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.

Amateur survey of mathematics teachers

There is a lot of talk about what kind of knowledge mathematics teachers need in order to teach well. I am curious as to what practicing teachers think about this. Here are few questions for those of you who may stumble upon this page:

1. Do you think that mathematics courses you took as part of your preparation program (whether it be undergraduate, or certification, or anything else) are relevant to what you do in the classroom? In other words, do you think that what you learned there is directly or indirectly applicable to your profession?
   
   
2. Same questions about methods courses you my have taken.
   
   
3. In light of your experience in the classroom, if you had a say in what should be taught to future teachers as a part of their preparation, what would it be? Or, what do you wish you learned before you started teaching?
   

It is possible that I am asking wrong questions. If you think that is the case, then offer your own questions. And answers :)

Research vs. Practice

I just spent a few days in to me foreign environment: mathematics teacher educators' conference. Until few months ago I didn't even know that these things existed and now I know that there is a professional development for professional developers!

I don't think I made this clear so far, but I am in between two worlds right now: mathematics and mathematics education. I feel I'm in a no man's land, and there aren't too many of us hanging out there (or we just don't know each other?). Until a year ago I was a semihappy postdoc working on my own little projects, proving my little lemmas, was happy and felt guilty when I taught. Why semihappy? I guess I didn't feel that my contributions to the field or the world at large would be big enough to justify spending my life picking at the mathematics pie and hanging out with people who think that what they do is earth shattering (especially since most of the time I disagreed). Where I did think I could be more useful was with my teaching. I like to think that I am a pretty good teacher, I certainly love doing it, although I may not see myself in an objective light (see the post and post below, and I plan on revisiting this later). In any event, I taught a course for teachers this past semester, and as I was getting ready for it, I started realizing that I don't really know much about teaching, or methods, or pedagogy, or anything really. I decided I ought to learn and started talking to people over in education. It didn't take me too long to realize that they are more similar to mathematicians than either group would like to admit. It seems to be a widespread opinion, especially in education circles, that mathematicians don't care about teaching. That may be, but I would venture to claim that education faculty do not care about teaching any more than mathematicians do. This may need clarification, apart from the one where I say that I haven't actually conducted any research on this and everything I say are observations only and the samples aren't too huge :)

Educators as well as mathematicians largely think that teaching takes the time away from scholarly work. From the professional development programs that I saw, I can not claim that I am convinced that the benefits for teachers are what is on the education faculty's mind, but rather data that they may collect along the way. There also seem to be a big issue of who teaches content courses. Education stance: people who teach it (a.k.a. mathematicians) know the content, but not in the way that is relevant to teachers, so it should be taught by education people. Mathematics stance: the teachers need to know lots more content than they do, and all they get from them (a.k.a. math educators) is this touchy-feely, hold each other hand and reflect nonsense, and consequently they should never be allowed to teach the content courses. Am I exaggerating? Maybe, but only slightly. So what is is missing in this picture? Could it be conversation ? But who is to start it when everybody is busy with their research??? The obvious answer to me is the people who do not want to do research, but want to practice. If they are diplomatic enough (hmm, guess that rules me out) they could bridge the divide between the two worlds. Mathematicians who are also knowledgeable about results of research by mathematics educators (slight misnomer: mathematics education researchers would be more precise) seem to be a natural choice. So, if you are out there, and are reading this, or know somebody who is, let me know.