Research School Network: Metacognition in the mathematics classroom (Part 2) thinking about our own thinking

Metacognition is not just ​“thinking about our own thinking”, it is much more than that and incorporates a process of planning, monitoring and evaluating our own learning. If we want our students to display metacognitive behaviours, we need to actively support them in the acquisition of such behaviours and processes. Earlier this year, I wrote the first blog on my attempts to incorporate the teaching of metacognitive strategies into my teaching (https://researchschool.org.uk/blackpool/blog/metacognition-in-the-mathematics-classroom-part‑1) – I present here a summary of my learning since then.

The Metacognition and Self-Regulated Learning Guidance Report from EEF has made seven recommendations for encouraging metacognitive behaviour in school-age pupils. As part of the report, some misconceptions with regards to the development of metacognitive skills are highlighted. One of these is that we can develop these skills outside of subject context, leading to improved academic performance across all subjects. However, the evidence suggests that the teaching of metacognitive skills is most effective when it is subject specific. Another misconception claims that metacognitive skills can only be developed in older students. We need to make the conscious effort to teach these skills as early as possible, hence even young children are capable of displaying metacognitive behaviours (Whitebread, D. & Coltman, 2010).

So how does this look in the maths classroom for lower secondary groups?

As stated in the EEF’s Guidance Report, we need to teach pupils how to plan, monitor and evaluate their learning. For this reason, I have produced a diagram, Mathematical Problem-Solving Cycle , earlier this academic year, which worked well for my Year 11s. However, as I carried on with my research on metacognition and re-read the EEF’s guidance, I concluded that I needed to update this to reflect the importance of ​“explicitly teaching pupils metacognitive strategies, including how to plan, monitor and evaluate their learning”. So, here is the updated version.

This is most effective when working on ​‘problem-solving’ questions that have no obvious connection to the topic that is being studied, but can be linked to previous learning.

The second recommendation from the report suggests modelling teachers’ own thinking in order to support pupils development of cognitive and metacognitive abilities. Because of the nature of our subject, we all use worked examples. However, after listening to Craig Barton’s talks and reading his book (Barton, 2018), I started to think about the importance of using carefully selected example-problem pairs to model my thinking, and asking students to reproduce this during ​‘their turn’. Here is an example that I created for my Year 8 class:

On the left hand side, I modelled my thinking on how to approach a question like this, and then I showed how I would solve the question. Students have to copy the worked example and then solve their question independently in silence so that everyone can go through the process without disruption. There is no discussion at this point to avoid early misconceptions. Once students mastered this, I then ask if they could link the question to previous learning and if there is another way of solving this question. Such opportunities for discussing different ways of working out something can promote the development of metacognitive talk in the classroom as suggested by the EEF guidance.

When I first introduced substitution to my Year 7s, I carefully sequenced the worked example pairs to make sure pupils are able to build their own schema and deepen their understanding as we move along.

After the example-problem pairs, pupils worked (again, independently) on minimally different questions which got harder as they progressed. You can create your own sets of questions or use ready-made ones from Craig Barton’s website: www.variationtheory.com.

The aim of this ​‘intelligent practice’ is not just to scaffold students’ learning, but also to help them to become more confident in their ability of solving more challenging looking questions, which in turn will increase their motivation through success. However, we should not forget that being able to solve these questions does not in itself lead to ​‘being metacognitive’.

According to Mayer (1998) ​“an important instructional implication of the focus on metacognition is that problem solving skills should be learned within the context of realistic problem-solving situations. Instead of using drill and practice on component skills in isolation – as suggested by the skill-based approach – a metaskill-based approach suggests modelling of how and when to use strategies in realistic academic tasks”.

So what does this mean in our practice? It means students need to be exposed to problem-solving tasks, which build on prior subject knowledge. We need to select these carefully and model our own thinking, while engaging students in dialogue. However, we need to be careful that we are not just assigning those tasks for the sake of problem-solving.

In my previous blog I promised that I would report back on the results of my attempt to develop metacognitive skills in my Year 11 class. I implemented interleaving practice with the aim of students evaluating their own knowledge and understanding of given topics, students planning when and how they are going to revisit the topic they struggled with, and monitoring their own progress using a target-setting sheet. Students who actively engaged in these metacognitive processes have made excellent progress over the last 3 months, with some of them making 2 GCSE grades of progress which is very encouraging. Unfortunately, not all of the students were as engaged in the target setting process as they lacked motivation. My conclusion here is that we need to nurture motivation from an early age as it is key for successful learning in mathematics and one of the pillars of developing metacognition in the mathematics classroom.

Metacognition and motivation

According to Mayer (1998) motivation is based on interest, self-efficacy, and attributions, which are skills that required for successful problem solving. Extrinsic motivation is driven by external rewards such prises, good grades, and praise. On the other hand, intrinsic motivation, which originates inside of the individual, derives from the feeling of being good at something or having an interest towards it. We can help our students to develop this positive attitude to learning, if we provide challenging tasks, which we scaffold carefully or by simply providing them with the tools for planning, monitoring and evaluating their own learning. 

References


Barton, C. (2018) How I Wish I’d Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes (Woodbridge: John Catt)

EEF (2007) Metacognition and self-regulated learning; https://educationendowmentfoundation.org.uk/tools/guidance-reports/metacognition-and-self-regulated-learning/

Mayer, R. E. (1998): Cognitive, metacognitive, and motivational aspects of problem solving, Instructional Science 26: 49 – 63. https://pdfs.semanticscholar.org/3b78/2d47a31757f2465ab4c3461f955985e4d361.pdf

Whitebread, D. & Coltman, P. ZDM Mathematics Education (2010) 42: 163. https://doi.org/10.1007/s11858-009‑0233‑1