Plan ahead for your questions

Posted by Kevin Houston on Mar 21, 2019 in How To Think Like A Mathematician, Mathematical thinking, Mathematics education | 0 comments

Yesterday’s post on asking a question about which method to use is also a failure on my part to prime the students. If I had spent more time stressing which techniques are the important ones, they would probably have known which method I was looking for.

For example, the ratio test is a simple and reliable test that is a good method to try first when testing for convergence of series. I find it useful to repeatedly note when we have used it: “We’ve used the ratio test again. It’s a good one to go for first when testing for convergence.” This primes the students so that they will use it in their own work (perhaps with a bit of prompting).

Another example: To prove convergence of a sequence we show that the sequence is bounded above and increasing. It is well worth drawing attention to the use of this result. Then when faced with students who can’t show convergence ask them which method we used repeatedly.

This does not have be for particular results. It could be an overarching principle. For example, in projective plane geometry using determinants solves many problems. One can prime students by pointing this out. In this case the prime is that “Note how we recast the problem into one involving determinants”.

Thus when planning a lecture course, I ask myself, “Which results should I prime the students to note?”

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