I'm at Intel ISEF, the world's largest HS math, science, and engineering fair, as part of a team from Chicago trying to increase the number of students doing math research in high school. On Monday, I walked down the math aisle and talked to the five or six kids I found setting up their projects--cool ideas, like using fractal dimension to quantify the distinction between cancerous and noncancerous cells, or linking quadratic residues to the number of digits in the base b expansion of 1/p. And I asked them three questions: Do you do a lot of math contests? Have you ever done a summer math program? Are you part of a math circle? All eighteen answers: no.
Now I like to think that doing these extracurricular math activities makes kids more interested in math and more likely to investigate mathematical ideas on their own, but this makes me wonder. Some hypotheses in search of more data...let me know what you think and I'll report back after more extensive conversations on Thursday.
- Maybe the kids who do math research are doing it because they don't have any other outlets for their math interest, as a sort of last resort.
- Maybe the kids who do lots of other math stuff simply don't have the time or energy to do math research, because the other math stuff they do consumes all that time and energy.
- Maybe the kids who do lots of other math stuff are also the kids driven (literally) to lots of other "Race to Nowhere" activities, so that they don't have time or energy to explore and play, not because of the math they do, but because of everything they do.
- Maybe the kids who are driven to do high-quality research are exactly the kinds of curious loners unlikely to be attracted to math contests and summer math programs (ugh! other people!) in the first place.
Hypotheses #3 and #4 are most benign, because #1 and #2 are suggesting--to my chagrin--that part of the reason more kids aren't doing the most authentic math--the "I'm wondering about..." kind of math--is that many of them are doing math contests instead. And that seems oddly backward.
Thoughts?
== pjk
PJ - That's an interesting observation, but I'm not extremely surprised by these students not doing math contests. High school math contests, at least through the AMC level - and I hesitate to say AIME, but I think so - involve questions that do not take a lot of deep persistence to answer. The message is: solve as many as you can and move on.
ReplyDeleteSummer programs should open the door to more, perhaps in a summer camp many high schoolers are learning how to write proofs and learning about deep exciting ideas in math (say, group theory, number theory), that took a long time to develop and they would not come to on their own. A professor in grad school once told me, "At first, I did not publish anything because I thought my results were not as beautiful as the theorems in complex analysis. Then I realized that the work that I was comparing myself to was developed over the course of 100 years." Do the kids get this feeling, too?
I know some do graph theory, which doesn't fit this way of looking at things, so it's not perfect.
Comments from those more closely involved with high school math camps?
Hypothesis Generating Question #5: Who mentored you in your work?
So a larger sample yielded several students who did do contests and summer programs. Still, many of the most creative projects I saw at ISEF were from students who DON'T attend super-rigorous schools. I'll chalk this up as partial support for the RTN theory.
ReplyDeleteI just noticed the "Math in the News" announcement at http://mathdl.maa.org/mathDL/?pa=mathNews&sa=view&newsId=1302. Of the five students mentioned for Intel STS, one was a participant in the USAMO and IMO.
ReplyDeleteA question that I have is what is the overlap of the different areas of math enrichment that you identified?
* Math contests / Math team
* Summer math program
* Math circle
* Math research project
Content overlap -- depends, but I'd say fairly high. Many of the math research projects I saw at ISEF were advanced work that could have grown out of summer experiences in number theory, game theory, etc.
DeletePeople overlap -- I think the first three basically cater to a single group of people, more or less. And, again, relatively few of those wind up in the last category.
In my first year of teaching, I was handed the MathCounts/MathLeague extracurricular assignment. I was quite terrible at it. I just could not get excited about solving a bunch of clever puzzles quickly, and frankly I had (still have) no idea how to make kids better at it.
ReplyDeleteI handed it off like a hot potato as soon as I could.
What I don't know is whether any of my Math League kids could have been recruited to a more in-depth researchy sort of extracurricular activity (for which I would have been an excellent leader!) Perhaps they don't conflict so much as attract different types of kids-not just on the dimension in your hypothesis 4, but on their math personalities. Some of us are sprinters, thriving on the quick bite-sized challenge. Others enjoy the weeks of work that lead to a big-picture sort of breakthrough.
Nice observation, and thanks for posing the question.