Monday, October 25, 2010

Math for People Who Don't Do Math Good

I don't need to tell you that the state of our mathematics education is deplorable. For some reason New York Magazine does need to tell you. A few days ago they released an article entitled "The Ten Most Ridiculous Classes Currently Offered at Liberal-Arts Colleges" that showed the terrible state of mathematical literacy amongst writers New York Magazine.

In order to find the ten (10) classes in question, the magazine assembled a panel of five (5) experts to read random course catalogs until they found something that sounded ridiculous. How ridiculous are they? So ridiculous that the authors filed their article under the New York Magazine sections for fuzzy math and math for people who don't do math good.

Actually, the classes they found weren't very ridiculous at all. But the fact that they didn't realize these were perfectly legit shows the disconcerting lack of mathematical understanding in this country. It's sort of like how Iran-Contra proves that Ronald Reagan was write about the evils of big government. The fact that the article decrying the state of mathematical literacy demonstrated a complete lack of mathematical literacy shows that the authors' hysteria was justified.

Let's take a closer look.
The Ten Most Ridiculous-Sounding Math Classes Currently Offered at Liberal-Arts Colleges
October 19, 2010

Every year, liberal-arts majors anxiously scour their college's course listings looking for classes that will fulfill their math requirement but aren't so, you know, math-y. Here's what they're signed up for this year.
Bear this bit in mind. All ten of the below classes are, according to the authors of the article, "not math-y" and just a cheap excuse for liberal-arts types to fulfill their math requirement without doing any math. Even if this was the case, there's not much of a problem. If you're trying to become an actor/waiter, then knowing advanced math isn't going to help much anyway, so you might as well have fun. But even if you accept that all college students should learn legitimate math, how do you explain the list's inclusion of . . .
10. Topology: The Nature of Shape and Space: "In geometry we ask: How big is it? How long is it? But in topology we ask: Is it connected? Is it compact? Does it have holes?" [Sarah Lawrence]
You're not getting off to a very good start, New York Magazine. Topology is a standard math course that appears in pretty much every college and university in the world, not just liberal-arts colleges. It can get pretty tough, too. You know that problem, the Poincaré conjecture, that was part of the Clay Math Institutes seven biggest unsolved problems of all time until Grigori Perelman solved it in 2003? That was topology.

The only problem I can see with that course is that the description isn't very detailed. It lists the sorts of things topologists look for without getting at the main point that topology considers shapes to be equivalent if you warp them, but not if you break them, so size doesn't get preserved, but compactness, connectedness and number of holes does. The fact that that's not included in the description makes it look a bit silly . . . at least until you click on that link it gives and read the complete course description.
9. The Mathematics of Chance: "Most topics are introduced in a case-study fashion, usually by reading an article in a current periodical such as the New York Times." [Bard]
If you think topology is a ridiculous not-so-math-y branch of math, then check out this other ca-ray-zee thing called "probability". Once again the actual course description is a lot longer than what appears in the article. But they singled out the most ridiculous part of the course: the fact that students are expected to (gasp) apply probability to real life scientific studies! I mean, how crazy is that? Why are students wasting their time taking classes that apply math to real life when they could be doing . . . uh . . . I don't know, irrelevant stuff, I guess.
8. Mathematics in Many Cultures: "Mathematical ideas are found in many cultures, among both literate and non-literate peoples. This course examines both mathematics and the role it plays in the cultures. Examples chosen from the mathematical ideas of present-day peoples of Africa, Asia, Oceania and the Americas, as well as historic Egypt, Mesopotamia, Greece, Islam and China." [Pomona]
So now we finally get to something that resembles the article's opening paragraph. It's a math history class, rather than a math class, that fulfills the math distribution requirement for non-math-majors. Oh the horror. Still, it looks like a perfectly good math history class and, given that it's likely to cover different numerical systems it's at least going to get into some legitimate math as well. Maybe it would be better suited for a humanities requirement than a math requirement. Maybe.
7. The Magic of Numbers: "This course will explore the beauty and mystery of mathematics through a study of the patterns and properties of the natural numbers 1, 2, [and] 3." [Harvard]
Okay, now you're talking! And at an ivy league university, no less! Magic? Beauty? Where's the actual math? Oh, its in the part of the course description the panel of five experts decided not to include. Oh, and it's actually a perfectly respectable discrete math course dealing with things like prime numbers, factorials and binomial coefficients.

But, man isn't it insane that they're doing a course only about the numbers "1, 2 [and] 3"? I mean, there are an infinite number of natural numbers, man. Wait a minute, why is the word "and" in brackets? That should to mean it wasn't in the original version but the panel of five experts thought it would clarify things to insert it. So what does the original version say? Oh, it says "This course will explore the beauty and mystery of mathematics through a study of the patterns and properties of the natural numbers 1, 2, 3, ....".

Well then, it is just an ordinary discrete math course. As for the "magic" and "beauty" stuff, that just means the professor is enthusiastic about the subject, which is a good thing.
6. Models of Life: "In particular, we will ask such questions as: How do you model the growth of a population of animals? How can you model the growth of a tree? How do sunflowers and seashells grow?" [Kenyon]
Wow! This is just like those crazy "math for poets" classes only it's "math for biologists"! Good luck trying to apply math to that pseudo-science!
5. Mathematical Origamist’s Toolkit: "Topics include modular origami and how this models the creation of polyhedra and coloring of graphs, comparison of origami-axiomatic constructions to straight-edge and compass constructions, the combinatorics of possible crease patterns, the mathematics of origami design (circle packing, optimization), matrix models for paperfolding, spherical geometry, Descartes’ Theorem, and Gaussian curvature." [Hampshire]
Time to be serious, now. The title of the article, "The Ten Most Ridiculous-Sounding Math Classes Currently Offered at Liberal-Arts Colleges", does, indeed apply to this course. The class sounds ridiculous. If you are unfamiliar with the mathematical study of origami, this might sound like a class where people make paper cranes and call it math.

But that doesn't mean it is. If you look at the description, you find that there is a lot of incredibly intense math involved. On top of that, if you are familiar with mathematical origami theory you would know that it is an important developing field that NASA depends on to get their space telescopes to work. That's because you need to fold the lenses for transportation, and be able to unfold them and still have them work. This needs to be done by carefully selecting creases in the right locations, i.e. origami.

Furthermore, let's go back to the first paragraph of the article. This isn't a course for liberal-arts students to fulfill their math requirement without doing anything "math-y". It's a summer high school course for gifted high school students to learn about advanced mathematics.
4. Mathematics and Narrative: "Many literary works (Arcadia, Proof, and Uncle Petros and the Goldbach Conjecture) use mathematics as an integral part of their narrative. Movie and television narratives such as Good Will Hunting and Numb3rs are also mathematically based. Nonfiction works about mathematics and mathematical biographies like Chaos, Fermat's Enigma, and A Beautiful Mind provide further examples of the connection between mathematics and narrative. " [Vassar]
I took a course like this at Brandeis that even included a lot of the same books. It was taught by a math teacher, but it counted as an English class, not a math class. I suppose the panel of experts would at least admit that this is a pretty neat idea for an English class, and their issue with it stems from the fact that it's listed in the math department.

And this time, they're right. Oh, no, wait. They're wrong. Maybe they'd be right if it wasn't for the little message at the end of the course description that they kindly neglected to include in their article: "Open only to freshmen; satisfies college requirement for a Freshman Writing Seminar." So this is the exact opposite of a class for liberal-arts students to fulfill their math requirement without being math-y. It's a class for math majors to fulfill their writing requirement while being math-y.
3. Borges and Mathematics: "Jorge Luis Borges was one of the most important writers of the 20th century. Many of his short stories and essays were concerned with philosophical, metaphysical, and mathematical questions. The thesis motivating this course is that if we know the mathematics that Borges referred to, then we will read him differently, and we will read him better." [Bennington]
Hey, it's another interdisciplinary class. This time dealing with the Argentinean magical realist writer Jorge Luis Borges. The esteemed panel of five experts seem to be of the opinion that interdisciplinary stuff is inherently bad. Of course, if they were familiar with Borges they might know he incorporated a lot of mathematical concepts in his writing that could easily form the basis for a good class. If they didn't know that, they'd figure out had they bothered to look at the course announcement on the website.

So this class is covering the combinatorial implications of a Borges story "Library of Babel" about a library containing every possible book with every possible collection of letters. And there's other stuff dealing with group theory and the mathematical concepts of the infinite and infinitessimal. So it's basically a regular math class but with magical realist word problems. Considering how strained most math word problems are, that comes of as perfectly reasonable. Not as good Sarah Greenwald's Simpsons and Futurama talks but still good.
2. Mathematics and Science as Art in Contemporary Theatre: "Playwrights such as Tom Stoppard, Rinne Groff, Michael Frayn, and others have effectively explored mathematical and scientific themes for artistic purposes. Through readings and exercises, and by conducting labs and staging scenes, this class will gain some first-hand insight into the complementary ways in which science and art aim to seek out their respective truths." [Middlebury]
Wow, this panel of five experts must really hate interdisciplinary classes. This time it's not even listed as a math class, but in a special "interdisciplinary" section. Apparently Middlebury College has an interdisciplinary first-year seminar program that includes courses like this. It has nothing to do with filling the math requirement with a theatre class. It's about fulfilling the interdisciplinary requirement with an interdisciplinary class.

What makes this classes inclusion on the list extra-inexplicable is that it isn't even included in the list of math courses. So to even find the class, they would have to go to the interdisciplinary section and should have immediately found out about all of this.
1. Meaning, Math, And Motion: "Quoting a charming articulation by Kinsman (a mathematician-turned-oceanographer, in the preface to Wind Waves): 'To the beginner, science is a conversation that has been in progress for a very long time.' Our collective work is to catch up on the conversation." [Evergreen]
Somebody really needs to explain to the writers of this article what an ellipsis is. Not only did they think "1, 2, 3, ...." means the same thing as "1, 2 [and] 3", they threw out a big chunk of the Kinsman quote without using one, in such a way as to remove its actual content. Here's the full course description.

This is a bit of an unorthodox math class. It's also interdisciplinary, but it's between math, physics and linguistics. All of these are perfectly legitimate sciences, making it more serious a math class than the artsy classes earlier in the list. As for what it's really about, look to the line where they explain what they mean when they say "catch up on the conversation": "which means being deliberate about how we calculate and convince, speak and write, listen and read, and also means acquiring the science content and process skills required to judge what is being argued".

The course includes plenty of serious math, taking students through first-semester calculus, first-semester physics and first-semester linguistics in once class. And it's being done with the intent on improving scientific and mathematical reasoning in everyday life.

I can't help but get the impression that the authors think that math means calculus and that everything else is poetry. If that's the case then math is no more important to real life than English. Most people will never have to do integration by parts when they finish calculus just as most people will never have to read Dickens when they finish English. Mathematical reasoning is the main application that math has to everyday life, so this is a perfectly reasonable course for somebody who doesn't actually want to be a math major, rather than forcing them to take a straight calculus class they'll forget about afterwards.

Lack of mathematical and scientific reasoning is a much bigger problem than lack of calculus. That's what causes people to take intelligent design seriously. That's what causes people to take demagogues like Glenn Beck seriously. And that's what causes a panel of five experts writing for New York Magazine to list a bunch of perfectly respectable math courses and conclude:
This is why Asia is winning, by the way.


  1. Oh god the picture. "Get it? It's funny because she thinks she's a serious mathematician! But she's a *woman* and possibly *Latina*! Haha... hahaha... Um."

  2. I'm sure when the first digital calculator came out they said people will get worse at math. They were right and wrong. Right with the commoner and wrong with the mathematician.

    Today, we have smart phones that make TI-83s look 100 years old. You can get applications with the ability to solve an equation with multiple variables. Since most math we teach, (and also that the average person really ever needs to know) is time-consuming and not necessarily "difficult", it should come as no surprise that once again the mathematical layman will get even worse at math.

    I am not great at math. I'm very analytical, but am so in other areas. My problem is attention, which stems from interest...which are both excuses.....anyways....

    My greater worry is when this technological edge encroaches into the area of social behavior. It has in some respect. Our ability to reason with each other on a personal level has been slowly eroded by the internet. Intensive social-networking has accelerated this threat.

    Beyond the inescapable reality that humanity is losing its ability to think critical (reason being either the internet ((quick answer to everything)) or our nature in conjunction with the internet) we are losing our ability to compromise. The easiest example right now is in politics. It doesn't matter what side you are on, one must admit both sides are polarized to paralyzing degrees.

    This is a different technological beast than the assault on math. Math is being attacked by the "smart" capability of technology, whereas the behavioral attack (which also attacks attention, hmm....this is all adding up) is an encroachment by the sheer aggregation factor brought on by technology.

    Perhaps I've digressed, perhaps I sound crazy. But this is how I see it. I stumbled upon this blog and I felt like voicing my opinion on the subject, from a social science perspective.

    As for the article, it sounds like they're trying to put a cute dress on math that already has a name. Some are a little strange though.

  3. PS-

    My argument as stated is not well supported, but I didn't want to leave a horrendously long comment.

    To clarify a bit, the aggregation factor will lead to statistical majorities that will be represented by both large and extremely small margins. Long-tail theory, which is used like crazy by Google and most other search engines, furthers the problem of people only encountering similar content. It is dangerous to rarely competing ideals on any subject.

    Thanks for reading. Have a nice day.