Sunday, February 3, 2008

Do Away with Fractions? That's 1/2 Nuts

Per USA Today, professor of mathematics Dennis DeTurck suggests that fractions should go the way of roman numerals:

"Fractions have had their day, being useful for by-hand calculation," DeTurck said as part of a 60-second lecture series. "But in this digital age, they're as obsolete as Roman numerals are."

This brought some understandable criticisms:

Questioning the wisdom of teaching fractions to young students doesn't compute with people such as George Andrews, a professor of mathematics at Pennsylvania State University and president-elect of the American Mathematical Society. "All of this is absurd," Andrews said. "No wonder mathematical achievements in the country are so abysmal.

"Arithmetic is the basic skill. If children do not know arithmetic, they can't go on to algebra, which leads to calculus. From there you go on to other things," Andrews said. "It's fine to talk about it, but this is not a good pedagogy."

I hesitate to challenge a mathematics professor on math, especially based on a second hand account of his position. However, I will say I find the idea of delaying learning about fractions until the student has learned calculus highly dubious, for most of the reasons Mark Chu-Carrol and Jason Rosenhouse list. I object per se to the idea that we should change the way we learn arithmetic based on existing technology. I don't care if we have machines that have the psychic ability to anticipate the problem we are going to ask and pop the answer in front of our faces before we ask. Everyone should be able to do basic arithmetic. Any adult who can't make change, or divide by ten, or understand that every portion of a total is going to be less than the total, ought to be embarrased. They are abdicating the responsibility of understanding the world to others, and opening themselves up to scams both large and small. How much better might our debt problem be if everyone understood basic math?

Fractions should be taught more, not less.


Harriet said...

Fractions belong in grade school.

calculus: you need fractions well before encountering calculus.

Basically, the premise of some math ed types is this: "if it is hard for some students to learn, then don't teach it".


Anonymous said...

Actually, preferring decimal notation makes real sense to some extent. After all, things in The Real World are decimal by nature. Every country's currency is divided into a hundred sub-units; nobody moans that there is no exact representation for one-seventeenth of a dollar, two-ninths of a euro or one-eighth of a pound! You do some cooking, and you need to weigh and measure out some ingredients. Well, weighing scales and measuring jugs are intrinsically decimal devices: there are a thousand millilitres in a litre, and there are a thousand grams in a kilogram. You do some DIY, and you need to measure your pieces of wood. Tape measures are also intrinsically decimal devices: there are a hundred centimetres in a metre.

Keeping things written as ratios is more important when you are working with abstract quantities and need to be exact, but I would say that belonged more to the realm of algebra than arithmetic.

But what earthly point is there in rewriting a ratio as an integer and a ratiometric fraction smaller than one? If you have 5/2, call it 5/2 (if you're going to do more maths with it) or 2.5 (if it's a real-world thing, or 2.50 if it's money), but don't try to pretend that "2 1/2" is a sensible way of expressing a quantity.

Nobody does maths using Roman numerals anymore. There's a good reason for that: Arabic numerals are easier to use! And decimal representations are easier to use than mixed integers and ratiometric fractions.