| > Secondary math education, for me in the UK, didn't deal with anything outside of elementary algebra, Euclidean geometry, some statistics, and relatively simple calculus. I've been a secondary math teacher in the UK and I want to defend this point a little. The job of a secondary math teacher at this level is to teach everyone math, particularly including a majority who don't have a strong interest and won't go on to study more mathematics. You probably underestimate how difficult a job this is. With that in mind, this is already quite a long list of diverse topics. You neglected to mention an introduction to number, up to the real numbers, perhaps because you now think it is obvious. You were taught that. I personally try to teach 'looking forward': explaining how these concepts link towards what direction you might take in the future. However, it's very difficult to cover the whole scope of mathematics and mathematical subjects. For example, I personally knew only a little about what's relevant to EE (although I've learned over time). But, it's not that you could skip anything from the school curriculum anyway - my general advice is that potential EE students need to show interest enough to study independently outside of school. Something like algorithmic complexity, you should be learning from Knuth. Well done for that: there are not many educational experiences better than learning independently from someone who has devoted his life to making his subject accessible. |
It's like teaching science where there's no innate notion of biology, chemistry and physics as three separate disciplines... or teaching history without putting everything in its place on a timeline and your students end up not knowing whether Tudor times ended before or after the Ottoman empire fell.
It's the big picture exposure that I think maths lacks, and I personally never bothered to step back and actually look for that big picture until I was already in my 20s. The way maths is taught makes you feel like it's suddenly going to open up, but all that actually happens is you follow one branch.