Wednesday, January 30, 2008

Are fractions obsolete?

In a USA Today article titled, Professor: Fractions should be scrapped, Dennis DeTurck argues that, "Fractions have had their day, being useful for by-hand calculation, but in this digital age, they're as obsolete as Roman numerals are."

i couldn't disagree more.

According to DeTurk, after he publicly made his "Down with Fractions" proclamation, "There were blogs and rants, and there were some critical e-mails, they'd always boil down to: 'What would we do in cooking and carpentry?' "

It turns out fractions are pretty important for things like ratios and rates (to name a few). What i think the proposition actually boils down to is something more along the lines of: 'What would we do in science and engineering?' If your idea of math is to put some numbers in and get a number out, then DeTurk may be right...as long as you have a calculator (try doing 9.33*.429 in your head...now try (28/3)*(3/7)). But you can't even do simple algebra without a fairly good understanding of fractions...much less trigonometry or calculus!

DeTurk goes on to attack long division, the calculation of square roots and by-hand multiplication of long numbers. It looks like 90% of what i learned in math after 3rd grade isn't really that important after all.

8 comments:

Ben said...

Not only that, what about following the stock market, shopping sales, gratuity at restaurants, calculating gas mileage, taxes and budgets? The guy who can get a sense of the numbers quickly always has the advantage.

Next he'll be wanting to get rid of imaginary numbers.

Ben said...

Also, how can you even PRETEND to understand math if you do not understand the concept of a fractions?

Old Grey Sliderule Geek said...

I agree with Ben, mostly.

Aristotle, Euclid and Pythagoras must be rolling over in their graves right now. we can always carry calculators that compute tips, but then we lose a great deal of mental discipline.

The Egyptians built the pyramids with little more than a stylus and knowledge of four function math - old fashioned fractions and long division. The engineers that sent men to the moon were seat of the pants sliderule guys, and that meant understanding logarithms, which become entirely buried if all you do is rely on your calulator. Yet, they never made an oops like trying to have computer chips communicate when one spoke metric and the other American measurements!

The problem is do we rely on the natural organic computer that we all possess or become slaves to the silicon gods?

Ben said...

I have no problem with becoming "slaves to the silicon gods" if we know why we're allowed to do so. Calculators and computer math programs such as MatLab and Mathematica are essential, at the higher level but they are next to useless if the background isn't there to guide the user.

To use physics as an example, the amount of material a student has to learn before they are at a level where they can do serious research is quite astounding. This means that to quickly become a productive member of the scientific community, one has to have an understand of everything that came before. This includes a working understanding of mathematics, of which fractions are essential.

Also, I did not think fractions were a big deal. It seemed like the greater majority of my peers had an understanding by grade 4 or 5.

sejwa said...

Fractions and ratios are very useful for describing the relationship between two quantities, among other things. In my opinion, fractions communicate this relationship better than the decimal system.

Reading DeTurk's comments makes me wonder what his view of education is. Fractions are such a useful tool for understanding the world around you, that I have to wonder if DeTurk thinks that getting results (e.g. from a computer or calculator) is more important than understanding.

sejwa said...

I am worried about where education seems to be headed in the United States. Reading stories like these makes me want teach in elementary school or highschool. I mean, this world is exceedingly interesting, and from what I have heard about the public school system, most teachers do not do a good job of communicating this wonder.

Ben said...

Sejwa,

I have an anecdote that will feed your fears. I emphasize it is only an anecdote and is no way representative of the ALL students of my undergraduate university, just several.

There was a student in my class who was the type who held up every lecture she was in with questions until they became almost stagnant. In our senior year, we had Abstract Algebra together. At the time, she and another of her ilk had managed to get the class taught in such as way that the same material was repeated three times a week, but that is besides the point. One day in class we were discussing a group that contained the imaginary number i. This girl raised her hand and asked , "What does that i mean?". This is after 20-some minutes of talking about this problem. The professor stared blankly for a moment and then responded "It's the imaginary number i, the square root of minus one" to which she relplied, "Oh...I always wondered what that was!" This girl was also heard to remark during her senior year, "I don't understand exponents." She is now certified (but not qualified by any means) to teach grade school math in Wisconsin. I'm quite sure she still does not understand exponents.

Anyway, I sympathize with your concerns. A strong understanding of math in the grade school years is essential to understanding any higher-lever mathematics and essential to not looking like a fool to someone who was familiar with i in grade three when he asked the teacher what it meant to take the square root of a negative number.

Anonymous said...

amazing. thanks for posting this.
i've been blogging about fractions
in math ed myself, by coincidence ...
here, for example ...
and'll probably be following up
on this horrifying story at some length.

looks like a great blog you've got
going here ... i found out about it
at "science after sunclipse".

yrs in the struggle.