This semester I started tutoring for math at my university to maintain at least a little income. Between that experience and most of the conversations I have with people when they learn what my major is, I have noticed a common trend. It's something I was already semi-conscious of, but the idea has been hammered home in courses I'm taking now as well. It is that apparently, no one likes math. If I had to put a number to it, I would say 90% of the people I talk to in tutoring and about my major say, and I quote "Oh, I never liked math."
Obviously, this makes me a little sad, because I like math. Shoot, that's not enough. I think math is the bee's knees. I think math is (or at least can be) the most beautiful thing in the world. I want everyone to see math the way I do, but I know that's not possible. So the question I must ask in return is, what do I see that this 90% doesn't?
As a senior in a mathematical education degree, I have taken more and higher level math courses at the university level than a great majority of people, but I don't think that is enough to explain why I like math when so many others don't. I recently had to read an article for one of my courses that went along really well with this line of thought. Paul Lockhart's "A Mathematician's Lament" is the article, and it is a fantastic read if you are interested by this topic, but I understand if you don't read it. My own thoughts and Lockharts are pretty close together from here on out, so bear with me if I'm repeating what the article says.
Essentially, the reason why people don't like mathematics in our public education system is because they are not learning math. "Hold the phone, SRC. I learned math in school. I mean, it has math right in the title of all the textbooks and the class itself," you may respond. That's a fair reaction. I stand by my statement nonetheless. The "math" we are taught in school is a series of rules and formulas to follow. We are given some "real world examples" in which the rule or formula of the week is always needed, but next week we might as well forget it, because this new week has a new rule. We don't get to explore problems in which a whole variety of rules can be discovered simply by exploring the situation. We are told what mathematicians of previous generations have discovered and given examples of where it works, so the what of math, but we never learn where those mathematicians got their ideas, or the why.
To me, public education doesn't ever move beyond arithmetic. Arithmetic is built on simply adding one to itself (more or less), and subtraction, division, and multiplication are applications of that adding process. Arithmetic is the machinery of all the rest of mathematics, the foundation upon which the towers of geometry, algebra, number theory, statistics, and many more are built. So it is necessary to be familiar with arithmetic, but it's no fun to be drudging about in a basement when there are beautiful views to be seen from immense towers.
It's the equivalent of a builder being handed all the tools of the trade, but never getting the opportunity to, you know, use them to build something. They are presented in a discrete manner (separated from each other) and only seen in use by themselves. The builder gets a hammer, a nail, and a board, and drives the nail into the board. Then that board is tossed out and forgotten, and the builder gets a saw and a new board, and cuts the board in pieces. And so on and so forth with each tool in the toolbox. The builder is tested to see if he can use each tool by itself. Then he is expected to appreciate all the work that goes into making a house and to appreciate the beauty of how the house looks, but without actually building one for himself, just using the same tools as whoever built the house.
If we can't expect a builder to make a beautiful and sturdy house without some experience actually building, how can we expect students to appreciate and apply mathematics if they never get a chance to use it on a situation in their own lives? Clearly, the builder needs to have a working knowledge of the tools needed (the basics, i.e. arithmetic), but they will build best and use the tools most effectively if they use them to achieve a means that they desire, not what someone else has designed. No student of any discipline should enjoy being forced down a single road of understanding. Why has mathematics been so cruelly curtailed?
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