Research School Network: Thinking Mathematically: using the ‘Think Aloud’ and ‘De-brief’ to develop problem-solving An overview of our research project working with 30 schools across the north of England
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Thinking Mathematically: using the ‘Think Aloud’ and ‘De-brief’ to develop problem-solving
An overview of our research project working with 30 schools across the north of England
Mathematics is not just about carrying-out calculations and evaluating equations.
To nurture effective mathematicians, we need to support our pupils in developing their critical thinking, reasoning, and problem-solving skills.
At Blackpool Research School, we have developed the ‘Thinking Mathematically’ pilot project to help our pupils to enhance these skills.
What is ‘Thinking Mathematically’?
‘Thinking Mathematically’ is an evidence-informed initiative designed to improve Year 7 pupils’ mathematical problem-solving. It focuses on equipping teachers with tools to guide pupils through unfamiliar mathematical problems for which they don’t have a ready-made method of solving.
The 20-week programme includes weekly problem-solving sessions, where teachers model their thought processes – the ‘Think Aloud’ – and facilitate reflective ‘de-briefs’. We have been working with 30 schools from across the North of England to put the approach into practice.
The core components of the programme include:
The use of genuine problems which pupils don’t know how to solve
The ‘Think Aloud’: teachers modelling their own thinking to show how they themselves tackle an unfamiliar problem
Collaborative working: pupils discussing and collaborating on problems, discussing strategies and using prompt questions to select appropriate strategies for solving problems
Metacognitive reflection: through activities like the de-brief, pupils are encouraged to reflect on their own approach and evaluate its effectiveness through comparison and discussion
By integrating these elements, Thinking Mathematically seeks to improve not only pupils’ problem-solving skills but also their confidence and resilience when faced with unfamiliar problems.
Feedback from schools involved in the Thinking Mathematically programme
What is the ‘Think Aloud’?
The ‘Think Aloud’ involves teachers modelling their thought processes while solving problems. This helps pupils to understand how experts approach complex tasks, breaking down problem-solving into manageable steps.
By modelling planning, monitoring, and evaluating, teachers scaffold pupils’ independent thinking. Thinking Mathematically support pupils in developing independence in this area through the use of prompt questions which mirror those the teacher used during the ‘think aloud’.
Research supports this approach as a key metacognitive strategy for improving problem-solving skills (Barker, 2024). The EEF’s guidance on improving mathematics also highlights its effectiveness in making abstract reasoning visible to learners.
What is the ‘De-brief’?
The de-brief is an opportunity for structured reflection that follows problem-solving activities. It allows pupils to analyse their approaches, discuss challenges, and refine their strategies for future tasks. This process is essential for consolidating learning and addressing misconceptions.
In Thinking Mathematically, we have identified the following features of effective de-briefs:
Discussions: A successful debrief involves pupils discussing the reasons behind choosing their strategy, and comparing strategies used by other pupils to evaluate which strategy was most useful
Reflection: teachers use targeted questions like “How did you start?” or “What could you do differently next time?” to guide discussions. These prompts encourage pupils to reflect on their methods and explore alternative approaches (EEF blog, 2024)
Addressing misconceptions: de-briefs provide an opportunity to unpick errors in pupils’ work. By discussing why certain approaches didn’t work and how they could be improved, pupils develop a more robust understanding of mathematical principles (EEF blog, 2024)
Different strategies: teachers discuss different problem-solving strategies used by pupils during problem solving sessions, possibly by showing pupils’ work on whiteboards or using visualisers to compare strategies in discussions
De-briefs shift the focus from simply finding the correct answer to understanding how and why solutions work. They foster metacognitive awareness by encouraging pupils to evaluate their thought processes critically. As one teacher noted in an EEF blog: “The answer isn’t the end of learning — it’s the beginning of a rich discussion” (EEF blog, 2024).
The Thinking Mathematically pilot is due to run until April. We look forward to sharing the findings of an independent evaluation of the pilot during next academic year.
References
Barker, E., “Voices from the Classroom: Thinking aloud to support pupils’ mathematical problem solving,” Education Endowment Foundation Blog, 2024.
Education Endowment Foundation blog: “How I use the debrief to support mathematical problem-solving,” 2024.
