[gimagon]

One small change I'd like is to teach a lot of math from a more numerical approach. Learning to approximate sines, cosines, limits, derivatives, and integrals in university made me feel much more confident in my understanding of the concepts. An advantage of this approach is it still gives STEM bound students a good intro to core math, but allows all students to learn a bit of programming. It also teaches how to implement something concrete from an abstract specification. I felt like a lot of high school math was very algorithmic, so why not just teach kids how to implement basic algorithms?

[QuarterReptile]

Are you taking about mental approximation or writing programs for approximation? Or did you switch between the two?

I'll say that knowing mental approximations for sines is a wonderful thing. And, come to think of it, writing something to do the same approximation as the calculator sounds good too. And then analyzing the error introduced by the two methods... So many fun tangents!

[gimagon]

I guess I was trying to advocate for somewhat orthogonal ideas.

On the one hand, learning how to approximate functions with arbitrary precision definitely solidifies an understanding of what those functions are doing.

On the other hand high school math classes are often taught quite algorithmically. Therefore, rather than tests and problem sets, what if the student's chief deliverable was a small python package that performed the algorithms for that lesson? This has a really good advantage of teach basic life skills of turning a specification or intention into a physical product. It also does not significantly impair students that need a strong math background going forward. Finally, makes life a little easier for teachers because some of their grading work could be automated.

Now these two approaches could be applied independently, but I think they would work well together, particularly because the numerical approximation programs generalize a bit better than symbolic ones.