If we want more pupils to become successful problem solvers, we need to make the thinking behind problem solving explicit. High-quality classroom talk offers one way of doing exactly that, helping pupils articulate ideas, compare strategies and develop the reasoning needed to tackle unfamiliar tasks.
The Education Endowment Foundation (EEF) has consistently highlighted the importance of explicitly teaching problem-solving strategies rather than assuming pupils will acquire them through experience alone (EEF, 2022). Alongside this, the EEF’s TOLD guidance reminds us that high-quality talk is not simply about encouraging pupils to speak more. Instead, it requires carefully planned opportunities for every pupil to participate, make links between ideas and engage in purposeful discussion (EEF, 2022).
EEF’s TOLD resource : four evidence informed principles to promote high quality talk in mathematics (2022)
This matters because successful problem solving is about more than reaching the correct answer. Pupils need to recognise useful strategies, explain their reasoning and know when to apply approaches in unfamiliar situations.
As Colin Foster argues, leaving pupils to discover effective problem-solving strategies independently risks creating a “Matthew Effect”, where pupils who identify productive approaches early continue to accelerate while others struggle to develop the same strategic thinking (Foster, 2023). Explicit teaching helps to level the playing field by making these ways of thinking visible to every learner.
One of the most effective ways to achieve this is through purposeful classroom talk.
The EEF recommends the use of worked examples because they allow pupils to focus on reasoning rather than the mechanics of completing a task (EEF, 2022). Too often, however, worked examples become teacher monologues. We explain the solution, pupils nod and we move on.
Instead, the worked example should be the beginning of the learning.
As Foster (2019) memorably reminds us:
“The lesson begins when the problem is solved.”
A Year 7 example: Algebraic substitution
Imagine a Year 7 lesson introducing algebraic substitution.
Pupils are shown the expression:
When (a = 4), calculate (3a + 5).
Alongside it are two worked examples.
Pupil A
(3 \times 4 + 5 = 12 + 5 = 17)
Pupil B
(3 + 4 + 5 = 12)
Rather than immediately identifying which answer is correct, the teacher deliberately structures the discussion using three questions.
1. What do you notice?
This first question encourages careful observation rather than evaluation.
Pupils might comment:
“One pupil substituted the value before calculating.”
“The other treated the letter as another number to add.”
“Both pupils started differently.“
This stage encourages every pupil to contribute while allowing misconceptions to surface naturally.
2. Why does that work?
The conversation now shifts from describing to reasoning.
The teacher probes thinking with questions such as:
- Why doesn’t (3a) mean (3 + a)? - Why must substitution happen before calculating? - How could you convince someone who disagreed with you?
Rather than simply identifying the correct answer, pupils justify mathematical decisions using precise vocabulary.
3. Where else could we use this?
Finally, pupils are presented with three new expressions:
(5x – 2) (2(y + 6)) (7m – 9)
Before calculating, partners discuss what stays the same.
The focus is no longer the answer itself but the underlying strategy: substitute the value first, then evaluate the expression while respecting the order of operations.
This final conversation is crucial because it encourages pupils to transfer their thinking beyond a single example.
The TOLD guidance summarises productive mathematical talk through four principles: Take Part, Opportunities, Links and Debate (EEF, 2022). This routine deliberately draws on each. Every pupil contributes through structured partner talk. The worked example provides a meaningful opportunity for discussion. The final question encourages pupils to make links between examples, while comparing the two solutions creates authentic mathematical debate rather than simply spotting mistakes.
Importantly, none of this happens by accident.
Teachers orchestrate productive talk through carefully chosen questions, sufficient thinking time and purposeful partner discussion. As highlighted throughout the EEF guidance reports, high-quality talk is something we teach — not something we simply allow to happen.
When pupils explain why a strategy works, compare different approaches and discuss where they might use it next, they begin to develop the strategic knowledge that underpins successful problem solving.
Perhaps, then, the most powerful question in a mathematics lesson is not “What’s the answer?” but “Why did that strategy work — and where else could it help?“
Those conversations matter. They make mathematical thinking visible. They give pupils the language to reason, justify and refine their ideas. Most importantly, they ensure that the strategies expert mathematicians use become accessible to every learner, rather than remaining hidden beneath the surface of successful answers.
References
Education Endowment Foundation. (2022). Improving Mathematics in Key Stages 2 and 3: Guidance Report. London: Education Endowment Foundation.
Foster, C. (2019). The fundamental problem with teaching problem solving. Mathematics Teaching, 265, 8 – 10.
Foster, C. (2023). Problem solving in the mathematics curriculum: From domain-general strategies to domain-specific tactics. The Curriculum Journal, 34(4), 594 – 612.
Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59 – 89.
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