Exploration Before Explanation: How exploring first empowers pupils to think mathematically

When pupils grapple with ideas first, the teacher’s explanation has somewhere to land. It makes sense. It sticks.

Every teacher knows the moment: you’ve modelled a method clearly, the class has practised it with you, and then — when it comes to working independently — half the pupils suddenly look lost.

This pattern can be seen in many classrooms across the UK. The structure feels sound, the routine reassuring, yet the depth of learning just isn’t there. In many cases, pupils have been shown how to do the maths, but not always given the same chance to think mathematically.

What’s striking is that when lessons shift to exploration before explanation, not only does pupil understanding grow stronger — teacher confidence does too. Instead of relying on a script, teachers see first-hand how pupils reason, spot misconceptions in the moment and feel empowered to guide learning rather than simply demonstrate it.

Over the last decade of working with schools, I’ve found that this change makes lessons both more effective and more enjoyable to teach. Pupils wrestle, discuss, test ideas and, by the time the efficient method is introduced, it sticks.

At the heart of Maths — No Problem! is this surprisingly simple principle: pupils explore before the teacher explains.

• Explore: Pupils are presented with a carefully chosen problem to attempt, often with a partner or in small groups.
• Discuss: The teacher draws out and connects different strategies, including common misconceptions.
• Explain: Only then does the teacher model the most efficient or generalisable method.
• Refine and Practise: Pupils consolidate through guided and independent practice.

It’s the same ingredients as “I do, we do, you do” — modelling, shared practice, independence — but in a different order with exploration at its heart.

In the rest of this blog, I’ll share six reasons why exploration-first teaching achieves the best student outcomes, drawing on research, theory and classroom experience.

Why sequence matters

Cognitive science shows that learning is deeper when pupils encounter productive struggle before being told the answer.

• Manu Kapur’s research on Productive Failure shows that pupils who attempt problems first (even if they get stuck) develop stronger conceptual understanding and can apply their knowledge more flexibly.
• Schwartz & Martin’s invention activities demonstrate that trying to devise a method primes learners to notice key features when the teacher explains them.
• Hattie’s research shows that problem-solving and Piagetian approaches have some of the strongest impacts on learning — both built on exploration before explanation.

In short, when pupils grapple with ideas first, the teacher’s explanation has somewhere to land. It makes sense. It sticks.

Backed by the great theorists

This approach isn’t new. It sits firmly on the shoulders of the great educational thinkers:

• Zoltán Dienes cautioned against premature abstraction: don’t generalise too soon — give pupils concrete experiences before moving to symbols.
• Lev Vygotsky reminded us that learning is social: “What children can do with the assistance of others might be more indicative of development than what they can do alone.”
• Jean Piaget stressed the importance of time: children need space to process, test and accommodate new ideas before moving on.
• Jerome Bruner told us we are storytelling creatures: learning is best presented through narrative and scaffolded carefully.

Each of these insights is visible in Maths — No Problem!’s design — exploration, discussion, time for processing, careful modelling and story-like lesson journeys.

Teach less, learn more

Singapore, whose maths mastery curriculum inspired Maths — No Problem! carries a national mantra: “Teach less, learn more.” It’s a reminder that the goal isn’t to cover content at speed, but to design learning so that pupils do the thinking.

One challenge in many other approaches is that they can sometimes prioritise speed over depth. In practice, ‘I do, we do, you do’ often leans towards pace, while Maths — No Problem! places greater emphasis on depth — fewer concepts at a time, explored more richly, leading to genuine understanding and long-term retention.

More than a lesson routine

‘I do, we do, you do’ is a helpful structure for shaping individual lessons, but to deliver a full curriculum, you need to put all the jigsaw pieces together: strategy, sequencing, lesson design and assessment opportunities. Maths — No Problem! successfully combines all these things, helping to secure progress year on year.

Maths — No Problem! is different. It is fully aligned with the National Curriculum for Mathematics and underpinned by teaching for maths mastery principles. Lessons are sequenced using variation theory so that each small step builds carefully on the last. This is why it has had impact not only in Singapore, where it underpins world-leading outcomes, but also in schools across the UK that have committed to the approach.

Bringing it back to pupils

Ultimately, this isn’t about teaching fashions. It’s about what helps children become confident, flexible mathematicians.

• ‘I do, we do, you do’ can help pupils produce correct answers in the short term. Maths — No Problem! focuses on developing deeper thinkers — children who understand why methods work, can compare strategies and apply knowledge flexibly.
• Maths — No Problem! mastery approach builds deeper thinkers — children who understand why methods work, can compare strategies and can apply their knowledge in new contexts. It gets children to think mathematically.

That’s the difference.

A call to confidence

It’s understandable that schools might drift back to what feels familiar. But as a profession we have to ask: do we want the safest option, or the most effective one?

Maths — No Problem! is grounded in research, international success and the wisdom of educational theory. By leading with exploration and then layering in explanation, it transforms a lesson routine into a mastery system — one that has already demonstrated impact internationally and here in the UK.

So the next time you hear ‘I do, we do, you do’, remember there are other ways to begin. With exploration before explanation, you can help children move beyond simply doing maths to truly thinking mathematically.

Why “exploration before explanation” is more than a slogan:

Kapur – Productive Failure

• Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424.
• Kapur, M. (2014). Productive failure in learning math. Cognitive Science, 38(5), 1008–1022.
• Kapur, M. (2016). Examining productive failure, productive success, unproductive failure, and unproductive success in learning. Educational Psychologist, 51(2), 289–299.

Schwartz & Martin – Invention Activities

• Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129–184.

Rittle-Johnson & Koedinger – Exploration before worked examples

• Rittle-Johnson, B., & Koedinger, K. R. (2009). Iterating between lessons on concepts and procedures can improve mathematics knowledge. British Journal of Educational Psychology, 79(3), 483–500.

Hattie – Visible Learning

• Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.