A question for y’all:
Elementary mathematics (say, anything below calc) is a hard subject to teach because there are very few applications. It’s like several years of grammar without reading a single good book. I’m trying to find some good topics that can get a student interested in the subject, without requiring extensive background knowledge. So far, I’ve thought of:
- Classifying strangely shaped polyhedra, and thence into problems in geometry,
- Computability theory – recursion, Godel’s theorems, and so on, maybe using Godel, Escher Bach as a text
- Something involving fractals – but what?
- Probability, and teaching them why not to draw to an inside straight.
Each of these seems like they would only work for a fraction of students, and all seem a bit half-baked. Those of you with math backgrounds, or those of you who have recently been taking classes at this level, or for that matter everyone: What are the topics in math that interested you the most that don’t require full command of differential equations?