This week, Jon and Becky are back for a half-term special that explores the foundations of mathematical understanding — and the curious maths behind our PIN codes.

Jon unpacks what number sense really means, why it underpins everything else in maths, and how fragile number sense can often go unnoticed until it becomes a barrier to progress. They discuss what teachers can look out for, from over-counting and weak part-whole relationships to over-reliance on formal methods, and share practical classroom routines to help strengthen number sense — including number talks, subitising games, estimating, and developing mathematical vocabulary.

Becky’s Maths of Life segment takes an unexpected turn, starting with the Battle of Hastings and ending with data on the world’s most common PIN numbers. Along the way, she reveals what our number choices say about us and why probability makes the world more surprising than we think.

Jon then wraps up with a Research in 60 Seconds(ish) segment, sharing a new study from the British Educational Research Journal on how peer and self-assessment shape motivation, metacognition, and resilience. The findings suggest that peer assessment, in particular, helps pupils clarify their own thinking — and why talk and reflection are central to real learning.

Next week, Jon is joined by early years specialist Michelle Windridge to discuss what effective early maths looks like in practice and why every phase can learn something from EYFS.