/sci/ - Science & Math

Hello there sci. I am graduate student of pure mathematics with some knowledge in programming languages. I opened this thread for the purpose of disusing best ways of teaching these two subject.

First of all, i have some experience working in both fields as well as teaching high-school students in both of them and would like to share some interesting observation. First of all, as I was teaching programming (mostly easy stuff with C# and some web development with basic javascript and PHP) I figured out I could make a simple algorithm for putting my material in front of the students. I used same examples all the time (with different groups) and students look like they grasped the concept on the same level (of course, those who were actually interested in the subject). This made my job pretty easy ( a bit boring, though) since I could do it with almost no effort.

I noticed, however, that same pattern was not possible in teaching mathematics. It looked like questions could appear from almost any sentence i spoke. At first, I was confused as in "What could possibly be unclear in this statement", so I just repeated it. This was no good, but i needed a fast solution. When I got home, I tried doing the same presentation from different point of view, and on next class I would elaborate the previous one. Soon, I realized I couldn't go like this forever since I don't have that much time. Then I realized that most of my mathematics student weren't generally interested in that field, so I was working with less motivated ones. It was tempting to me to bring down requirements to something less But where was the limit?

It was on one of my geometry classes that I almost snapped when I realized that student didn't quite get the concept of rigor proof (in my country, and I assume in most, the only mathematics field where one does rigorous proofs is in Euclid geometry). The sentenced that student spoke was a typcial "Isn't it obviouse from the picture?".

Im going to be taking a position as a high school math teacher tasked with teaching the AP calculus courses, helping run a math club and helping to set the entire high school math curriculum. Dont know how long Ill be there, I have a masters in math and am hoping to get an industry job soon.

In the meantime, what would you teach in calculus? What would you do in math club and how would you alter the curriculum? Ill be teaching the AP classes so I dont need to keep the material brainlet tier.

I was thinking of introducing either basic proofs and logic OR basic numerical methods in the math club depending on the students interests. Thoughts?