Research School Network: Transforming Mathematical Thinking Through High-Quality Discussion Why is it that students can often solve a calculation but struggle to explain how they got there?

This was a question that led us to a closer look at how we teach mathematics. We found that while our students were proficient in procedures, they often lacked the language and confidence to articulate their reasoning or identify links between topics. Drawing on evidence from the Education Endowment Foundation (EEF) guidance report, Improving Mathematics in Key Stages 2 and 3, we decided to focus on Strand 3: Teach Strategies for Solving Problems and Strand 5: Develop Pupils’ Independence and Motivation, to bridge the gap. High-quality talk became the cornerstone of our approach, empowering students to articulate, reflect, and build deeper mathematical understanding.

The Power of Talk in Mathematics

The EEF highlights the role of disciplinary oracy — using talk to think, learn, and communicate in ways specific to a subject. In mathematics, this means empowering students to verbalize their thought processes, explain strategies, and connect ideas across topics. It’s not just about solving problems — it’s about thinking, speaking, and reasoning like a mathematician.

Key to this work has been integrating the tiers of vocabulary model:

Tier 1: Everyday words (e.g., ​“happy,” ​“jumping”).

Tier 2: Complex, generic terms (e.g., ​“reasoned,” ​“informed”).

Tier 3: Technical, subject-specific words (e.g., ​“quadrilateral,” ​“median”).

Tier 2​“false friends” — words with different meanings in other subjects, like ​“expression” or ​“product” — highlight why precise, subject-specific vocabulary is crucial. By explicitly teaching these terms, we’ve unlocked a new level of precision in mathematical discussions — and eliminated unnecessary confusion.

Planning for Talk: A Structured Approach

We didn’t just tell students to ​“talk more”; we built a robust framework to guide meaningful conversations and embed high-quality talk:

Select Authentic Questions: We use engaging, context-rich questions tied to the National Curriculum to spark discussion.

Use Deliberate Practice: Teachers prepare and refine resources for structured discussions.

Integrate the Oracy Framework: Sentence stems and prompts guide students in articulating their thoughts clearly.

The result? Dynamic discussions where students dig deeper into concepts, challenge each other’s thinking, and grow more confident in their use of mathematical language.

The Thinking Mathematically Pilot

For Year 7, we’ve integrated the EEF-supported Thinking Mathematically pilot. This 20-week program enhances problem-solving skills and develops their resilience. Every Friday, students tackle a new problem, supported by structured prompts and modelling. The de-brief stage fosters oracy as students explain their solutions, compare methods, and reflect on mistakes — essential steps in developing metacognitive skills. Students have embraced this initiative, dubbing it the ​“Friday Enigma.” The excitement of solving challenging problems together has transformed their approach to mathematics, cultivating a culture where mistakes are valued as learning opportunities. They relish the challenge and grow more confident in articulating their thinking.

High-quality talk is not just an add-on — it is fundamental to improving mathematical understanding. By combining evidence-based strategies from the EEF with deliberate practice and structured support, we are enabling students to think, talk, and connect like true mathematicians. The benefits are clear: engaged, resilient learners ready to tackle complex challenges and a classroom buzzing with rich mathematical conversations.

Written by KM