Why study higher mathematics and other stuff most people don’t use in everyday life?
This video was posted in a Facebook group of mine here:
I find it ironic that some of the most listened-to speakers about education explain that the cure to our educational ills is to point out that education is unnecessary. I call this educational anti-intellectualism. Here’s another representative sample and another.
It is possible to make the argument, “X isn’t going to be necessary for most students in life, therefore X should not be taught,” for almost everything that is taught beyond the sixth grade or so. After that, we should be taught “critical thinking” and vague “analytical abilities” and “reading comprehension” and other such claptrap; that seems to be the natural consequence of this commentator’s thinking, and sadly, he is not alone.
The fact that educated people like this teacher, and all the people who approve of this stuff, cannot answer the question is very disappointing. It’s not surprising, perhaps, because it’s philosophy and philosophy is very hard. Moreover, there are a variety of sort-of-right answers that subtly get things wrong and might end up doing more damage than good.
In the latter category I might want to place E.D. Hirsch, Jr., one of the most prominent education traditionalists alive. (He just published a book I got today called Why Knowledge Matters, and he might have updated his views on this; I’ll find out soon.) Hirsch’s argument is that we ought to learn classics and, essentially, get a liberal arts education, because this is the knowledge we use to interact with other educated adults in our culture. It is “cultural literacy” and “cultural capital” and this is something we desperately need to thrive as individuals and as a civilization.
That’s all true, I think. If Hirsch made the argument as, essentially a defense of Western (or just advanced) civilization—that we need to educate people in Western civilization if we are to perpetuate it—then I’d be fully on board. But Hirsch as I understand him appeals particularly to our individual desire to be a part of the elite, to get ahead, to be able to lord it over our less-educated citizens. This is a very bad argument that won’t convince many people. If Hirsch or anyone makes it, I would put it in the category of arguing for the right conclusion for the wrong reason.
The argument I’d give to this math teacher is the same I’d give to someone who says we shouldn’t memorize history facts or read boring, classic literature or learn the details of science or what have you. Of course you don’t need that stuff to get through life. Most people are as dumb as a box of rocks when it comes to academic stuff (yes, in all countries; some are worse than others).
The reason you get an education, and study stuff like higher math, is more along the following lines. Education trains the mind and thereby liberates us from natural prejudice and stupidity. This is the proper work for human beings because we are rational creatures. We are honing the tool that comes more naturally to us than to any other animal. One must realize, as people like this educated fool and so many others seem not to, that education, such as math education, is not merely a tool in the sense of “abilities.” The content, or what is known, is a deeply important part of the tool; in fact, as Hirsch does argue correctly and convincingly, any “analytical abilities” brought to a text will be very poor without relevant subject knowledge. If you want an analogy, it is a poor one to say that a course in logic sharpens your wit, to say you want to have sharp wits, and therefore you should study “critical thinking”; the heft or substance of your wit’s ax is all the rest of the knowledge behind the cutting edge. Getting an A in a logic class (a course I taught many times) without knowledge of math, science, history, literature, etc., gives you about as much heft and effectiveness as a sharp-edged piece of paper: capable of paper-cuts.
The core of the argument for knowledge is that academic knowledge forms a sort of deeply interconnected system, and the more deeply and broadly that we understand this system, the more capable we are in every bit of life. This is true of us as individuals and also as a society or civilization. It is completely and literally true that the fantastic structure of modern civilization as we know it, all of the historically unprecedented developments we have seen, is a direct outgrowth of the deep commitment of our society’s leaders—since the Enlightenment—to education in this system.
The system I refer to is deeply connected, but that doesn’t mean it isn’t also loosely connected in the sense that one can learn bits here and there and benefit somewhat. That’s absolutely true. This is why it’s possible for the math teacher to say, “Well, you don’t really need to know higher math in order to live life.” Some people are geniuses about literature but don’t remember anything about any math they learned beyond the sixth grade.
But as everybody with higher education knows, in fact it is absolutely necessary to learn higher math if you are going to learn higher science—both the hard sciences and the social sciences, both of which require heavy calculation—and deal intelligently with statistics and probabilities, as is necessary in politics, or the financial part of business, or some of programming, etc.
This is because the “deep structure” of reality is mathematical. To declare that “you don’t really need to know it” is to declare that you don’t need to know the deep structure of reality. Sure, of course you don’t. The birds of the air and the fish of the sea don’t. But do you want our children to be more like them or more like fully rational, aware, human creatures?