3 ms·

UPenn Math Professor: Fractions should be scrapped

3 points by raghus 19y ago

utnick 19y ago
Its hard if not impossible to describe decimals to a new math student without using any fraction terminology. But ya, maybe fraction arithmetic by hand is a little outdated.
bayareaguy 19y ago
If students spend less time on fractions, long division and so on then presumably they will have more time for something else. If I had to offer a suggestion it would be something that still involves fractions in an applied setting, like basic ideas of probability and statistics.
geebee 19y ago
Fractions vs Decimals was a big debate in my 5th grade classroom. The teacher asked us, after showing us each way, which one we preferred. The class was split. At the time, I thought the debate was just about convenience in hand calculations - a mistaken notion that seems to be at the core of the link. I didn't realize how conceptual fractions were until college, though, when I saw a proof in number theory that the square root of two can't be represented as the ratio of two integers. It wasn't until real analysis that I started to understand why "natural" numbers like pi and euler's constant can't be represented through fractions (and why this is what you should expect), why factions can be counted but real numbers can't, and so forth. Personally, I think kids need to learn fractions to get mentally ready for this sort of realization... but maybe that's just because that was my path toward understanding it. On a purely computational level... the symbolic reasoning needed for algebra and calculus (which isn't just math theory, but almost everything mathematical) is probably more related to mentally managing fractions than decimals (the quadratic equation, for example, uses the dividing line. A decimal representation wouldn't be useful here, would it?) All in all, kids probably need to understand that most numbers can only be approximated with fractions and decimals.

3 ms·

UPenn Math Professor: Fractions should be scrapped

3 points by raghus 19y ago

utnick 19y ago
Its hard if not impossible to describe decimals to a new math student without using any fraction terminology. But ya, maybe fraction arithmetic by hand is a little outdated.
bayareaguy 19y ago
If students spend less time on fractions, long division and so on then presumably they will have more time for something else. If I had to offer a suggestion it would be something that still involves fractions in an applied setting, like basic ideas of probability and statistics.
geebee 19y ago
Fractions vs Decimals was a big debate in my 5th grade classroom. The teacher asked us, after showing us each way, which one we preferred. The class was split. At the time, I thought the debate was just about convenience in hand calculations - a mistaken notion that seems to be at the core of the link. I didn't realize how conceptual fractions were until college, though, when I saw a proof in number theory that the square root of two can't be represented as the ratio of two integers. It wasn't until real analysis that I started to understand why "natural" numbers like pi and euler's constant can't be represented through fractions (and why this is what you should expect), why factions can be counted but real numbers can't, and so forth. Personally, I think kids need to learn fractions to get mentally ready for this sort of realization... but maybe that's just because that was my path toward understanding it. On a purely computational level... the symbolic reasoning needed for algebra and calculus (which isn't just math theory, but almost everything mathematical) is probably more related to mentally managing fractions than decimals (the quadratic equation, for example, uses the dividing line. A decimal representation wouldn't be useful here, would it?) All in all, kids probably need to understand that most numbers can only be approximated with fractions and decimals.