Did a lot of these things in Physics. I always wondered that if we fundamentally used another way of writing numbers, say in fractions or multiples of Pi (and powers of) or another common and major constant, how our understanding of things would change and that even very young children would understand (not just memorise) some of the things we end up studying in higher education. Some basic equations today might end up looking more complex while others would be cleaned up considerably. Rather than counting using integers in a straight line, we may count differently and peoples basic understanding of certain things may change completely.
I hate the 'Some people just cant do maths attitude' people develop when their motivation to understand is defeated by their willingness to accept that the fault of not understanding is not theirs but just is. I understand some people take to it more naturally but i also understand that is because it is a language based on rules and logic. Some people understand the rules and logic straight away while others just have to memorise it until it clicks.
This 'not everyone can do everything' school attitude has led to a poor standard of education regarding maths up until until college I would say. It seems that standards in most countries are higher at the same age group. Concepts we consider advance like imaginary/complex numbers are in actuality very easy and basic from a skill point of view and we only avoid teaching it at lower levels because understanding what these numbers may represent could be considered not difficult but the sums involved to start learning the concept is not. In some other countries these things are taught at primary school level, so many develop an understanding of complex numbers before the 16 year olds in this country make the decision to take Further Maths A-level (yes it counts as an advanced mathematics a-level module -.-) and get to learn that imaginary numbers even exist.
A student here normally learns integration, differentiation in A-level. Parabolas, complex numbers, matrices too if they take certain modules. It is ridiculous that some of that stuff is taught at primary school or secondary school level in many countries but there is no option to learn it here until you are legally old enough to have a kid.
