Saturday, May 05, 2007

Math Lovers Unite!

Great article in the Times about two local brothers going to a math competition. I hadn't thought to post it (except as a feel-good piece) but for the last sentence. One of the brothers says he likes math competition questions better than in-class questions because they are more creative. Dorothy, our resident math expert, might be able to answer why math can't be taught more creatively if this is what gets kids going. Maybe I can track down some of the questions and see what he means.

2 comments:

Dorothy said...

Aw shucks, Mel, I don't know about the resident expert bit, I'm just the loudest when it comes to commenting on math issues.

I did however read the article before seeing your post and was struck by it also.

What struck me was that at first glance, the example questions didn't seem all that creative, more of an arithmetic exercise. All they require is a solid grounding in factoring.

Here's how you could approach the first problem. First, since you most assuredly know the times tables up through 12x12, you know 221 isn't there. And since you know 15 squared is 225, you can reason very quickly that if 221 isn't prime, 13 must be a factor. Try it, and since you have learned how to do long division efficiently and accurately, the 17 is quickly found. Hmmm, after solving the problem I think I understand the appeal. Something that at first glance might seem tedious can be solved quickly with just a little thinking and a lot of arithmetic mastery. That philosophy is, I believe, the core of MathCounts.

The second sample question, similarly, is something that only requires fast and accurate arithmetic (no you don't have to divide all the way to the hundredth decimal place). Now, I have seen lots of MathCounts questions and not all are so simply expressed, many of them do rely solely on fast and accurate arithmetic with some logical reasoning mixed in.

There's that theme you've heard from Michael Rice and myself over and over. Make sure all kids have a strong mastery of arithmetic. Period.

Not all kids are cut out for Math competition, even the strongest of math students, because not all students enjoy the time pressure. But many kids could find these and other problems (un-timed) interesting, creative, confidence building, thought-provoking, a vehicle to deeper reasoning skills, etc. Provided that they have a strong mastery of arithmetic.

As for why this student characterizes competition problems as more creative than regular school math, I can only hypothesize that his school is teaching a constructivist math in the mistaken belief that having kids create their own beliefs in algebra even though they haven't mastered arithmetic is making math education interesting and creative. (Oh wait, I just dug up the info from the school website, they use Connected Math).

The Int II classes at Eckstein open each day with a Mathcounts problem. I have been able to observe lots of problems and how the kids solve them. Sometimes the problems work well pedagogically, but too often, the kids don't use any logical thinking and go directly for the calculator (allowed in class, not in competition) and 'guess and check'. The overuse of guessing significantly detracts from the usefulness of the problem-solving exercise. On two occasions, student teachers have come to observe these classes. In both instances, I struck up a conversation and chatted about math and math teaching. However when I shared my observation that for these kids, overuse of 'guess and check' has detracted from their learning, both visibly bristled. (sigh)

There's a similarity with Jerry Large's column about the Bryant math team. The cream of the crop in math get to leave the constructivist curriculum 40% of the time to get solid instruction in arithmetic and how to use arithmetic to solve problems, while their less fortunate classmates are trying to create the arithmetic laws from scratch. Which group is being more creative?

Anonymous said...

not to sound sarcastic, but

looking at the kids who succeed in math lets you know what works for the kids who succeed, and 10 or 20% seem to always do well regardless of what we adults do to mess things up.

please please please identify precisely WHAT you want, HOW you want it, HOW MUCH time it will take per student / per class / per day / per year,

AND PAY FOR IT.

I've suffered through hundreds of hours of magic math ed classes

constructivist destructivist obstrutionist up-paid-for-ist

and the amount of baloney out there would take care of a weeks worth of wonder bread production.

pay for it.

anonymous for now.