Bill Kerr, a teacher/blogger I read regularly, wrote a post recently that I enjoyed immensely, called “What is maths?” He doesn’t answer the question, but what I like is he cites some other articles that talk about what math is not. They make it clear that a) we’re probably not being taught math completely in schools–even though we think we are, and b) our perception of what math is causes us to discredit it in our daily lives.

Ever since I was a teenager I heard the occasional adult who said, “I learned X, but I never used it.” We take the math skills what we learned for granted. By “math skills” I don’t just mean how to solve equations, but the mental skills we learned *in order to* solve equations but the mental perception that is acquired as a result of solving them. My guess is lots of people use those skills it in other aspects of their lives, but math doesn’t get the credit.

This is something I became concerned about when I wrote a post around a video M. J. McDermott produced about math education in the state of Washington. She said that high school students were not learning about higher math skills like algebra, and Trig., but instead were put into a focus on “everyday” math skills that people could use to solve arithmetic problems in their heads. I looked into this a little further and it sounded like this curriculum came out of the mindset of these people who say, “I learned quadratic equations in school, and I never used them again.” It sounded like they’ve just chucked those disciplines out, because hey, nobody’s going to use them in real life, right?

Kerr’s quotes make some really good arguments against what people think of as “math”. I’ll give a couple examples.

Kerr cites a math professor, Dr. Robert H. Lewis, who talks about the snide remarks he gets from some adults who complain they were taught quadratic equations, but never used them again–they were “useless”. His response is basically, “Yeah, so what?” He said it’s like saying, “You know, I can’t remember anymore what the name of Dick and Jane’s dog was. I’ve never used the fact that their names were Dick and Jane. Therefore you wasted my time when I was six years old.” He said the point was not to learn about Dick and Jane and their dog. The point was to learn to **read**.

A commenter to Kerr’s blog, named Maggie, cited another good example. Athletes use weight training to develop their bodies for their sports, like football. Does weight training have anything to do with throwing a ball, catching a ball, or running it down the field dodging linemen? No. So what relevance does it have? Exactly. It has no direct relevance to the sport, but it’s a supportive activity that promotes better performance in the sport. She said, “Math is exercise for your brain.”

There’s a larger point to Kerr’s post that I don’t really cover here, but I think is worth exploring.

As for me, I think I got an OK math education in school (public school and college). A lot of it was pattern matching and symbol manipulation, but I didn’t have a good grasp for what was going on half the time. For the courses I took where I “got it”, I was grateful. I truly enjoyed the experience of delving into the math, understanding it, and exploring by myself how it applied to problems in the real world. In the other courses, I was able to do the symbol manipulation–go through the motions–but I didn’t have the foggiest notion as to why we were doing what we were doing. What did it mean? I felt like a dumb machine. This happened mostly in my college math courses. I could produce the correct answers on a test some of the time, but when it came time to apply the math concepts to a non-theoretical problem (outside of math coursework) I was as ignorant as I was before I took the classes that taught them. This is a frustration of a different sort. It’s not that I thought the math concepts I was taught were useless. It’s that I went through the course not truly learning the math the course was ostensibly supposed to teach. To all appearances though, I’d learned it to the school’s satisfaction.

I think I’ve ended up learning more about the aspects of math I didn’t learn in school from my work as a programmer. I can compare and contrast math forms that I can work with in programs with the math forms I saw in school that were purely theoretical. Some of them are similar, and some are different. What’s helped is seeing “math in action” in my programs, not just declarative symbols.

I think the math I learned in school helped me in my programming by driving home the notion that something that looks complex can be transformed into a simplified form by deconstructing it to its essential elements, without losing any of its meaning. The symbol manipulation skills really help, too. The set theory I learned in Discrete Structures (in college) has helped out a lot. In terms of direct relevance, that was the most relevant math course I’ve had.

Anyway, Bill Kerr asks some really good questions. Check out his post.

**Edit** 2/29/08: I made some corrections, because I realized that in the 2nd paragraph I had mischaracterized what is really learned in math. Kerr’s post delves into this more. I realized that instead of saying “math skills” that are acquired from the activity I should’ve said that the activity helps us gain a new mental perception, which allows us to form new ideas on how to see things.

—Mark Miller, https://tekkie.wordpress.com

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on February 28, 2008 at 12:58 amJustin JamesWhat helped me more than anything else to learn math was taking Physics & Calculus at the same time. The Physics course was essentially Newtonian motion stuff (gravity, momentum, work, force, inertia, friction, a few other items) so it meshed PERFECTLY with the calc I was taking (Calc I, ending with integrals). There was nothing better than learning about derivatives in one period, and in the verty next period, using formulas created with derivatives to calculate velocity & aceleration of motion we were seeing with out own eyes. I think that if we could devise a combined math/science course that taught the math and immediately put it to work on things better than the traditional “a train leaves Chicago at 3 PM traveling 57 MPH…” type word problems.

J.Ja

on March 16, 2008 at 4:47 pmMark Miller@Justin:

Just getting to the old comments. I think your experience validates what Alan Kay believes about math and science. He’s said that they should be taught together, in the same course. I think he said that math was invented to study science, or something like that. Sounds right, though I’ve heard that philosophy had a hand in math as well, like the concept of nothingness (zero), and the concept of negative numbers.