Blog Post #4: Metacognition in Mathematics... using your internal motor to question yourself!

Reflection and metacognition are super important in gaining a deeper understanding of the mathematical processes that you're using when problem-solving. Many students simply solve problems but they may not think about the steps they are taking or the strategies they are using. In the last few weeks we have focused on the internal motor and reflecting on the key ideas and to intensify the critical moments! The use of internal questioning and internal reflection definitely strengthens your understanding and arguments, which consolidates the learning even more!

Some things to think about when you are problem-solving & questions to consider:

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~ Getting Started ~

What is the question as a whole?

What is the question asking me?

How is this question like others that I've enjoyed? How is it different?

~ Getting Involved ~

Which notions can I introduce?

Are there diagrams I can use to help clarify the question?

How can I relate this to my prior knowledge and abilities?

~ Mulling ~

Which questions have I done that may be similar to this one?

How can I specialize or generalize this question?

Can I look at the question in a different way?

Is there a way to re-organize the question in a way that will help me?

~ Keeping Going ~

What is making me stuck?

Why does this problem make me want to keep going?

What is telling me to stop? How can I move past this?

~ Insight ~

When and why did something 'click'? 

What triggered my 'aha' moments?

What helped me get 'unstuck' and how did this help me?

~ Being Sceptical ~

Am I sure that this idea works?

Would this approach still work if this were the case?

Does this answer the question at hand?

~ Contemplating ~

What were the key components in finding this solution?

How does this relate to the broader context?

What have I learned from this problem?

How has this question and solution developed my understanding of certain concepts?

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The internal motor and the internal questioning steps are very important in problem-solving, as asking yourself questions helps you develop metacognitive skills that make you aware of your learning. Reflection in math can help students come to realize that they are using certain strategies, which then they can use again to make future problems easier and more familiar. 

Here is a link to an article that emphasizes the importance of metacognition in mathematics, and different ways to help your students develop these skills!