: Using Metacognition to Improve Mathematics Learning in Secondary Schools The 7‑step metacognition model working towards self-regulated learning
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Using Metacognition to Improve Mathematics Learning in Secondary Schools
The 7‑step metacognition model working towards self-regulated learning
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by Cornwall Research School
on the
John Rodgers
Director of Cornwall Research School
John Rodgers has been a teacher for 24 years, the last 19 in Cornwall. He currently works as the Director of Cornwall Research School and Assistant Principal at Mounts Bay Academy, Penzance.
Mathematics is a subject that demands not only knowledge of numbers and formulas but also a deep understanding of problem-solving strategies. One of the most effective ways to help students become independent learners in mathematics is through metacognition — the ability to plan, monitor, and evaluate one’s own thinking and learning. The Education Endowment Foundation’s Metacognition and Self-regulated Learning Guidance Report suggests that explicitly teaching metacognitive strategies can significantly enhance students’ ability to tackle mathematical problems independently.
This blog explores how secondary school teachers can embed metacognition in their mathematics lessons, using the 7‑step metacognition model to support students in solving a common mathematical challenge: algebraic problem-solving.
The 7‑step metacognition model provides a structured approach to teaching students how to engage in self-regulated learning. Here is an example of how one could apply it to solving an algebraic equation, such as:
Solve for x: 3(x – 2) = 12
1. Activating Prior Knowledge
Before introducing a new problem, the teacher helps students recall what they already know about solving equations. This might involve asking:
What does it mean to “solve for x”?
Have you encountered equations like this before?
What steps did you take to solve them?
This activation phase ensures students connect new problems with prior knowledge, making learning more meaningful. It also elicits knowledge of self and knowledge of task.
2. Explicit Strategy Instruction
The teacher explains the key steps to solving equations explicitly, such as:
Using the distributive property to expand brackets.
Isolating the variable by performing inverse operations.
For example, they might say:
“To remove the brackets, we multiply 3 by both terms inside. Then, we work to get x alone on one side.”
While demonstrating, the teacher verbalises their thinking:
“I need to remove the brackets first. Now, I see that subtracting 6 is the next step. Finally, I divide to find x.”
This step helps students understand how expert learners approach problems. It increases knowledge of strategy (see image below).
4. Memorisation of the Strategy
Students summarise the steps in their own words, reinforcing understanding. A teacher might ask:
“Can someone explain the process in their own words?”
How do we remove the brackets?
“Why did we divide by 3 at the end?”
5. Guided Practice
Students solve a similar equation in pairs while the teacher provides scaffolding:
Solve: 2(x + 4) = 16
They are encouraged to discuss their strategies and check each step. The teacher circulates, guiding students with targeted questions like:
“What’s the first step?”
“What operation will you use next?”
“Does your answer make sense?”
6. Independent Practice
Students attempt more problems independently. The teacher encourages self-explanation:
“Before moving to the next step, ask yourself: Does this make sense?”
“Check your answer by substituting x back into the equation.”
Students will need to plan, monitor, and evaluate their learning and progress as they gain greater independence. These are aspects of metacognitive regulation (see image below).
7. Structured Reflection
Finally, students reflect on their problem-solving process:
What strategies worked well?
What challenges did I face?
How could I improve next time?
They might write a brief reflection or discuss in small groups. This step strengthens their ability to self-regulate their learning in future tasks.
Embedding metacognition in mathematics lessons can held support independent problem-solving skills, confidence, and deep learning. Research shows that metacognitive strategies improve mathematical reasoning and achievement, particularly when students have ample time to practice and internalise these approaches.
By using the 7‑step model, teachers can help students become more reflective and strategic in their mathematical thinking, ultimately enhancing their problem-solving abilities and long-term success.
