# Tag: metacognition

Your assignment for the next week is toÂ try to prove the conjecture that your group created in class on Tuesday, 10/14/15. Â You must spend at least 90 minutesÂ working on this. Â Trying to prove somethingÂ can consist of many different activities,Â such as the following (you do NOT have to do all of these things – you can choose how to spend your time – they are provided for inspiration only).

• coming up with ideas, and testing them out (for example, by creating puzzles and trying to solve them)
• trying to understand what the conjecture says
• trying to solve puzzles that other people created
• trying to create puzzles (and solve them yourself)
• communicatingÂ with other members of your group (talking, emailing, etc.)
• trying to write down a proof
• other stuff…

As you work, keep track of what you are doing, thinking, and feeling (this is metacognition – an idea that discussed way back in OpenLab #2). Â What did you do during the time you spent? Â Did you create any puzzles? Â Did you solve puzzles? Â Did you change your mind about whether the conjecture is true or false? Â  Did you have any new ideas about how to prove the conjecture? Â Did you have any ideas that you gave up on? Â How did you feel as you worked – were you frustrated/confused/happy/depressed? Why? Did your mood change along the way?

Assignment (Due Thursday, 11/3/15): Â Submit a journal of your efforts in the comments below. Â Your response should be at least 300 words. Â DescribeÂ what you did during the 90 minutesÂ you worked, andÂ express in some way what you were thinking and feeling during the process. Â Your response can include puzzles (use sketchtoy.com) or other work you did along the way.

Extra Credit. Â Respond to a fellow student’s comment. Â Did you do similar things? Different things? Do you have any suggestions for them? Be kind.

GROUP CONJECTURES:

This assignment is due Thursday, September 8, at the start of class.

Assignment. Â Choose ONE of the following two topics. Â Write a reply to this post, responding to the topic. Â Begin by telling us which topic you chose. (1-2 paragraphs).

Topics.

1. Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened toÂ you, tell us about it.
2. Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college). Â Describe what happened. Â Do you think you could explain it to others in a way that they could have the same flash of understanding?

Extra Credit. Â For extra credit, write a response to one of your classmates’ comments. Â Do you feel the same, or different? Â Did you learn anything? Â Did you get any ideas about teaching, or about learning?

Why are we doing this, anyway?Â  We are following two ideas that have come up already in class — things that mayÂ notÂ seem related to learning math, but research shows that engaging in these activities canÂ dramaticallyÂ increase the amount that you learn, and change the way you learn it. Â The first isÂ writingÂ â€“ something not typically associated with mathematics. Â When you express your ideas in words, it forces you to think them through very carefully, detail by detail. Â A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing. Â Example: if you know how to add fractions, try teaching it someone who doesnâ€™t know how. Â The second is calledÂ metacognition, or â€śthinking about thinking.â€ť Â This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. Â What train of thought did you follow? Â Where did you get stuck, and what did you do next? Â What were you feeling at the time? and so on. Â Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. Â However, like any skill, it takes practice. Â Thatâ€™s why weâ€™re getting started by writing a little about our past experiences with mathematics.

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