Research School Network: Problem solving is everywhere, 25 – 30% of the time. In this blog Kelly Duke considers the rise of problem solving within maths and how to move forward.

As a classroom practitioner it at first seems counterintuitive to explicitly teach problem solving, after all, surely that is an independent task for students?

However, with 25% of the GCSE foundation paper and 30% of the higher GCSE paper weighted to problem solving (DfE, 2013), it seems necessary more than ever, for teachers to increase focus within this area.

Recognising the importance of problem solving is the first step to improvement.

We may need to ask ourselves some reflective questions;
- Are students completing questions which are 25% problem solving based?
- Are we planning a curriculum at Key Stage 3+ with this weighting in mind?
- Where can we make improvements with an already packed maths curriculum?

Where to start – Evidence based problem solving

The guidance report ​‘Improving Mathematics in Key Stages 2 and 3’ (EEF, update 2022) recommendation 5, states that;

​“while demonstrating the solving of a problem, a teacher could model how to plan, monitor and evaluate their thinking…”

We can use the EEF problem solving checklist (2021) for a maths-specific approach, EEF (2021). This checklist, with example questions, features the three metacognitive areas noted in the guidance report – planning, monitoring and evaluating.

Through the use of self-questioning as seen above, students can work through this metacognitive cycle systematically. It also gives teachers guidance as to how students can navigate through problem solving activities by use of a set of straightforward questions.

The ​‘evaluating success’ on the problem solving checklist, as cited above, must not be overlooked. Without this time and discussion, students may not move their problem-solving skills forward as effectively. It is a key part of the metacognitive cycle, and feeds back into the planning part of the cycle. However, difficulties in finding spare time in the classroom to undertake this are recognised.

Practical approaches

Faded examples are one approach to be considered (EEF FAME Framework). This is where the complete solution is removed in small, backwards steps, to allow students to be scaffolded throughout the problem solving.

​“Research suggests that removing the steps in the solution in reverse order (backwards fading) provides greater support for novice pupils.”

(EEF, Improving Secondary Science Guidance Report Additional Tools, 2018)

Within the classroom I have used these in many ways such as a question completion task as part of the general lesson. I have also found that they work well as a revision aid where there may be a longer process to follow. They provide students at any point with a structured model as an alternative teaching method.

Here is an example of how a faded example is structured;

From my classroom experience, I have found faded examples highly effective despite my initial misgivings about, what felt like, ​‘giving students the answers.’ When students reach the final independent practice, they know they have been successful.


Summary

The collision of metacognitive and maths teaching approaches can potentially strengthen outcomes for students. Particularly those disadvantaged students who, as some evidence suggests, are most likely to gain from metacognitive approaches including explicit teaching. (EEF, 2025)


Further Reading

Voices from the Classroom: Using worked examples to support pupils’ mathematical problem-solving

EEF blog: Working with worked examples – Simple techniques to enhance their effectiveness


References

Department for Education (2013) GCSE mathematics: subject content and assessment objectives. London: Department for Education.

Education Endowment Foundation (2021) INTEGRATING EVIDENCE INTO MATHS TEACHING A checklist for problem solving

Education Endowment Foundation (2018) Improving secondary science: guidance report. London: Education Endowment Foundation.

Education Endowment Foundation (2018) Metacognition and self‑regulated learning: guidance report. London: Education Endowment Foundation.

Education Endowment Foundation (2018) Using worked examples to support high quality teaching: the FAME approach.
London: Education Endowment Foundation.