### Polite Fictions While Teaching

- This morning's classes were unified by the theme of questioning who knows what.
- With my gen-ed class, during most of the semester I can pretend that some students aren't getting it because the material is novel. They've never had to write proofs* before, so maybe they really do think "Because they go on forever" really is a proof of the infinitude of primes. They've never seen the Platonic Solids before, so maybe that's why they struggle to remember the names of the Solids.
- This morning I cheerfully and earnestly explained the following problem:
You invest $100 at 5% interest. How much is in the account after one year?

Some of the class was bored, but there were students who didn't know how to do this. (Probably a set with non-trivial intersection with the set of students who think the lottery is a good deal.) I pretended that my purpose for starting with such a basic problem was to introduce key terms like "principal" and to remind students that we need to convert percents to decimals. But really I know the truth: some of my students can't do this type of problem. - For all the time that my students spend with calculators in K-12, why, why, why can't they enter complicated expressions into their calculators? (On Wednesday we will use the amortization formula.) If these calculators are such a wonderful tool for real world problem-solving where the answers are not integers near zero, then why can't my students use their calculators to solve real-world problems where the answers are not integers near zero?
- This morning I also taught Newton's Method (to the calculus students). I walked them through an example, explained it geometrically, and gave them a few standard problems for practice. After they worked on these independently, we went over them together. I answered questions. I cautioned them about the short-comings of the method. I told them the story of Hubbard's discovery that the method has a sensitive dependency on initial conditions. It was as if I knew what I was talking about.
- The first time in my life that I ever used Newton's Method? That would have been on Saturday.

*The standard of proof in my class is fairly modest -- these are gen-ed freshmen.