MDTP San Diego Conference 2007

MDTP stands for "Mathematics Diagnostic Testing Project". I attended the conference without really knowing (or caring) what MDTP actually does. I went because I was interested in learning about teaching and expanding my ideas about teaching.

The first talk I attended was given by Jeff Rabin (UCSD). I've met him a couple times on an inter-personal level and I took his course mathematical methods course my first year here. He opened by introducing the following problem:

Give an example of two triangles that have 5 congruent parts but are not congruent triangles.

He gave everyone about 10 minutes to work on it. I think I got it at around 7-8 minutes. More important than actually obtaining the answer was the intellectual process that one takes to get from the question to the answer. I can write down an answer and (if you're mathematically inclined) it will take mere seconds for you to conclude that it is a valid example. However, the point was to notice the thought patterns involved in working out a problem like this. There were two important features in play:

1. I did not know the answer ahead of time. I only knew that an answer existed. (Alternatively, the question could be phrased "If possible, give an example..." This would create an interesting situation in a classroom setting with more time for interactions.)
2. I did not know the specific tools required in order to obtain the result. However, the fact that we were talking about incongruent triangles gave enough of a hint as to where to start.

This is the essence of problem-solving. Finding and justifying answers to questions whose answers and method of solution were not previously known to the problem solver. I actually don't remember what else he had to say, but this was already useful information to me. I would like to keep this in mind as I plan problem sets for students in my classes. Of course, there is also the necessity for having exercises (straight-forward computations, questions where the method of solution is actually known in advance -- perhaps given in lecture at some point).

The plenary session was given by Guershon Harel. I met with him once when I was thinking about post-grad school jobs and ways to perhaps transition into math education instead of researching in pure math. He talked was titled "Thinking in Terms of Ways of Thinking." He talked specifically about DNR-based instruction (Click here to read a short paper on it), I would like to find some way of having math students (especially those not going into math) to evaluate themselves and how they think about things. I do like to emphasize that there are different skills in mathematics, which is something I talked about in the Teaching Statement I used when I was applying for jobs. My ideas were not nearly as refined and technical as his, which is perfectly fine by me.