Monday, July 30, 2012

+1 for Algebra Education

Often there are arguments about whether Algebra should be taught in school. After all, so many people don't use it in real life. But I think a well-rounded education is important, including Algebra, History, Physical Education, English Literature, and other subjects that people might not use in real life. But why do I believe that? Is there a good reason?

Well, humbug, I can't prove it. But people that lack breadth of education are not really able to understand the world, and so they may be deceived more easily by their government, their news media, their companies or their churches, and they may make large numbers of poor decisions, all the while being unaware of it. At best, this annoys those of us who are more competent; at worst, when such people are placed in positions of power, they can do a lot of damage. I'm reminded of Hugo Chavez here, about whom I saw an interesting documentary: he is apparently well-meaning but arrogant, believing himself to be a far better leader than he really is and certainly better than his appointed ministers; though I guess in a place like Venezuela, where average education levels are low, Chavez is relatively smart.

A comment on Slashdot gives another example of such a person. This person probably knew algebra, but he didn't know all those other subjects whose merits we seldom argue about:
"You shouldn't have to study Shakespeare to get a physics degree."

I disagree.

I spent a fair amount of time once with a man who was educated in the fashion you seem to think is appropriate. In his case, he'd started out working on the factory floor at an IBM manufacturing facility in Texas (30 years ago when they still made stuff in the US), and had qualified for and taken a technical math and computer science education culminating in a master's degree. IBM's "school" was accredited and his degree was a real one, but it included only technical subjects; no liberal ed at all. Prior to his IBM education he had barely graduated from high school -- and I'm not sure how he did, frankly.

He was a highly intelligent man, very articulate and perceptive. However, as soon as the discussion left technology his utter lack of education became instantly apparent. He was even ignorant of basic principles of physics -- he knew a fair amount about electronics, but in mechanics he understood less than most high school dropouts I've known. His ability to understand politics was nonexistent because he didn't know any history, or even understand basic civics. And don't even attempt to talk about literature, philosophy, etc.

Now, obviously, a big part of his ignorance was due to his own utter lack of interest in anything outside of computer science. You can't obtain a MSCS without being able to read, and anyone who can read can educate themselves. But the point was that the difference between him and the typical college graduate -- even though he was almost certainly smarter than said typical graduate -- was stark and obvious, and it wasn't in his favor. His lack of general knowledge wasn't just a problem when socializing, either, it often caused him to make dumb decisions that affected the business, and you simply could not put him in front of customers, because unless the discussion was laser-focused, he'd eventually say something that made him look like an idiot.

After my experience working with him, I decided I wholeheartedly agree with the liberal education philosophy. The worst part about it was that his deep, narrow knowledge and utter lack of knowledge outside of a single field made him believe, quite firmly, that there really wasn't much to know outside of his field. It's often said that that the primary purpose of a BA/BS is to teach the student the breadth of his own ignorance. Well, this guy never learned that.

We don't all need deep knowledge in every area, but an introductory course in each of the major areas of human knowledge really does add significant value. It makes us more rounded, teaches us some much-needed humility and, well, educates us. That education is what differentiates a university degree from a vocational certificate, and the former is more valuable than the latter.
I can see how most people might not use algebra. The thing is, basic algebra isn't really hard to learn, so learning it shouldn't really be a big deal. I do suspect, therefore, that there is something wrong with the way it is taught. Certainly I remembered that I didn't really understand it at first, back in grade 8 or 9, but now that I understand it seems fairly simple.

And I actually do use algebra at work, occasionally, and even basic calculus, in my programming job. Yet I have heard multiple programmers who are not very good at algebra say that they never use it, and never saw a use for it. Well, that makes sense. In life there are often several roads to a destination. Sometimes there is a short road that uses algebra and a long, winding road that does not. I will use the short road and those that can't do algebra will take the long road, probably never even realizing that the short road existed.

I have to admit though, there are some things that people really must know that were not taught in my school: how bank accounts and mutual funds work and the terminology involved; what a mortgage is and how it works; how the university/college education systems work; the basics of the legal system; principles of ethics; and so forth. Maybe there is an argument to be made that all these things should be given higher priority than Algebra. But if we do education right, we could teach all of this stuff. How to do it right, though, I can't say.

A response to the above comment offers a plausible counterargument, though:
I agree with both of you and the GP. I agree with the GP that such classes are annoying and largely useless to the specific discipline that the person chooses. I agree with the parent that you need to look beyond your discipline. A little background: I'm currently a college student (becoming a sophomore) at a big-name university, studying robotics. At this university, we have general education requirements of the following: Humanities, Social Science, Language, Natural Science. We also have a mandatory writing class and "Intro to the humanities". The goal, obviously, of these requirements is to make students well-rounded. This sounds good in principle, but in reality it fails.

Before I explain why, I must note that there are different types of students who respond differently to attempts to make them well-rounded. The first type, I call "robots." Robots essentially drag themselves through a fixed course in life - birth, elementary school, middle school, high school, college, career, marriage, kids, retirement, death. What kind of robot you get depends on the school you attend, but essentially they are all the same person. You get people who are insanely good at some subject (chemistry, biology, etc.) but not so good at everything else. Or so you'd think. What you actually get are people who have no intrinsic motivation, but are good at anything they have to do. That means they'll learn what they need for their career and they'll do well in these sort of general education classes if they have to get a degree. But, there's a problem: they'll never apply that knowledge to anything else. For example, if you have a robot who studies neuroscience and takes a required philosophy class, they won't consider the impact of neuroscience upon moral philosophy. Basically, requiring these students to take these sorts of classes is like programming an industrial welding robot to play a violin. While it might seem like you've done something, all you've really done is make a weird demonstration that doesn't really do much after it quits.

The second type of student here is the party animal. These students just party through college - they're not here for academics really, they're here for the connections. They are here for a variety of reasons - legacy, decent test scores, athletics, etc. As you might expect, they take a "C's get degrees" attitude to required courses. They don't gain anything from such courses but at least they push down to curve for the rest of us. Or you might assume. Actually, they take up valuable resources including TA and professor time, ask basic and banal questions and worst of all annoy the course staff and make them angry at the student body as a whole.

Lastly, there are some students who are truly intellectual. They actually integrate the ideas from the various disciplines together and create better ideas as a result. These students don't actually need much help being well-rounded. They'll read articles and get ideas from other fields on their own because that's part of there personality. They may take non-major related classes out of interest (I'm doing this with physics, chemistry, and maybe biology) for entertainment. The only benefit they may receive from these classes is a little push on the envelope (which they may hit anyway). The disadvantage is that they take required classes, which are bad because forced education is an inherently bad process. Students who don't want to learn are a pain to teach. This annoys professors that take that anger out on the student body. They also force professors to dumb down the course, in turn causing students who are actually engaged to be bored out of their minds. This bordem in turn causes them to become disinterested. Essentially, the entire thing fails for everyone at the same time.

So, to recap, required courses fail for each group of students for different reasons. Robots learn the material and then fail to apply it. Party animals flunk the classes. Intellectual students become disinterested in the basic classes and disconnected teachers. Solving the problem of making "robots" intellectual is not going to be done by dragging them through a few GE's. I don't know what the answer is, but I know we need to find it before the flesh-and-blood robots are replaced with silicon-and-steel ones.
Of course, I fall into the last category, and I can't entirely agree: I learned some interesting things in university, including things outside my core interests in computers, that I probably would not have learned otherwise. Sure I study stuff in my free time, but when it's a requirement for the degree, I study it harder and longer. That said, the quality of education at the U of C was (mostly) so bad that I would have been able to learn a lot of the same stuff in less time, with less stress and spending less money, if I studied without the university's "help". As for the other two categories of people--the robots and the jocks--I can't accurately comment on them because I have a lack of experience with them, because of my lack of social skills. I must say, I would be grateful if Social Skills was a required subject. Maybe then I would be any good at it.

[Is it just me or did I just write a boring, rambling blog post? Oh well.]

One final thought, maybe the trouble with Algebra is that it is treated as an end goal--our goal is to teach you algebra!--when in fact it is just a tool. We must then use algebra to see its value. You can't truly learn physics, for example, without algebra. But maybe the same people who argue we don't need algebra might say we don't need physics, either. Perhaps in the modern world, a more useful thing than physics is probability and statistics:
I would actually say statistics is probably the *most* broadly-applicable branch of mathematics. *Everyone* - scientist, politician, gambler, civic-minded citizen, and commercial watching bumpkin would benefit from a firm grasp of at least the basics of statistics, and of those scientists are typically the only ones who have any clue at all, and even their grasp on it is often shaky, especially in the softer science. And you don't actually need much more than basic algebra to learn it either.

No other field I can think of is as broadly used with as little understanding (how many times have you seen a % today?), which makes it ripe for exploitation. There's a reason for the phrase "there's lies, damned lies, and statistics" - statistics is (mostly) actually pretty simple from a "solve this equation" perspective, the difficulty is that there's a whole lot of counter-intuitive aspects to probability so it can be tricky to answer the question you think you're answering - which makes it ridiculously simple for someone to make a rock-solid sounding statistical argument that's completely spurious.
To me this ties back into the ability to understand the world and not be deceived. Statistics are easy to misuse, both accidentally (incompetence) and deliberately to deceive. More competence in statistics gives people a better chance to detect the liars and the idiots and to refute or ignore them.

1 comment:

Keith said...

Hm. These courses are obviously designed to keep you suffering in college as long as possible. Part of the sadism of the college professors and staff is to prolong the students' suffering. Though, the person whom you quote might have a point about Statistics. Maybe I'll read a book about it one of these days. I'm certainly not going to college for that: I've been there, done that, dropped out, and have had a lot of therapy because of those horrible years and a lot of regrets for not having had dropped out sooner.