Paul Hazzard is joined by Katrina Bradley, a former music teacher turned numeracy specialist, resource designer and entrepreneur, for a conversation that ranges across curiosity, confidence and what it actually takes to make maths click.

Katrina traces her own path from a music degree and eight years as a peripatetic music teacher to retraining as a primary school teacher, and explains how the skills she used teaching rhythm, notation and metre turned out to be exactly the skills she now uses teaching mathematics. She talks about her love of "puzzle solving" over "problem solving," a deliberate reframing that removes the anxiety many children attach to the word problem before they've even attempted it.

Katrina shares a lovely workshop story about asking primary pupils whether there's maths in the supermarket and watching the thumbs-down paddles slowly turn to thumbs-up once they realise maths is already everywhere in their daily lives, including, inevitably, in their maths homework.

The conversation moves into early years practice, where Katrina describes auditing nursery outdoor spaces to build mathematically rich environments, the kind where children naturally sort, measure and pattern without being taught a formal lesson, and argues that primary schools could learn a great deal from what nurseries already do so well.

Paul and Katrina discuss the deep link between self-belief and mathematical ability, with Paul sharing his own lifelong sense of not being "a maths person" despite a natural knack for estimation, and Katrina makes the case that maths should be broken into smaller components rather than treated as a single subject you're either good or bad at. She talks candidly about how maths can "annihilate confidence" in a way few other subjects do, and why celebrating different routes to the same answer, not just the right answer, matters so much in the classroom.

Conversation moves to mathematical talk and vocabulary, including the striking example of a resource that couldn't be translated into Polish because English has so many different words for multiplication and why children without the language to explain their thinking often stay silent or overuse whatever words they do have. Katrina explains the origins of her business, born out of the pandemic when parents were crying out for the manipulatives and visual resources schools use but families didn't have at home and how that grew into Connectrio and a full suite of tools now used everywhere from nursery classrooms to regional colleges teaching essential skills.

Katrina is refreshingly honest about the tension between being pushed towards "ed tech" framing by investors and staying true to her belief that children need concrete, physical resources rather than more screens.

There's a brilliant moment where Katrina explains how modern times tables teaching uses mathematical reasoning, working from a secure fact like ten sixes to reach a trickier one like nine sixes, and recalls a parent in one of her sessions accusing her of "cheating" for teaching it that way rather than by rote.

Paul and Katrina also get into the pressures of running a business built on a teacher's instincts, from product compliance and manufacturing to social media and the guilt of never quite switching off, and draw some sharp parallels between burnout in teaching and burnout in entrepreneurship.

The episode closes on a genuinely important question for anyone involved in maths education: at what point does teaching to the test start working against a child's ability to use maths for life? Katrina's answer, rooted in years of classroom and boardroom experience, is that children need to understand the why of mathematics, not just the how.

This is an essential conversation for teachers, parents and anyone who has ever doubted their own mathematical ability.

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