Math Isn't That Hard

I am not a big fan of an open curriculum, especially given the intellectual maturity of most college students. Once upon a time, a university degree meant that the graduate knew everything worth knowing. OK, I exaggerate, and even if I weren't exaggerating, I am talking about a time when it was possible that a person could learn at least a little about a very high percentage of what was thought of as the western world's knowledge. Today I would expect someone with a college degree to know at least a little about at least the general areas in which we have knowledge: literature, music, history, math, several branches of the sciences, and so on. Otherwise, isn't it just a vocational degree?

I agree with you. A liberal education should be wide, and some sort of mathematical skills (along with writing skills, and knowledge of the world) should be part of it. I don't think I'd be a big fan of an open curriculum, although a flexible curriculum is very important for many students.

As for what kind of math, I would much rather statistics be required than, say, linear algebra or calculus. Even poets need to know about variation in the world, and how to tell if something is chance or not, and a well-taught stats class can open a lot of eyes.

I certainly agree that probability and statistics is a very important area of math for the general population. How many people would buy lottery tickets (that is, waste their money on lottery tickets) if they had any real concept of the probability of winning?

The impact of that silly Newsweek cover story 20 years ago ("The Marriage Crunch": college-educated single women over 40 are more likely to be killed by a terrorist than find Mr. Right) was greatly magnified by people's inability to recognize bogus statistical reasoning. That article was ridiculous on the face of it, but many college women were in a panic.

Newsweek recently ran an apologetic retrospective that was extensively covered in the news and the blogosphere. I wrote up some comments and lots of links at Math for self-defense.

"As for what kind of math, I would much rather statistics be required than, say, linear algebra or calculus."
The mathematicians (and statisticians) I know are pretty adamant that stats is not math! A big problem with teaching a liberal arts stats course (at least at my university, based on what students have told me) is that the course tends to be taught at the level of the slower (= mathphobic) students, which means it rarely proceeds beyond the mean (the concept, that is) and maybe variance- there is little or no time left over for even simple statistical tests, such as a t-test. Another problem is that, until students have data want to have analyzed (e.g, from a research project), it is hard to get them interested in statistics.

The utility of the open curriculum really has to be measured against the typical Smith student. Things may have changed in the last five years, but most of my friends and classmates took a broad spectrum of classes just because we could -- unlike at schools where the first year or two are spent fulfilling strict requirements, an English major could take science classes and still graduate on time. And they did -- partly because they were curious, and partly because Smithies are heavily interested in Latin Honors, which necessitates a pretty good distribution.

I agree that people should have a broad range of knowledge, but I think the most effective version would be if we could inculcate an interest in learning, and then allow students to follow that interest. At Smith, this lead to people taking a range of subjects just out of interest -- and sometimes changing their majors because of it (geology was infamous for this, since it seemed that nobody could take intro geology without switching majors). I took both calculus and high-level English seminars, even though neither was related to my major (history of science).

Math is important, but freedom shouldn't be underestimated. Increasing requirements is one way to get people to take a greater range of subjects, but so is increasing interest, and increasing the plausibility of completing a major while still studying other fields. The last one becomes less possible as requirements increase.

That said, I'd probably soften my position if formal logic counts as "mathematical reasoning." I kind of think all college students should be required to take formal logic (partly because I just finished teaching at a university where they're required to take rhetoric but not logic -- what the hell?). And Smith's main mathematical logician was great.

Math is important, but freedom shouldn't be underestimated. Increasing requirements is one way to get people to take a greater range of subjects, but so is increasing interest, and increasing the plausibility of completing a major while still studying other fields. The last one becomes less possible as requirements increase.

Absolutely.
I'm not in favor of a complicated list of specific required courses-- I think that style of program has the perverse effect of leading to a narrower distribution for many students, as it encourages a sort of check-box mentality ("Well, I've taken Psychology 101, so I never need to think about that department again...").

But, today's students being what they are, I think some requirements are necessary, just to keep people from skipping whole regions of the curriculum. I personally tend to favor a "distribution requirement" sort of system, where everybody has to take at least a couple of courses in the humanities, social sciences, and natural sciences, but without requiring specific courses. Not coincidentally, this is the system my alma mater had, and I think it struck a reasonable balance between forcing people to take a broad range of classes, and allowing them the freedom to explore classes that interested them.

Again, Latin Honors is a major motivator -- really a de facto requirement -- at Smith. Even screwups like me want Latin Honors (I didn't get it because of extenuating circumstances and I'm still steamed). So in a sense we've always had a distribution requirement, if an unofficial one.

The fact that Smith is the college under discussion acts as a bit of a red herring. Smith is a very good school with an unusually high number of intellectually curious students; 25% of them get Latin Honors, and I would guess that at least another 25% try but don't have high enough GPAs, so that's 50% of the students taking math of their own accord -- and that's a very conservative estimate. The problem is that this is a real rarity among colleges. I wasn't very much in favor of the distribution requirements and CORE curriculum at the school where I did my MA, because they just made students resent every required class, and furthermore made a five-year stay the status quo. But it's certainly true that most of my students, if given the choice, wouldn't have taken ANY classes. I feel like that's the first issue that needs to be addressed -- why would college students rather not be in college? And shouldn't we consider obliging them? (That's my secret academic elitism coming out: I kind of feel like, if you don't want to take math or stats or analytical philosophy, why are you in a liberal arts program in the first place?)

I think Latin Honors must mean something different at Smith than at places I've been. Assuming you mean "cum laude," and the like, that's just a straight GPA threshold at the schools where I know the policy. It didn't matter what courses you took, so long as you had a high enough average.

I think some students do very well with an open curriculum... but a lot of them need more guidance than that.

There's a real cultural problem at least in the USA that it's OK among intellgent and educated people to be completely incompetent at very basic math. College-educated people (including professors) who gleefully say, "I can't do math," would never freely and openly admit "I can't really write a complete paragraph."

Right now, as I'm teaching the introductory astronomy class at the summer session, I'm more annoyed that math and science types can't assume that students learned anything in high school or before. I have to spend a lot of time going over rate problems, because students find the math very advanced and very confusing. Yet, I just talked to my sister, who teaches 6th grade: this is 6th grade math. And yet the students seem to find it very advanced. It's quite frusturating, because I can't use those things as tools without risking loosing a lot of students and getting negative student evaluation comments about a "too advanced" class. So I could teach a content-light, overview, regurgitate-the-facts class without any mathematical or proportional reasoning in it... but, dammit, this is a science class. And yet I can't assume students are conversant with 6th-grade math.

Sigh.

-Rob

I gotta take issue with the title of the post. Math IS hard, but we don't want to admit it. The problem is not that math is hard but that we don't tell everyone "Not only is it hard, it's something that it would be good for you to learn about. And it will probably improve your life at some point to know about some of this..." If that argument fails, you can always say "Well, may be not math, but statistics will for sure."

Then you ask tell them, "I'll give you a dollar if you give me a buck twenty." When they say that that's stupid, why would they do that, congratulate them on understanding the usefulness of math in context.

Really? I had no idea that Smith handled Latin Honors differently than other institutions. To be eligible there, you need to have taken courses in the "seven fields of knowledge." It's been a long time, so I had to look them up: literature, historical studies, social science, natural science, mathematics and analytical philosophy, the arts, and foreign language. You need to have the distribution before your GPA can even be considered.

College-educated people (including professors) who gleefully say, "I can't do math," would never freely and openly admit "I can't really write a complete paragraph."

I'm not sure I agree -- I think you just have to be in the field to hear the excuses. I have encountered a number of otherwise intelligent people who think that since I have a postgraduate degree in English, I'm going to judge them. So they'll launch unprovoked into an explanation of how they can't spell and they're not very good at grammar. On the literature side, they'll often throw in a list of books they had to read in school that totally turned them off to reading forever.