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Knowledge of fractions and long division predicts long-term math success

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Re: Knowledge of fractions and long division predicts long-term math success

#11

Post by shriphani »

raverbashing wrote: post #7

Let me call BS on this one Does anyone remember how to do long division by hand today? I certainly can't But math is much more than your "grocery shopping math" You don't need a calculator for most of math. And I really find it difficult to correlate "how to do long division" in success in areas like statistics, number theory and even calculus, because it's mostly concepts, not "1+1"

I don't see long division as some algorithm to be memorized. It is a fairly simple application of the theorem:

Dividend = Divisor * Quotient + Remainder. and the distributive law.

I was never taught long division as some algorithm to be followed and knowing what it accomplished and how has been enough to perform the operation with ease.

Contrasting that with stuff from later on in my life, I am not so confident with the math I picked up starting high-school. I guess I began following an approach that asked me to commit to memory - focusing on grades as opposed to concrete understanding.

Re: Knowledge of fractions and long division predicts long-term math success

#12

Post by Someone »

I haven't read the paper itself, but that text, to me, does not give a "clear message [...] that we need to improve instruction in long division and fractions".

The text talks about correlation between the two, but does not give any arguments for causation. Judging from the title of the paper ("Early Predictors of High School Mathematics Achievement"), neither does that paper.

Re: Knowledge of fractions and long division predicts long-term math success

#13

Post by yk »

"We need better teaching of fractions" sound like a dangerous cargo-cult solution to the problem of poor understanding of math. If the teaching of fractions would be better, than the understanding of fractions would simply become a worse predictor of long term math success.

The main problem of math teaching is not, that students do not understand fractions (they could easily learn them later), but that they do not understand that math is a (sometimes really helpful) way to think about problems.

Re: Knowledge of fractions and long division predicts long-term math success

#14

Post by thaumasiotes »

tokenadult wrote: post #4

Poor teaching of fraction arithmetic in elementary schools has been a pet issue of mathematics education reformers in the United States for a long time. Professor Hung-hsi Wu of the University of California Berkeley has been writing about this issue for more than a decade. http://math.berkeley.edu/~wu/ In one of Professor Wu's recent lectures, http://math.berkeley.edu/~wu/Lisbon2010_4.pdf he points out a problem of f…

>> An average United States student is at the bottom quartile level for Singapore, or from another point of view, a top quartile student in the United States is only at the level of an average student in Singapore.

http://nces.ed.gov/pubs2009/2009001.pdf

Looking at the US-flattering 4th grade scores, it appears that the Singapore average is 599, whereas the US Asian average is a pitiful 582. 8th grade sees the US suffer: Singapore declines to 593, and US Asians to 549. I don't know how to get a breakdown of US distributional information by race, but your language is, at best, highly misleading. The US 8th grade average all-included is 508, far below Singapore, but I think Singapore (and Taiwan!) are a little closer to 100% Asian.

On the 2009 PISA, US students tended to outscore students of the same race in "native" countries. http://super-economy.blogspot.com/2010/12/amazing-truth-abou... http://www.vdare.com/articles/pisa-scores-show-demography-is...

I've heard nothing but great things about Singapore math, and on a gut level I'm shocked too that US 8th graders were barely able to approximate "almost one plus almost one", but in the big picture it's hard to conclude that our education is failing.

Re: Knowledge of fractions and long division predicts long-term math success

#15

Post by raverbashing »

wcarss wrote: post #10
raverbashing wrote: post #7

Let me call BS on this one Does anyone remember how to do long division by hand today? I certainly can't But math is much more than your "grocery shopping math" You don't need a calculator for most of math. And I really find it difficult to correlate "how to do long division" in success in areas like statistics, number theory and even calculus, because it's mostly concepts, not "1+1"

I am not a mathematician and I do not do long division on any regular basis. I certainly haven't written it out in over a year. But occasionally I have to think about whether a number like 365 is divisible by a number like 7, and I don't have a calculator or computer beside me. I can wait until I'm around electronics, or I can think: "How many times does 7 go into 36? 5 times." "That makes 35, so now, there's 15 left…

I agree, and of course can do this 'approximation' by hand

(even though I may do it backwards sometimes, like, 365/7 ok, 365 looks like 700/2 so that's a start, or 7x5 = 35 so 7x50 = 350 so there goes)

What I meant to say is that math is not only about juggling numbers

Re: Knowledge of fractions and long division predicts long-term math success

#16

Post by Paul_S »

I'm unfair judging this by the press article rather than the study itself but isn't that like saying kids who are smarter do better at math later in life? IQ tests of small kids are wildly inaccurate because of how kids develop at different speeds so how can you control for it?

But whatever argument they need to get to teach better maths to kids I'm all for it.

Re: Knowledge of fractions and long division predicts long-term math success

#17

Post by comicjk »

raverbashing wrote: post #7

Let me call BS on this one Does anyone remember how to do long division by hand today? I certainly can't But math is much more than your "grocery shopping math" You don't need a calculator for most of math. And I really find it difficult to correlate "how to do long division" in success in areas like statistics, number theory and even calculus, because it's mostly concepts, not "1+1"

Agreed. I never learned long division, and now I'm getting a PhD in engineering. Computers are good at arithmetic - let them do it! Teach your kids to code instead.

Re: Knowledge of fractions and long division predicts long-term math success

#18

Post by prophetjohn »

raverbashing wrote: post #7

Let me call BS on this one Does anyone remember how to do long division by hand today? I certainly can't But math is much more than your "grocery shopping math" You don't need a calculator for most of math. And I really find it difficult to correlate "how to do long division" in success in areas like statistics, number theory and even calculus, because it's mostly concepts, not "1+1"

I consider myself pretty decent at math and I would have to look it up if I needed to do long division. It wouldn't take me terribly long to do figure it out, but I don't currently "know" how to do it. Hasn't prevented me from being successful in mid- to upper-level college math yet.

Re: Knowledge of fractions and long division predicts long-term math success

#19

Post by bnegreve »

comicjk wrote: post #17
raverbashing wrote: post #7

Let me call BS on this one Does anyone remember how to do long division by hand today? I certainly can't But math is much more than your "grocery shopping math" You don't need a calculator for most of math. And I really find it difficult to correlate "how to do long division" in success in areas like statistics, number theory and even calculus, because it's mostly concepts, not "1+1"

Agreed. I never learned long division, and now I'm getting a PhD in engineering. Computers are good at arithmetic - let them do it! Teach your kids to code instead.

What are they going start with if they don't even know how to write a division algorithm ? real time 3D engines ?

Re: Knowledge of fractions and long division predicts long-term math success

#20

Post by kjhughes »

Performance on fractions and long division predicts math "success" because those tasks embody math education's emphasis on procedural skills over conceptual understanding.

Tokenadult's comprehensive comment includes the 12/13 + 7/8 gem that sums up the problem. Kids see 12/13 + 7/8 and, if they're "good" at math, start turning the procedural crank they've been taught. (If they're "bad" at math, they freeze with a defeated feeling that there are too many procedural steps to remember.)

Get kids to see 12/13 + 7/8 primarily as "almost one plus almost one" (as thaumasiotes describes), and only secondarily as the beginning of a tedious procedure, to make substantive progress in math education.

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