Posts Tagged ‘why educate?’

Painters and Pure Mathematicians

April 26, 2013

The Atlantic posted an article this week with the title Here’s How Little Math Americans Actually Use at Work. The article is a good summary of what it is about.

This article annoyed me for four reasons. First, I do not think that the data in the article support its conclusion that people do not use much math at work. It cites that 94% of people use “any math,” which alone makes the title seem ridiculous (would they be happy with 96%? 99%? Would it have to be 100%?). The have a better point that only 22% of workers use any mathematics beyond arithmetic and fractions. But is this number actually low? Would at least one out of every five workers use American history at work? Science? French? Phy Ed? The only school subject that I can think of that would be higher is “English,” since many workers have to write at work. A better, less-provocative-and-more-accurate headline would be “Here’s How Much Math Americans Actually Use at Work.”

Next, I am annoyed because I feel that math teachers are largely the cause of this. As a community, we have put a lot of effort into teaching students that they should care about mathematics because it is useful. While this is true, we would have done a much better job motivating students if we had spent the same amount of energy switching to more effective pedagogies. And I can see why people like the author of the above article might be concerned: students were promised that mathematics would be useful, and then they feel let down/lied to/vindicated when 78% of the workforce only uses at most elementary school mathematics in their jobs (Edit: Thanks to Kate Owens for catching an arithmetic mistake here).

I am also annoyed at the double-standard. I have written about this before. But it still bothers me that mathematics is held to a different standard than other school subjects precisely because it is so useful, but then people (like the author of the Atlantic article) suggest that we over-emphasize mathematics because it is not useful enough. As I stated in the previous paragraph, I think that this is largely the fault of the mathematics community.

Finally, I am annoyed as a pure mathematician that my subject is being perverted. A quote from a recent This American Life (Episode 493: “Picture Show”) sums up my feelings beautifully. The show talks about how art is often traded, held, and re-traded as a commodity like wheat or corn. One artist found her works traded in this market and reflects:

 “Painters really paint because there is sort of like this beautiful magic moment in it, you know.  And after you are constantly making stuff all of the time, and people are buying stuff, and then they are flipping paintings, and it is all about money—it’s like you, you just crave for that magic moment again.  It becomes corrupted if you let it.”

Replacing “painters” with “pure mathematicians” leads to an accurate description of how I felt when I read the Atlantic article. I do mathematics because of the magic moment. The article seems as ridiculous to me as if someone wrote an article suggesting we should consider eliminating art classes because very few people have to paint the walls of their office as part of their job.


What new did your students get out of class today?

December 5, 2009

This post is a response to Erica’s post on the question what did your students get out of today’s class that they did not have before?

I think that she is completely right to challenge the premise of his question. There is much too much emphasis on “facts” in our educational system, and not enough emphasis on “habits.” “What did students take away from your class?” The only way to answer that simply is to answer with something akin to a “fact.” “They now know that Dostoyevsky is Russian.” “They now know that not everyone can have everything they want.” These are “facts,” and it really does not take very long to learn them.

Is this an important component of education? To a point, yet, but it should be secondary to other issues (below). Here are several things that I was taught in high school:

  1. The Teapot Dome Scandal
  2. The Krebs cycle
  3. How to conjugate the Spanish verb “pagar.”
  4. The Hawley-Smoot Tariff Act
  5. Hero’s formula
  6. The name of the male lead character from Wuthering Heights.
  7. Descartes Rule of Signs
  8. The maximum number of electrons in the third shell.

I remember some of these things, but not others. I am guessing that any reader of this list might know a few, but not all. I have a Ph.D., and I think it is clear that I, along with most of the readers of this weblog, am among the best educated people in the history of the world.

So how can I be extremely well-educated, but not remember many of these basic facts from high school (let alone college, when the courses were much more specialized)? I think that this is largely because “facts” are not terribly important in the scheme of things. (So you can probably guess that I am not a big fan of Hirsch, although I do not want to eliminate the content completely).

My opinion is main role of education is to nurture different thinking skills. Among the thinking habits I would like my students to have are:

  1. To value of clear, concise communication.
  2. To value, and use, evidence.
  3. To employ supposition (“what if…”)
  4. To employ empathy (think of things from other people’s points of view–this is different from “sympathy”).
  5. To value and look for connections among different ideas

(as you might guess, I am a fan of Deborah Meier).

Analogies are only somewhat useful (I am trying to get my education students to become aware of this), but here is one: I run almost every day. If you were to ask me, “What did you get out of running today?”, I might not have a good answer. “I got cold,” “My leg muscles might be 0.00001% stronger,” “I had some time to think or listen to a podcast.” Other days I might answer “Absolutely nothing.”

So why run when I get, at best, only tiny bit stronger each time? Well…that’s the only way to get stronger. I might not be able to measure how much stronger I got from that day’s worth of running, but the effects are noticeable over time.

We might not be able to measure how much our students got out of one class, but one semester of a class might make them more likely to provide evidence for an argument. To spend an extra 15 minutes revising a paper so that it is clearer. To be more likely to think about how Afghan’s think of the United States forces in their country (liberators or occupiers?).

After four years of this, we hopefully have a student who has become a lot “stronger” in these areas.

So the fact that I may or may not be able to say, “after today’s lecture, the students should know _____” is not evidence that I am a good teacher, and it is not evidence that I am a bad teacher. I goals like that for the semester: “After the semester, the students will know ____,” but it seems like it would be unwise to interrupt a classes struggle with larger ideas just to inject the mandatory dose of daily facts.

As for “assessment mentality,” I find much of it troubling. I will start by saying that I strongly value assessment, but that I think that it is hard for someone without formal training to do well. What ends up happening is people tend to measure what is easy rather than what is valuable (guess which is easier to assess: facts or habits?). In the process of measuring the easy, less important things, we slowly erode our values. Over time, what is measurable becomes what is important, and we end up ceding control of education to the test administrators.

Three years of college?

October 26, 2009

Senator (also former Secretary of Education and president of the University of Tennessee) Lamar Alexander wrote an article on education for Newsweek in last week’s issue. The title is “The Three Year Solution.”

Here is a brief summary of the article: The “Big Three” auto companies were once great American institutions. They ceased to be great because they failed to adapt to changing conditions. The American university system is currently a great American institution. It could cease to be great by failing to adapt to changing conditions. One way to do this is to provide options for well-prepared students to enter a three, rather than four, year college program.

I value ideas like these. Other ideas that Alexander alludes to: eliminating summer vacation, re-thinking tenure, and doubling the faculty to allow for year-round utilization of campuses. I have discussed tenure before—I think that it should be eliminated for community colleges and below (where research is not done), definitely kept for Research I universities, and unsure about liberal arts colleges like mine (“Well, that makes me feel better about me, worse about Giles. Kinda shaky about you.”). My justification for tenure is tied exclusively to research—I do not want researchers with unpopular ideas to be squelched. Certainly, great progress often occurs as the result of an unpopular idea. Thus, I disagree with Senator Alexander; while I believe that the tenure process may stifle creativity while a professor is working to obtain tenure, eliminating tenure would stifle creativity for a lifetime. After all, one is not likely to explore an odd idea if it would put one’s job in danger.

I am intrigued by the Senator’s ideas on eliminating summer vacation and holding college year round. There seems to be little reason to retain summer vacation, aside from the fact that we all like it (perhaps, though, this is reason enough). Senator Alexander also proposes that we double the size of the student body, double the faculty, and hold classes year round. This would allow students and faculty to retain their vacations (although it seems like they would not always be in the summer), but better utilize the campus. After all, the campus costs money to run even when students are not present.

One problem with summer classes is that I do not see a large, unfulfilled demand for college education. My institution(s) had fewer students enroll this year than desired. The only way to get more students would be to accept students who are less prepared (which may not be a bad thing).

My impression is that Senator Alexander is largely offering solutions to keep costs down for colleges. Although he did not mention this, eliminating tenure would almost certainly have the effect of lowering costs, since there is a large pool of cheap, recently graduated Ph.Ds who would like jobs (I, of course, would be opposed to this, since I believe that experience is important in education). While running classes year-round would not decrease costs, they very likely would increase revenue. These ideas make sense to me in the context of his article.

Most of the article, though, is about creating a system where well-prepared students could plan on graduating in three years. While this is an interesting idea (I graduated in three years from the University of Minnesota, and I am happy that I did), it eludes me how this relates to his article. He writes that this would save the student money—which it certainly would. However, this would come at the expense of the college—which seems counter to the point of the article.

I wonder if he thought that offering a three-year program would increase revenue, but I am skeptical here. The pool of well-prepared college students is small, and the pool of well-prepared college students who refuse to attend college because it takes exactly one year too long is even smaller. I cannot imagine that there are students who are not attending college for this reason.

I cannot figure out what problem the three-year solution is attempting to solve. I agree that it would be nice for some students (although I fear that too many students would attempt it—I am of the opinion that education is being far too compressed as it is), but I do not see the advantage it offers for colleges. Please let me know if you have ideas.