Research School Network: Metacognition in the mathematics classroom (Part 1)

The Education Endowment Foundation recently published their guidance report looking at Metacognition and Self-Regulated Learning. The full report can be found here: https://educationendowmentfoundation.org.uk/tools/guidance-reports/metacognition-and-self-regulated-learning/

One of the ​‘misconceptions’ highlighted in the report is that metacognitive skills can be taught in standalone ​‘thinking skills’-type lessons and are easily transferable from one subject context to another. The evidence base suggests that this is not the case.

So, what might metacognition look like in the mathematics classroom?

I searched high and low to find evidence on what effective metacognition looks like in the maths classroom and what explicit teaching strategies I should use in order to develop my students’ metacognitive skills. Unfortunately, I couldn’t find many approaches or strategies, but I came across some key ideas that I could adopt and adapt to the needs of my students. Some of these ideas are coming from the Singapore Maths Curriculum Framework, where metacognition is one of the five pillars of successful learning in mathematics.

The Singapore Model Method for Learning Mathematics outlines a set of skills, Heuristics for Problem Solving:

Act it out

Use a diagram or model

Make a systematic list

Look for patterns

Work backwards

Use before/​after concept

Use guess and check

Make suppositions

Restate the problem in another way

Simplify part of the problem

Solve part of the problem

Thinking of a related problem

Use equations

This is all well and good when you have time to teach these skills and practise these with your students, and can be embedded from Year 7 onwards, but I felt that I won’t be able to do so with my Year 11 class which I only started to teach this year. I wanted to find something that would be beneficial in the period before their final exams, which isn’t too far away.

I came across an interesting concept: teach them what metacognition is and how to behave metacognitively.

1. Start by defining the term
2. Ask students to give examples
3. Catch students being metacognitive
4. Encourage discussions and give examples of how metacognition can be applied outside of the classroom
5. Model metacognition on given task so that students can study how to use higher-order thinking strategies

I have created a diagram to aid students in the acquisition of metacognitive thinking, one that is specific to mathematical problem solving.

I asked them to stick it in their book and refer back to it when working on problem-solving tasks, either in form of a past paper question or an SSDD (Same Surface, Different Depth) problem.

I have modelled it how to use the thinking cycle on questions like this one where they had to remember formulas and properties of 2D shapes:

Before the October half-term, I gave some past paper questions to my Year 11s for revision, mostly focusing on angles, proofs and triangles. One of the students said, she doesn’t know where to start. Instead of offering instant help, I suggested she look at the Mathematical Problem-solving Cycle and use it as a checklist. She did think for a while and then said ​“Oh I get it now!” and solved a complicated task without my help.

She already had all the knowledge she needed, just had to retrieve this from her long-term memory and write the relevant ideas down. In this way, she wouldn’t overload her short-term memory and could concentrate on solving the task step-by-step.

I also started utilising the 10 skills check questions from MathsBox not just as a starter but as a mini quiz to see how much they can remember from previous topics and as a form of interleaved practise to recap topics that they haven’t seen for a while. The aim of this activity is:

• to get students to evaluate their knowledge and understanding of given topics using a target setting sheet (which is specific to given quiz),
• to plan when and how they are going to revisit the topic they struggled with (I usually suggest to go back to relevant video clips and quizzes on HegartyMaths or to use their revision guides)
• to monitor their progress (they need to decide if they think they reached their target and write it down when they did).

There are other things that I want to trial with my students, but I want to see first how effectively they can use the thinking cycle and the target setting exercise. Fortunately, I will be able to measure their progress as they are going to sit two sets of Mock Exams, one in November and another one in February. I will then revisit this blog with a follow up to summarise my findings and hopefully with a plan on how to support the development of metacognition in lower year groups in the maths classroom.