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August 26, 2006
What is Math for, Anyway?
Steph, in teaching Connor math, came across a problem that was difficult for her to solve. She did it, but it took a while. Mark's comments, too, are instructive. I learned a great deal of math calculation in school and college (side effect of engineering major), and it was only after I left college, and tried to explain math to people who didn't get it, that I finally realized that there are some fundamental truths about math that are generally not taught in school, but without which math makes almost no sense. Here they are:
Math is a tool for solving problems you encounter in life that are related to counting, comparison, estimation and the like. Problems come to you in life presented as fancy counting (everything up through algebra), like:
I have $23 and some change. Those pants cost $21, and tax is 8.5%. Do I have enough to buy the pants, or will I look like a fool at the register?
I have a quarter tank of gas. Each tank holds 12 gallons and I get 18 miles to the gallon. I'm tired and may or may not have remembered my credit card. Can I make it home and deal with this tomorrow, or must I stop at the gas station and deal with it now?
Or as geometry, like:
Do I have enough carpet to cover the living room? How about after I have to cut some out for the fireplace and add some for that odd corner?
Where can I put my garden where I have the most space for plants with the least inconvenience to mowing the lawn?
How far is it to that hill over there, and at what angle should I elevate my cannon to hit it?
Or in combinations, like:
What do I need to buy — how much wood, how many nails, etc — to build a shed in the back yard?
When you get an equation handed to you to solve, you are not doing a problem. The problem is already boiled down for you into an equation. Solving the equation is an exercise in applying mathematical rules; there is little creativity and thought required, just memory recall (or learning new rules if you don't already know them). Word problems are what matters about math, unless you are a theoretical mathematician developing new ways of solving equations that will help others solve their problems.
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Comments
Great post Jeff, and very nice site. I came from Instapundit to read the fisking, which fore me was well-reasoned, and full of facts properly applied supporting logic.
I am a recent PhD in an applied science, which was a career 180 after a liberal arts BA.
I do A LOT of problem solving, have become adept at applying math rules, and find it interesting that we don't really teach this.
My students can 'plug and chug' when I give them essentially all the elements of a problem, but aren't good at figuring out what those elements are.
My guess is that if more people understand math as you describe it, as a tool rather than ane end to itself, they would be more interested.
Anyway, keep up the good work, I'll be back.
Cheers,
Bob
Posted by: Robert Ward at August 27, 2006 1:02 PM