“Humanities” is what we can teach

Hypothesis: the difference between the humanities and sciences is that we have (or at least had) a pretty good idea how to teach the former and we have no idea how to teach the latter. In philosophy and theology and literature there is a longstanding canon of books to read and start with, in languages there is a clear order in which one learns grammar and vocabulary. We have a vague but simple enough sense of why these things are worth reading (because they are influential, or worthy in themselves) and we no more or less what they are good for.

All this gets lost by, say, math. Are we teaching math, or proto-engineering? What is even the vague order between geometry and algebra? What do we want the student to learn about? Is this a useful language, or are the relationships themselves of the quantities (if that’s even what they are) what’s important? One gets the sense that math, above all else, should be systematic, but the chapters of a math text largely arise at random: factoring, motion problems, rationalizing denominators, the FOIL method, complex numbers, the Pythagorean theorem…

St. Bonaventure:

Since, therefore, all things are beautiful and in some way delightful, and beauty and delight do not exit apart from proportion, and proportion is primarily in number, it needs must be that all things are subject to number. And for this reason number is the outstanding exemplar in the mind of the Maker, and in things it is the outstanding trace leading to wisdom.

If we could teach mathematics in light of that – which would require teaching it just as rigorously as we now teach it – math would be considered one of the humanities. As it stands, our mathematics is a witch’s brew of an old desire to beat the Soviets at science, a tool that SAT boards like because it is a good predictor of success at college, the demands of the Texas textbook industry, fifty years of inertia of having done it “like this” for reasons no one understands… etc.

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5 Comments

  1. October 22, 2014 at 9:12 pm

    I was left cold by algebra, trig, and calculus in highschool. I did alright, but didn’t give it anymore time than I could stand. It was all a bunch of fiddling with numbers. I was a disappointment to my family of engineers.

    I stumbled onto a collection of Oresme’s works as a sophomore in college while writing a paper. It was my first encounter with mathematics outside of textbooks. It was like a different language (quantities “measuring” one another? geometry of mobile bodies? intensities?). Such an adjustment, this sounds like thinking about things!

    I came out the other side with a terrible fondness for fractions. On my own time, I went back to the Elements, then forward to the Principia. Euclid and Newton read more like Oresme than they do Messrs. Houghton and Mifflin.

  2. Janet said,

    October 23, 2014 at 6:59 am

    But that’s exactly the way mathematicians view their field– as the study of a particular kind of beauty. The thing is, very few people ever get to the level where they can appreciate that. Language is an innate and powerful drive– most people spend much of their day, every day, talking/listening/reading, and the lack of that drive even in infancy is proof of a profound brain disorder. Not so with math. Some level of mathematical ability is universal, but at the equivalent level of point-and-grunt.

    Imagine how hard it would be for you, if I dumped you in the back woods of China (say), starting at point-and-grunt level, and I gave you a textbook and exposure for one hour a day, three days a week, to a partly-competent Chinese speaker, in a group of 25 people. How likely would you be to end up with an appreciation of Chinese literature? Or, would you end up with the “survival skills” language, and a grudge against Chinese (shared by your classmates), a resolution to use Chinese as little as humanly possible?

    Putting it another way, is it really surprising that what people learning Chinese experience, and what people fluent in Chinese experience, are totally different, even when they both are “studying Chinese”? Very few people will ever get to the point of being “fluent” in mathematics, that is, able to appreciate the whole and to be creative (or at least recognize and enjoy the creativity of others).

    PS: I don’t believe that the humanities are doing much better at imparting a love of literature, art, etc. to the general populace, despite being much more natively accessible. I’ve heard that, if you ask the American populace “How many books have you read this year for pleasure?” the median answer is “zero”. And the “average” high school graduate will give you an earful about the drudgery of English classes, with nitpicking on grammar and slogging through impenetrable “great books”. Just as hated as high school math, actually.

    • October 23, 2014 at 9:13 am

      You’re advancing a “just eat your peas” theory of education, where the kids just need to accept that the meaning of it all will become clear at some later date, until which they have to soldier on with the promises of the teacher. This is certainly an element in education, and one that becomes more controlling the younger the student is, and is particularly prominent in learning languages. There’s even a name for the virtue of soldiering on in hope of meaning: docility.

      But this virtue can’t be the dominant element in liberal education, or in any theory of education that claims to give the student things that are worth knowing in themselves. This is before we deal with the more fundamental problems mentioned in the post: lack of systematic rigor, muddling math and proto-engineering, having math ordered to tests that were written to gauge college competence and not to the actual structure of math, etc.

      Your account of math also can’t explain why Bonaventure said what he said. If we just have to eat our peas for ten years before seeing the point of math, then why is it that Bonaventure could say what he said when all that was known about mathematics could be held on less than a shelf? He was clearly deeply impressed by the power of mathematics after having a very rudimentary education in it, and without the benefit of ten years of algebra. Perhaps we could teach some of the books he read.

      • October 23, 2014 at 11:50 am

        I’d be on board with that, but you point to a problem – our schools are not places of liberal education. Nor are they places of industrial or vocational education. They are all patched together, without any governing idea of what they should be.

        We ask our students to eat their peas, and their bran logs, and their ice cream, and their styrofoam peanuts, all tossed together in one bowl.

        Some people are just unmoved, and others very much put out by Bonaventure – whether by his idea, or the man himself. Same as some might be by a Taylorite industrial education, or a beat-the-Soviets engineering and technical model.

        ‘Perhaps we could’ – if there were a we.

      • October 23, 2014 at 12:35 pm

        This is a good point. It would certainly be impossible to have some sort of nationalized liberal arts program. It’s hard enough to get five guys in a room to agree. I’d be happier if we could either be clearer about vocational training or decouple high school from college preparation. It might help to make competence tests a way to employment as opposed to making college degrees a proxy for this.


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