell

Subscribe to The Primary Maths Podcast Substack

https://primarymathspodcast.substack.com/

Contact the show

primarymathspodcast@twinkl.co.uk