Editorial Notebooks

Reconsider math education

In my last notebook as an undergraduate at RPI, possibly my last notebook that will ever appear in The Poly, I have decided to address two growing concerns from my time. The first will cover a few problems I have seen with professors; the second will deal with the courses of RPI’s mathematics department.

1. When I first entered RPI, my respect for the professors who were teaching me was high. They were the ones who had the knowledge and I hoped that, by the time I graduated, I would have enough of that knowledge to be a contributing member of society and, more importantly, get a job. However, the closer I got to graduation, the more I realize that my trust in professors has been misplaced.

I have had a professor who could not justify the fundamental assumptions that were used as a basis for his course. Without such justification, why should I consider anything I did in that class to be useful? When I confronted the professor, asking for a justification, he told me that it was obvious why the assumptions were true. At best, I would say that justification meant that he was out of touch with his students; at worst, that he had no idea and was attempting to embarrass me into leaving the matter alone. Either way, should someone like that be allowed to teach?

I have seen both professors and my peers defend theories as though they are fact. I tread lightly here because I realize the potential for the misuse of this argument and I do not want my words twisted into justifications for unscientific thought. However, I think that the distinction between the best-supported theory and a fact is important. In fact, I would argue that the misrepresentation of a theory as a fact is as irresponsible as using magic as a justification. As a physicist, the example I will give of this is Einstein’s theory of relativity. Thus far, evidence is overwhelmingly in favor of special relativity, the implication of which is that acceleration to faster-than-light speeds is impossible. Of the professors and physics students I have discussed this with, all of them have treated special relativity as proof that faster-than-light travel is impossible. Is it not possible to devise another theory that fits our observations equally well? Do we even have enough data to say with reasonable certainty that Einstein’s theory is correct? I would argue no. Einstein’s theory is simply the one that best fits the information we currently have available. To treat it as otherwise is a misrepresentation.

2. I have begun to take more and more issue with the way mathematics is taught here at RPI. Here, I will focus on the introductory differential equations course, but the problem is present in several other courses as well. When I took Introduction to Differential Equations my freshman year, I had very little idea why it was useful. In fact, to most of the people I have talked to who did not have any previous experience with differential equations, the course was simply memorizing a bunch of steps for some reason only known by the professor. There was no attempt to explain why differential equations are useful.

Now I am definitely in support of everyone having a basic knowledge of every subject: enough to know where and how to learn more. Is knowing how to follow a recipe to get to a solution to a differential equation that knowledge? I argue for knowledge of how to use math as a tool, how to construct models using mathematics. In fact, is knowing the steps to solve a differential equation even relevant if the equations being solved are not modeling anything useful? I was in my second semester of junior year before I finally learned how to construct mathematical models. All that math that I had learned was finally useful to me. So I have to ask, do non-mathematics students ever reach the point where they understand why all of this is useful? The point where they can begin to construct their own models instead of mindlessly following the steps laid down by others?

Further, I have only taken one course in the math department that asked me to make my own assumptions and justify them (oddly, the only other course that has asked me to do this was a course in biology, which I have seen many math and physics students look down on with something resembling scorn). What did I discover from these two courses? That the assumptions used in constructing a mathematical model will define the results of said model.

I cannot answer any of these questions for you, but I hope I have convinced some of you to at least think about these matters.