Subtracting fractions from the curriculum

College Dean Dennis DeTurck often challenges math department colleagues to tell him when exactly he would need to know that 5/7 plus 3/5 equals 46/35.

"The answer is never, except in a specifically mathematical context," DeTurck said.

That's why he wants Americans to rethink how and when they teach fractions.

Though fractions play an important role in math, he said it may make sense to teach them at higher levels - when students can better grasp their meaning and value.

Most studies show students lose touch with math between fourth and eighth grade.

"There's a divergence between math in the world, which is important and makes sense, and math in school, which . has to be memorized and spit back at the teacher," DeTurck said.

Students are willing to struggle with concepts like multiplication because they grasp their usefulness in the real world, he added.

But fractions confront them with numerators, mixed numbers and equivalents - jargon that seems arcane and impractical. Decimals may be a better answer, he said.

"We don't live in a world anymore where people are required to do complicated calculations by hand," he added.

And as technology evolves, so should teaching.

Educators should determine what the process of learning fractions helped students understand about other aspects of math and convey it in other ways, he said.

But not everyone's a fan of his proposal.

Harvard University Mathematics professor Wilfried Schmid called the proposal "misguided" and questioned how to teach the meaning of decimals without fractions.

"What is the significance of 1.1? It's one plus one-tenth," he said. "Fractions are more basic in development of understanding of numbers than decimals."

Schmid added that the sequential nature of mathematics makes fractions a "natural stepping stone" to algebra and advanced concepts.

"You have to ask if the best way to deal with problems in math education is just not teaching what is somewhat difficult," he said.

Mathematics graduate student Asher Auel voiced a similar sentiment, saying fractions are vital to understanding ratios and relative sizes.

"The only thing decimals are good for is plugging into a calculator or computer program," Auel said. "Nobody thinks in terms of decimals."

In recent weeks, DeTurck's ideas have been picked up by a number of media outlets, including USA Today.

DeTurck said he plans to release a book later this year that addresses the fraction debate and other questions about teaching in a technological climate.

Mathematics graduate student Paul Rowe said the U.S.'s lagging math performance makes education reform an important discussion to have.

"Whether or not you agree with the exact proposals [DeTurck] is making, it's good that he's getting people to talk about it," he said.

Comments (3)

So the "Dumbing Down of America" continues. A good title for that book? American IQ levels continue to decline. (a google search of "dumbing down of america" returns some interesting reading. and search amazon.com for relevant books). College curricula today sounds like what high schools did twenty years ago. I suppose college now has a graduate level full semester course where you learn phrases like: "do you want fries with that?" "welcome to WalMart". It sounds like Harvard still appreciates intellectual learning and the need for an ability to master concepts that you may not have great need for, and measuring that ability. Let's see, if a college graduate serves 2/3's of a two year sentence, and 3/4 of a ten year sentence, how many months will he spend incarcerated? No calculator allowed, and show your work. a) 53/6 b) 9 c) 106 d) 54 e) hey, I'm only a college senior we haven't had fractions yet! So how isn't this relevant to today's students? It would be instructive for the DP to find how many Penn College graduates (vs. Harvard, Cal Tech, MIT, etc.) get jobs at Google, Microsoft, etc., or end up driving cabs and flipping burgers. Cause and effect. I guess that is a Ph.D. course now. Answer: c). Unless my IQ has dropped too. A finite possibility. "finite": that's a post doctoral term now.

Today I was working on a project that needed two 3/16" x 1-1/4" machine bolts. (0.1875" x 1.25" until you learn fractions. The hardware store owner wasn't amused when I refused to say 3/16"). Then I had to cut the lumber to 6 1/8" (6.125"). The architect's drawings used these strange measurements that used lots of "/"'s as well. My automobile gas tank was getting less than 1/4 full (0.25 full) so I bought 10 gallons of gasoline for 2.95 and 9/10 (0.9) per gallon or 2.959/gallon. Let's see, the residual gasoline, plus 10 gallons in a 13.2 gallon tank is what fraction (higher or lower than 3/4 of a tank)... oops. Never mind! We haven't had fractions yet. An outboard motor gasoline tank needs 5 imperial gallons of gasoline, and being a two cycle engine, oil needs to be mixed in at 1/50 oil to gas (0.02). [And a certain weed eater uses a 1/32 oil to gas mix (0.03125)]. Good luck with doing this with decimals. (and which is larger, an imperial gallon or a US gallon?). Back to the outboard motor. Oil comes in pints or quarts. Let's see, a pint is 1/8 of a gallon... oh sorry, 0.125 of a gallon. But the fuel tank gauge says it is 1/4 full (0.25 full) so how much oil do I need to mix with the gas to fill the tank? You can do it in your head with fractions and a little practice, but probably need a calculator if you use decimals. Then I went to the liquor store and bought 1/5 of scotch (that's 1/5 of a gallon, well, now 3/4 of a liter). Can you figure out who lost when bottles went from 1/5 of a gallon to 3/4 of a liter and the price remained the same? I guess that's a graduate level calculation now? Thank goodness the stock market got dumbed down from 1/4, 1/8, 1/16 points. It is now 1/100 of a point. (damn! still a fraction! 0.01 to the fractionally impaired). Quick, which is larger, 1/16 or 0.01? And for extra credit why were stock brokers against the move to 0.01? (hint: it has to do with the question immediately preceding this one). And any preschool kid knows when they are "three and a half". And the "half" is very important. You can tell by the way they say it. Too bad they have no idea what it means. So, I guess knowing fractions isn't necessary. No one should have to learn them. Unless you want to build something, design something, own a car, a boat, a weed eater, a lawn mower, or to buy liquor (and know what you are doing). (Of course, if you drink the 1/5 of liquor first, oh, never mind...) My disconnect with math came because I was ready for calculus by 7th or 8th grade. I was fortunate enough to take calculus in high school by attending a weekly evening class offered to 5 qualified seniors from each of 5 local high schools. I wish they had offered it to me as a high school freshman. I was so bored with math in high school. Speed it up, don't slow it down. But, I guess consistent with the No President left behind educational policy, everything is measured based on the C- president, I mean student. Enough for now. This is taking up too large a fraction of my time. Oops! Too large a decimal of my time I guess.

More thoughts on the importance of fractions at a young age. Telling time, cooking, and using a ruler. My parents taught me fractions, base 60, at about kindergarden level. They fashioned a construction paper clock, round face, two hands, one short, one long, and the hands held centrally with a brass fastener. Less than an hour later, I knew how to tell time, and had learned a subset of base 60 fractions. (since an hour is 60 minutes, quarter after the hour is 15 minutes, half hour is 30 minutes, and 3/4 hour is 45 minutes). The hour is 1/24 of a day, and class increments are 1 hour which is 1/24 of a day, or 1/12 of 1/2 of a day that is visible on a typical analog clock. Base 10 fractions are intuitively obvious after this. In fact, I still prefer an analog clock because it goes well with the human massively parallel computer, the brain. (an interesting note is that savants often have brain traits that are highly digital) When I have an appointment, I can look at the hands on an analog clock, and a complicated analog computation happens that tells me when to leave for that appointment, factoring in all the required variables (what time it is, when the appointment is, how far I have to go, what speed of transportation I'll use, what delays I might expect...). I look at the clock, and crunch, I simply know when to leave. I can't do that with a digital clock. Everyone's day, at any age, is strongly based on 1/24 of a day time increments. The sum total time of The Daily Show and The Colbert Report is 1/24 of a week day. (That's 1/12 + 1/12). I don't even remember school teaching how to tell time. Perhaps because when they got around to it, it was irrelevant to me since I already knew how to tell time. Same thing with long division. My Dad taught me that. And how to do square roots (now I have forgotten that and will use a calculator for it, but the pedagogical value of learning that trick was valuable). And he taught me how to use a slide rule too. That skill was quite useful. My slide rule and knowing how to compute the proper number of significant figures (something a calculator can't do) got me through high school and college science and math courses. An excellent introduction to the concept of adding/subtracting logarithms. (which is multiplication/division for those who may not realize it). Another important use of fractions is cooking. Almost all recipes use 1/4's, 1/2's, 1/3's of cups liberally. So say a child has one of those incandescent lamp toy ovens and wants to bake 18 cupcakes for a party for their friends tomorrow. The recipe is for a dozen and has many fractions in it. How to scale up from 12 to 18? How is the poor kid going to figure out that you make two full batches of 12 and eat 1/4 of them the night before, of course). Now to a ruler. If fractions are so unimportant at a young age, why do most parents equip their kids with a 12" notebook ruler? It has 1/4", 1/2", 1/8", 1/16" markings on it. And adding two fractions becomes very real if you want to add two such fractional distances to cut the construction paper to the proper length. And what is that mm stuff based on 1/10's on the other side of the ruler? Arghhhhh! Life is SO HARD! Fractions, fractions, everywhere! They help with telling time, having your cupcake and eating it too, and simple ruler measurement!

Comments are closed for this item.