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