A couple of years ago, I ranted about the value of mathematics, its utility in our lives, and the reasons– both valid and invalid– for why learning mathematics is important for everyone, not just mathematicians or people who work in mathematics-intensive fields.
As usual, the words most worth reading in that post weren’t mine, but instead were those by Underwood Dudley in an article that I mentioned almost as an afterthought, titled “What is Mathematics For?” In it, Dudley argues, and I think I agree with him, that the importance of everyone learning mathematics is not because everyone will need to use the particular mathematics learned in their jobs or personal lives. For example, once students learn the quadratic equation in their algebra class, most of those students will never use it again after their education.
So why do we teach it? Dudley suggests that it is not the particular “nuggets” of mathematics that are most generally useful, but the mathematical way of thinking critically that everyone benefits from. As he puts it, teaching mathematics is the best way that we know “to teach the race to reason.”
Or is it? In the latest AMS Notices, Peter Johnson responds to Dudley’s article with the criticism that:
“There appears to be no research whatsoever that would indicate that the kind of reasoning skills a student is expected to gain from learning algebra would transfer to other domains of thinking or to problem solving or critical thinking in general.”
The article is a short and interesting read. Johnson has a point that there is an unfortunate lack of available data one way or the other. However, that also does not warrant rejecting Dudley’s main point outright.
As I read both articles, I think that perhaps the problem is in focusing on algebra in particular as the “useful subject to teach and learn.” Personally, I think (formal) logic is a more appropriate “common denominator” among all mathematical subjects, and is perhaps the single most generally-useful mathematics that everyone should learn… and yet how many non-mathematics-majors are exposed to it in any detail? Whether proving a theorem, or troubleshooting faulty electrical wiring in your home, or observing (or participating in) an election debate, everyone should be able to reason logically, recognize common structure in logical arguments, and understand and identify when those arguments do or do not follow.