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.

news and blogs

Following blogs has reminded me of following news. I read news and I get upset by them, then I wonder if it wouldn't be easier just not to pay attention. But of course, that would be an easy way out, and completely irresponsible. So I keep reading. I've been getting upset by a lot of blogs that I read. At first I was very excited by the numbers of math teachers who were writing and I started reading their blogs. A lot of them talked about very interesting topics within math and teaching and policy. But then I realized that for a fair number mathematics is a rather marginal interest. I've made some comments about mathematics that I've seen here and there, some people write it off to nit picking. Makes me sad. Then, of course, there are people who seem to think that mathematics classroom should be divorced from issues whose consequences students encounter every day, such as (in)equity, and social (in)justice, and poverty. Others may be well in tune with those, but forget that they are supposed to be teaching mathematics. So lately, I've removed a whole bunch of blogs form my bloglines to save me some time, energy and stress. I've come down to about 10. I wonder if this is as irresponsible as quitting the news. Maybe I should stick to reading them, so that I can get to know these people better, what they think and how they feel about various topics.

Really cool

It's amazing to me how many things, one might want to say "easy" things, in mathematics I never really thought about. I was reading an ed article today, which reminded me of something I saw a while back about how people explain why a product of two negative numbers is a positive number, so I tried searching for it. Needless to say I wasn't able to find it, but I ran into something else which was even better! Here is the source, and an excerpt follows:


We take any Euclidean line, mark point 0 on it, choose a unit length and mark point 1, and then the non-negative "numbers" are associated (identified) with all the points on the ray from 0 through 1in the usual way. The negative numbers are then identified with the remaining points on the opposite ray in the usual way so that we have now a Cartesian coordinate number line L. Now choose a second line M through 0 and mark a 1 on it at the same unit distance as we used on L, and complete this so M is also a Cartesian coordinate line. Now for any number b (point) on L, and any nonzero number c on M, the product point b*c can be found: let J be the line from 1 on L to c on M, and K the line parallel to J through b on L, then b*c is the intersection of K and M.


Here is a picture that shows L as x-axis, M as y-axis, and we are looking for 4*3.




The only problem with this explanation is that the students need to know about similar triangles! Regardless, this was way cool. If I had thought about this on time, I would have given it to my students on their final that had them think about similar triangles. Next time!

If I can't be an actor

Lately I've heard lots of talks about equity in education, and in mathematics education in particular. Jeannie Oaks from UCLA gave a very informative talk at UofM last week where she talked about the consequences of Proposition 209 (banning affirmative action) in CA. The reason this was relevant is that almost identical proposition passed last year in Michigan. As a side note, she gave some frightening statistics about math teachers' qualifications, or the lack thereof, in CA schools. Mrc just yesterday said he was going to Math and Social Justice conference. You might want to check out a very good film The Boys of Baraka. It is a documentary about boys from Baltimore's projects who are sent to boarding school in Kenya. A tidbit from the special features, just for math teachers:

I'll go to LA to go to college to become an actor. If the whole actor thing doesn't pan out, I can always be a math teacher,

said one of the boys from the movie.

New: Coincidentally, I just saw this article in NY Times:

A scathing 18-month evaluation of California’s public schools has concluded that the state’s educational system is “broken,” crippled by a complex bureaucracy, flawed teacher policies and misspent school money, leaving it in need of sweeping reforms that could cost billions of dollars.

Assigning unworked problems?

I taught geometry for teachers course last semester. Towards the end I showed them an animation which depicted a geometry classroom in which students were given a problem to work on, to come up with conjectures and to prove them. The way I went about this was to give my students exactly the same problem before they saw the movie. They came up with conjectures, but didn't have to prove them immediately. Then they saw a movie. I guess I should point out that the students in the movie gave a partial solution, but there were loads of misunderstandings both on the side of students and the teacher. The goals were many, but one of them was for my students to be able to follow what students are saying at a pace at which things happen in reality and to try to determine what is correct, what is incorrect, what they should follow up and what they should leave alone. Things went fairly well, and now I am thinking whether to stick with the same plan or to alter it slightly. One questions is: Is it fair to show them the movie and expect them to be able to follow the action live :) When I saw the movie for the first time, although I have not worked out the problem before hand, I could see where the students were going, and why, and what was causing misunderstandings. Is it fair to put my students into the same position? Should I expect them to be able to do the same? Will the benefit for them be as big as if they had enough time to think about the problem themselves? Why the title above? If teachers have a tendency to assign problems they have not worked out beforehand (I've been guilty of that) then this could potentially show them dangers in doing so. Is that a valuable lesson? On the other hand, if they see the movie first then they loose the perspective of the student trying to solve the problem for themselves. A solution is thrown at them and will they try to come up with something different from what they've already seen? What say you?

P.S. Jonathan, you still didn't tell me why you hate teaching geometry :)

Back in town

The reason I haven't written in a while should be obvious from the title. Not only did I not write, but I wasn't even following what others wrote (skiing was way too good), so I am trying to catch up. For now, just a link to the third carnival of mathematics. It's not linked here anywhere, so I am doing it now: I loved the second .