Part 3 - Put your hands together…

So on one hand, we’ve got focused, intentional play and on the other, generative practice - one from seminal theories of child development and learning, and the other from highly credible research in cognitive psychology. Which are you going to choose to help build better mathematicians? And why?

Approaches to mathematics education are never neutral. Teachers’ beliefs about mathematics profoundly shape their teaching and their pupils’ experiences (1). Beliefs matter, and they are personal and subjective. They will have been formed both consciously and sub-consciously since birth; as a child, at home, at school, through different teachers, messages and experiences that all add up to what we each believe mathematics is, and how it is best taught and learned.

This subjectivity is not a flaw, but a reminder: debates about “what works” in maths education must always be framed by what we value. Do we want children to be quick with repeating steps of algorithms, do we want them to see themselves as mathematical citizens capable of reasoning, questioning, and applying ideas across contexts, do we want them to feel safe in and enjoy mathematics…?

So, how do we build better mathematicians? Perhaps the most balanced answer is: through a combination of play, practice, and memory-building, facilitated and led by teachers whose beliefs include a valuing both rigour and flexibility. And cleverly designed games can include all of this.

Play allows mathematics to be experienced as transformative, immersive, and joyful; focussed on important mathematical relationships and connections.

Generative learning strategies deepen understanding and develop flexible thinkers.

Teacher beliefs’ shape the mix, reminding us that teaching is not mechanical but interpretative.

Mathematical fluency, then, is not just about speed or recall. It is about confidence, flexibility, and the ability to apply ideas in new contexts. Children become better mathematicians when they experience mathematics as both serious play and sustained practice – joyful, effortful, and enduring.

(1) Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy: Report of a study carried out for the Teacher Training Agency 1995–96 (Final report). School of Education, King’s College London.