What Cognitive Science Tells Us About Learning Times Tables - with Professor Lucy Cragg

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/

About Professor Lucy Cragg

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 Podcast

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.