Metacognition… thoughts on teaching mathematical problem solving skills

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11 Responses

  1. Kathy says:

    I love your list. I’m going to put it next to my desk for encouragement throughout the year.
    The methods are not new, though. I’ve used books with chapters focusing on one method, such as guess and check. Watching someone use a method isn’t the same as learning it. In the same way, walking through a method isn’t the same as internalizing and understanding the method. I think teachers need to explain the method, like we might explain a joke that someone doesn’t get. Then, I think students need to reflect on the methods they have tried.
    The reflection part is something I’m trying to focus on more this year by using journaling. I usually explain methods, but this to often takes a long time before students are ready to hear and internalize. The test might come before they are ready. I’m hoping journaling speeds up the metacognition.
    Thanks for sharing your journey!

  2. Iris Aliaj says:

    William I really like your idea to explicitly teach problem solving skills in bite size chunks. I also really appreciate the emphasis on meta-cognitive skills and your specific definition of it.
    When I read your list, I thought it would be helpful for me to sit down with problems and practice metacognition myself, noticing what strategies I am using. In this way we can create the catalogue of problems that go with each skill.

    Kathy, I am very interested in your comment of using journalling to facilitate the development of meta-cogntive skills. I used journalling a lot last year for that very same goal and would love to talk with you more about it. I wonder how I can design journalling prompts and activities that thoughtfully and deliberately target certain kinds of thinking. So far for me it has been a lot of intuition work. How have you approached this process?

    • Sakayombo says:

      How do you help students in Secondary School understand the concepts of probability to enable them solve problems associated with probability using metacognitive strategies?

  3. Gil says:

    Very interesting article William. I am putting together a day for year 7 on problem solving strategies. I want it to be inspiring, dynamic and creative. I thought about revolving it around a Murder in the Maths Dept theme. Any bright ideas would be welcomed!

  4. Jim Doherty says:

    I have to assume that you are also familiar with Polya’s approach. I think his is a bit more compact. The idea of transferring these habits to students is SUCH a challenge.

  5. sepideh says:

    Dear William
    Thanks for your helpful notes, I want to know more about your method and results, so can i see your articles or more guide?

  6. Sakayombo says:

    Students in my classes have learning difficulties to understand probability. What mnemonic aids or diagrams can assist them understand the concepts and language of probability? How do I develop and use metacognitive strategies?

  7. oil wins says:

    Thanks for sharing your thoughts about memory function. Regards

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