Master Maths with Metacognition

Metacognition

A metacognitive route to better teaching in mathematics

How can greater levels of thinking and reasoning improve our teaching of mathematics in primary schools?

We are at a point in time when there are new ideas published every day, with claims about ‘best practice’ in the teaching of mathematics. In many ways, this is an amazing place to be and an indication that the profession is taking ownership of its destiny. Social media has made the sharing of ideas so easy and teachers have access to suggestions from around the world.

At the same time as being really exciting, this comes with a possible danger. The raft of ideas that are available and badged as ‘best practice’ are, more often than not, untested in a rigorous or valid way. This means that, at its worse, teachers could be implementing practices that do not actually impact pupils. Worse still, having a negative impact on learning and progress. In essence, we can get hooked by ‘educational fads’ with little or no underlying evidence.

Metacognition is predicated on something slightly different than ‘best practice’. It comes from a place of ‘effective practice’. In other words, practice that makes a difference. Metacognition is not an instantly easy concept to understand, but when understood and actively used, is a hugely powerful vehicle for helping to unlock learning and progress. At its simplest, metacognition is the ability to reflect on and think about your own learning more explicitly.

In essence, metacognition has two key elements:

  • The awareness and recognition of how you are learning and progressing
  • The ability to self-regulate your behaviour as a result of your awareness

The reason for writing is not linked to an ‘educational fad’ but a large and consistent body of research, over time. One of the simplest presentations of this research is from the Education Endowment Foundation, which asserts that when well implemented, metacognitive approaches can have an impact of up to +8 months in terms of progress. On many of the recent global meta-analyses, metacognition is repeatedly in the top few strategies that have the most marked impact on progress. As a result, this ‘evidence’ would suggest it is worthy of active consideration.

In addition, there is a possible broader application of metacognition. We know that academic success alone is not sufficient in terms of making a difference for pupils. Pupils are growing up and going to enter a world of work that is underpinned by ambiguity. They are going to work in jobs that do not exist. They are probably going to have a number of different careers. As a result, students need strong academic outcomes alongside strong character development. Character development is a large and significant area in its own right. Surely, a central aspect of character development is metacognition. If you take a metacognitive approach more broadly than the classroom, it is simply about being able to ‘see oneself from outside’. Being able to understand what has gone on in a situation, understand why you responded the way you did and being able to use that to self-regulate in future situations. At its core, this is an amazing ability to possess in all walks of life and as a leader. A metacognitive approach is what is ultimately required of all colleagues in school. So this proposition of developing a metacognitive school is not confined to the classroom. You may wish to consider what metacognition looks like for adults, what you would see and hear if colleagues are being genuinely and consistently metacognitive? It is in these schools that children will see and hear metacognition in action. They will learn from great role models who will help them to develop their metacognitive ability.

In truth, we never know whether an educational approach will impact. Research aside, there is something inherently common sensible about metacognition. It is hard to comprehend how developing a metacognitive approach could be anything other than healthy for both children and adults – as learners and humans.

 

Mathematics and Metacognition

When applying these principles to the teaching of mathematics we need to ask ourselves some demanding questions. The most important one is: Are your tasks more about making a problem more demanding or are they about making the thinking more demanding? Applying the principles of metacognition in mathematics is not just about creating harder problems, it’s about demanding more thinking.

Metacognition refers to higher order thinking which involves active control over the cognitive processes engaged in learning.

Activities such as ……..:

  • Planning how to approach a given learning task; (before)
  • Monitoring our comprehension of the task, (during) and
  • Evaluating progress toward the completion of a task. (after)

….. are metacognitive in nature.

Therefore, when learners are behaving metacognitively they will be:

  • Drawing on prior learning to plan and prepare
  • Using appropriate experience to monitor their performance
  • Highly involved in self-assessing and peer-assessing
  • Recognising and preparing for what is likely to be hard and challenging
  • Recalling similar challenges and applying successful strategies
  • Identifying new and novel solutions
  • Collaborating and identifying expertise
  • Offering and accepting feedback

The important aspect here is ensure pupils are being encouraged to go through the three phases of planning, monitoring and evaluating. The following table captures some of the main elements involved in these three phases as it relates to the teaching of mathematics.

Consider the following example to help you gain a better understanding as to what this should look like in everyday practice.

Look at the different way a similar lesson is being planned:

Key Stage 2 Example Problem – Maximising opportunities for pupils to learn metacognitively in mathematics…

Continue the conversation on metacognition

To continue the conversation further,  join me on Twitter @CliveDaviesOBE or get in touch with the Focus Education office on 01457 821 818.

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Clive Davies, OBE

Clive is a former headteacher and inspector, having inspected over 200 schools. His school gained a National Curriculum award and was featured in the Times Educational Supplement, one of three schools recognised for their quality practice.
He was awarded an OBE for his services to education in 2007.

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