Tuesday, November 6, 2007

60 Second Wisdom/60 Second Drivel

The University of Pennsylvania has something called "The 60 Second Lecture Series." Each week, a professor, who is usually at the top of his/her field, delivers a one-minute lecture on a relevant topic. They have distributed a cd-rom of some of these and I'm listening to a few on my Ipod. Many of these are excellent, like this one, delivered by Vijay Balasubramanian, Merriam Term Associate Professor of Physics:

The most amazing thing about this world of wonders is that we can understand it. It is not at all evident why this had to be the case, but it is the case, and there are two reasons why. First, underneath all of the immense complexity and apparent randomness of the natural world, there seems to be an intricate order. To perceive this order we must look beneath the surface - often with specialized instruments, but it is there nevertheless. What is more, the human mind can apparently understand the underlying structure in the universe. A cat can’t understand calculus, and likewise there is no compelling reason why the inner workings of the universe should be comprehensible to us. But they are. The human mind apparently apprehends the abstract patterns within the universal weave. We can see, for example, that the orbits around the sun can be simply described as ellipses. We can give a complete description of the physics of light in four short equations that would fit on a t-shirt. Nature is replete with such miraculous orderly relations. And the human sense of aesthetic simplicity seems to be an excellent guide to comprehending that order. Perhaps, as the poet concluded, "Beauty is truth and truth beauty. That is all ye know on earth and all ye need to know."

Oh baby. That is great stuff. And this guy is a physicist, for Pete's sake, and he's pointing out how amazing and near miraculous it is that people can understand how the world works. And he's right; it is, and we need to revel in that more.

Then there's this guy. Ok, maybe I shouldn't lambaste him just because I vehemently disagree with him. But boy is he wrong. This is from Dennis DeTurck, Dean of the College of Arts and Sciences, Evan C. Thompson Endowed Term Professor for Excellence in Teaching, Department of Mathematics.

Math educators at Penn, Rutgers and the City University of New York have recently joined together to found something called “Metro Math,” which is a project funded by the National Science Foundation. One focus of the group is to study how schoolchildren cope with the arithmetic of fractions and to seek and test new ways of teaching fractions. Well, I have a simple suggestion when it comes to teaching fractions in elementary school. Don’t.


Now, it’s difficult for me as a mathematician to entertain the notion that fractions, or “rational numbers,” as they’re known in the math biz, should be eliminated, not only from the curriculum but from polite society as well. But I’d argue that imposing the study of fractions on kids does much more harm than good by replacing confidence and understanding with confusion and memorization, and by using up time that could be better spent understanding about more about decimals and other things. It’s not that writing ratios like 385 over 23 should be banned. But such expressions should simply no longer be considered to be numbers. After all, what kind of answer is “385 over 23,” when “about 16.7” conveys the same information so much more directly?


Fractions have had their day, being useful for by-hand calculation of non-integers. But in this digital age, they’re obsolete as Roman numerals are. And there’s nothing so rational about rational numbers anyway. You have different representations for the same number, like three-sixths and four-eights. Fractions are harder to add than to multiply. What’s with that? And you have all the jargon, like “improper fraction” and “mixed number.” My gosh, if Tom DeLay hears about this, he’ll be proposing a constitutional amendment to ban it.


Despite the fact that great historical and theoretical significance has been imported to fractions and rational numbers, its study should be deferred until it’s really needed and can be appreciated, which may not be until after somebody learns calculus. Premature emphasis on rational numbers is of little practical use and turns kids off to further mathematical study because it’s so confusing. So I say, “Down with Fractions.” Thanks.


I can barely believe my ears. I don't even know where to begin to attack this. Ok, how about this....visualize .125. C'mon, visualize it. I know you can do it. Can't? Ok, how about visualizing 1/8? Right.

And that political crack about the language of fractions and the Tom DeLay joke was so obnoxiously typical of an Ivy academic.

I don't care how good this guy's credentials are. I don't understand why the concept of fractions has become obsolete. Mathematical concepts don't really do that. And what about fractions "replacing confidence and understanding with confusion and memorization?" Huh? Not only doesn't he make his case, he is substituting mushy, misplaced liberal thinking for logic.

He's just wrong on this.

2 comments:

abandoning eden said...

i don't know, maybe it's cause i'm a quant researcher, but i think .125 is a lot easier to visualize than 1/8th. at least that's standardized to a 1...

ok so 1/8th is easy to visualize but what about 8/97...it's a lot easier to visualize .082 (that's just 8.2%!). The only reason 1/8th is easier to visualize is becuase it's a 1 part, but there are a lot of fractions more complex than 1/8th.

WebGirl said...

And there are a lot of decimals more complicated than .082. The reason that's easy to visualize is because it's easily made into a percentage, and percentages are easy to visualize because they are parts of a 100. Actually, 8/97ths is not so hard...it's around 1/12 (8*12=96). I still think fractions are easier on the mind than decimals. Think Pi.