# Tag Info

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Back in my student days I found that: Studying my favorite subjects could be done in almost any setting, regardless of distractions. But to study less favorite subjects I had to be a a quiet place with no distractions. This was in the Olden Days when I did not have distractions like an iPhone in my pocket that went with me everywhere. Believe it or not: ...

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First, metacognition may sometimes actively interfere with task performance. Second, the costs of engaging in metacognitive strategies may under certain circumstances outweigh its benefits. Third, metacognitive judgments or feelings involving a negative self-evaluation may detract from psychological well-being.

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In addition to the good answers already given, here are some additional ideas. Joseph's answer predates (or is just at the beginning of?) the official start off the TRIUMPHS project, which has many, many more such mini-projects. They are intended for not history of math classes, but are very useful for those as well. The Chinese linear algebra one is a ...

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Do you think you will enjoy learning calculus on manifolds? I think there is a lot to appreciate there, and it opens the doors to a lot of beautiful mathematics and physics(differential geometry, differential topology, general relativity, de Rham cohomology, Hodge theory, etc). You can mostly get by in calculus on manifolds with just Riemannian integration. ...

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Then, what is it that I can add in a class? That is what confuses me. That is the exciting part about teaching mathematics. No matter how clear the slides (or book or ...) and no matter how complete the proofs, there is a big role for helping students understand. I'll answer your comment rather than the question, as it seems that you would really like to ...

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Lay is the textbook I use. (And I love it.) I wonder if you'd find the true-false questions valuable. There are usually 8 of them (2 problems near #23 and 24, usually with 4 parts each). Those seem like questions you could ask after the reading but before lecturing. [I don't do what you're doing. I do have them take notes on each section, but they turn those ...

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The following is not a foolproof solution, but one thing I've done for remote exams is have questions where you have students make up their own numbers, you can add some restrictions to make sure they don't make a problem too easy or find a problem done in the textbook. For example, I've asked things like here is $3 \times 3$ matrix with two or three ...

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Many studies about active learning are summarized and linked to at this link. I do agree with the commenters Dirk and David, who mention that there are pros and cons to any teaching method, and that studies are usually based around averages, so they might not be applicable to every situation.

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Have them use an abacus. (I prefer to teach using a Chinese abacus, which has 2+5 beads per column, and not using a Japanese abacus, which has 1+4 beads per column.) I propose the following activity. (I've only done this in undergraduate classes a handful of times, but the students seemed to enjoy it.) Teach them how to use the abacus to add numbers. Do ...

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When doing a proof by contradiction of "if A then B", you get to assume A and you also get to assume NOT B. Proving it directly, you only get to assume A. So proof by contradiction gives you more to work with from the start. I think that's why students like it.

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