When I read the NSW mathematics syllabus, it stated that kids at stage 2-3 in middle primary school should start to develop their own methods along with methods taught by teachers. I thought if kids are really like that, they would all become PhDs by the time they reach University. Perhaps that's the ideal world that never exists.
my mum is a primary school teacher and one day saw me doing my maths homework when i was younger, and i was doing it a way she didn't recognise, and she got me to do another problem and watched me do it, and i'd developed my own methods for all different types of questions. so it does happen, but that's only because maths was my best subject. but i'm in year twelve now and there is no chance i'll become a phd in the next year, or four for that matter.
but, with the invert and multiply, i always think of it as a fraction over a fraction, and it makes sense. eg, 2/3 all over 5/3 the denominators cancel out and you're left 2/5, the same result as inverting and multiplying. it makes it easier with a common denominator, so you just multiply both fractions until you have one and it all cancels. makes sense in my mind anyway haha.
and i do agree, not many primary school/year seven or eight students would care about the origins of mathematics, many of them are only there because they have to be, and even those who choose to do 2 unit, or general, in hsc years only do it because they feel obligated to do maths because that's what everyone else does, and it's assumed knowledge in many uni courses.
for me though, maths=happiness, so i'd find all that stuff interesting =]]. i like teachers who make me figure things out for myself though, and i have a teacher who tells us pretty much everything in maths for hsc, so that's disappointing. but hey, here's hoping that it's more interesting in uni =]].
