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The problem with maths education is that it's often distant and unintuitive; there doesn't seem to be any connection between the manipulations and anything 'rea
by jacknews 3y ago
The problem with maths education is that it's often distant and unintuitive; there doesn't seem to be any connection between the manipulations and anything 'real' or 'visualizable'.
I don't know why we don't introduce elementary group theory at an earlier age. This is something quite intuitive; a bunch of things, and operations that convert between them, and gives a solid feeling for what the game is.
And although 'place numbers' are taught early, later we learn about 'bases' in a kind of fragmented way, whereas this is probably the time to introduce the whole elegant place-number system, showing places as exponents (including fractional exponents - ie 2^1/2 + 2^1/2 = 2^1 => x^1/2 is clearly the square root) in a coherent way, and toying with negative bases, base phi, ternary, etc.
'shut up and calculate' might work in some contexts, but it's not a good way to build understanding and intuition.
- _dain_ 3y ago>I don't know why we don't introduce elementary group theory at an earlier age. Whenever someone says "we should teach X earlier", that necessarily means we have to teach some Y later, unless you want to add more hours to the schoolday. What would you evict from the curriculum, to make room for it?
- 2snakes 3y agoSee iconicmath.com for one perspective on this using iconic visual math, math that looks like what it means. Symbol processing aka calculation is better suited to computer science than the distinction/difference and indication of maths.
- jacknews 3y agoNot necessarily; teaching some things earlier could make other things easier to understand. But to answer directly, I don't see a particular need to teach long division/multiplication - they are just algorithms, and as long as the place-number system is understood thoroughly, there's really little use for them.
- deleted 3y ago[deleted]