What is mathematics education?

This was a title of the talk given by Hung Hsi Wu in the Mathematics Department at MSU. He happens to be one of the two mathematicians (I hear there is a third appointed recently) who are on the National Mathematics Advisory Panel, but about that in a second. I have gone to the talk not quite sure what to expect. People I know have given me opposing views of this person's work, or rather of what they thought he represented. Wu has tried to give a definition of mathematics education that I haven't heard before. He said: "Mathematics education is mathematical engineering". From what I understand he views engineering as a discipline that customizes abstract notions so that they are usable by wide populations. Therefore mathematics educations should be taking mathematics and turning it into a user-friendly product, i.e. into a product usable by a population under consideration. I thought this was an interesting way to look at it. Otherwise, what I learned is this: this nation is in crisis, W. is the best president as far as the education goes, it is against constitution to have national curriculum (I asked about this), in 2007 mathematical engineering urgently needs close collaborations of mathematicians and educators, there are no mathematical engineers yet. Few of these, I must say, came as a huge surprise to me. But let's not dwell on the politics. After the talk a smaller group retired to a smaller room to talk to the speaker some more. As people would walk in they wold introduce themselves and inevitably would say "I'm from the math department". It felt as if this was a secret handshake, or a a secret club. They were surprised to hear that I was as well. The comment I got was "You were laying so hard that we thought you were from the education side". Needless to say that nobody from education side was there, in this smaller, more intimate setting. Anyhow, I've heard, yet again, what I heard from teachers: It is all somebody else's fault. These future teachers don't know enough math, they don't want to learn, it's high school fault, it's their old teacher's fault... Maybe, just maybe, we aren't doing a good job either! How novel idea. I asked about NMAP, what the goal is, and what he though of the panel's composition. The goal is apparently to make recommendations about algebra. And the panel could be better, but it could be worse. Couple of us agreed that that seemed like a fairly lame answer, and since he thought it was perfectly fine, I decided to ask what he thought in particular of the fact that there is only ONE mathematics teacher on the panel. He agreed that that was a shame. I asked why they didn't ask that that be changed. He said that these things don't work that way. I think my words were:"I thought your job was to make recommendations. Couldn't you have made a recommendation to add a teacher to the Panel?" He said no. But here is the kicker: apparently they've just added three new members: one mathematician, one cognitive psychologist and mathematics education researcher (elementary math), I believe.

Update A friend of mine emailed and was asking "What's up with tallying mathematicians?" Once again, I fail make myself clear (or clear enough in a single post). I have talked about this before: it's not the lack of mathematicians that I find troubling as is the lack of mathematics teachers.

Over-achievers

We listen about under achieving students, poor quality of education, inadequate preparation and low test scores so much, that it was quite refreshing to read this New York Times article. However, (I think I may have already mentioned this somewhere below) moderation isn't bad at all. A high school kid with a working day 6 am to 1 am is little scary. When do they get to relax and have fun?

Technorati tags: education, students, content quality

The Teaching Gap

I have often heard the following statements from teachers:

"There is no way my students could handle this."
"This is too hard for my students."
"Good luck teaching that. That's way above their heads."

If I complained that I didn't think that particular topics under discussion were that hard, I would get these answers:

"You don't have experience with (insert your favorite k-12 grade) students."
"You haven't been in our school."

These statements are correct. I do not have yet that much experience with K-12, but I am fairly positive that students respond to unstated expectations very well (and stated ones even better). What I mean by that is: if your students believe that you think they can not learn math or that the math is just too hard for them to grasp, then they do not have much incentive to prove you wrong. After all, you are the expert. However, if you set the bar high for them, their performance and in the process you let them know that YOU think they are able to become good in math, then they will try harder to prove you're right. I do think that the attitude teachers have influences greatly their students. The reason I am writing about this is the book I just started reading: The Teaching Gap by Stigler and Hiebert. I have a couple of quotes that I'd like to share:

One of the most striking impressions when watching the videotapes is that students in teh United States encounter a different kind of mathematics from that encountered by their peers in Germany and Japan. The content appears to be less advanced and is presented in a more piecemeal and prescriptive way.

As it turns out there were NO mathematical proofs in U.S. lessons. In contrast, there were proofs in 53 percent of Japanese lessons and 10 percent of German lessons.

Incidentally, German students did not perform significantly better on the achievement test then American students. The following figures also made quite an impression (I hope they will look decent):

Average percentage of topics in eight-grade mathematics lessons that contained topics that were DEVELOPED or STATED.

Percentage of lessons rated as having low, medium, and high quality of mathematical content (as rated by a team of mathematicians who did not know which lessons came from which countries).

Technorati tags: education, math, content quality