[kosciusko51]

A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

[John O]

I want people to read the book for the specifics of his arguments, but I want to discuss one important point that he makes. Many people in math education claim that in order to make math more understandable and interesting to students, we need to show how practical it is and how it is used in everyday life. I've always felt like this idea was wrong, or at least limited in its usefulness in that regard. Well, Lockhart demolishes the idea, essentially claiming that practical uses are simply by-products of math, and that the real excitement and beauty of mathematics is in the abstract, imaginary, and creative world of mathematical ideas that have no specific connection to the everyday. By-products and applications can make math seem boring and secondary to the uses it serves. I agree with him--and much more now after having read his argument.

(A quote form the first comment on the book.) Without applications almost any body of knowledge is next to useless.

Calculus was a total mystery to me for the first two semesters. The one question I had that none of my profs could or would answer was "Why do I need to know this?" The answer was always "Because your degree requires it, or because you'll need it for the next class".

Finally I had Dr Earl W Swokowski for the third semester of Calculus (He also was the author of the textbook we were using). So I asked my question "Why do I need to know this?"

We spent the next 2 sessions exploring where calculus is usefull using real world (but somewhat fanciful) examples. The one that sticks to me is if you were swimming and knew the topography of the bottom of the lake a second order deriviative of that topography would tell you which direction to swim to get to shallower water fastest.

Finally! an application for this stuff. The rest of the class just clicked. Everything suddenly made sense.

So sometimes, for some people, the application is all important while the "abstract, imiaginary and creative" is just useless noise.

BTW, to get back on topic. I loved high school algebra, geometry, trig and pre-calculus. I guess geometry was my favorite though. I'm one of those twisted, thoroughly damaged people that loves doing proofs.