USAMTS Round 1

by rrusczyk, Jun 17, 2006, 3:21 PM

Well, another learning experience for the USAMTS. This is our first year writing the questions ourselves, and judging by the buzz as the number of entries, I think we erred a bit in the structure of the first round.

We had many more students register for the first round, but somewhat fewer students actually participate. This strongly suggests that there weren't sufficient approachable problems at the beginning of the test to keep the newer students involved. Basically, I think that if we graded the problems on a 1-10 scale, we had something like two 4's, two 6's, and a 7. What would have been more appropriate would be a 1, a 3, a 4, a 5, and a 7. Sigh. We'll structure that first round better next year - just have to live with it this year. Difficulty calibration is dicey no matter how experienced you are. On the other hand, the results suggest we nailed the SD Math League Round 1 and the first WOOT test. They both had nice distributions.

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You have to experiment to get information, even if the experiment is unintentional. Previously, we selected the Round 1 problems from the problems that were easy to grade. This year, we didn't. (Looking over the solutions posted at the AoPS forum, I see certain problems that I hope the AoPS will grade instead of sending them to us NSA graders.) The easy-to-grade problems might tend toward other properties, such as being approachable.

I have little information on why students decide not to attempt a USAMTS problem, because as a grader I see only the submissions. However, I did spend four years with each of my daughters, trying to persuade them to participate in the USAMTS. They are strong in mathematics, but their true interest is art, so I failed.

They did look over the problems, and after a few minutes of not seeing a good solution for any of them, they gave up. Quizzing a daughter with an old USAMTS problem set, so that we could talk over the problems, I saw that she did have some workable ideas for starting, but she was not confident in the ideas. Her estimate of the low chance of success made the ideas not worth the work of testing them.

Thus, I suspect that it is not the difficulty of the entire problem that scares off the prospective participant, but the difficulty of starting the problem. Some students said in the AoPS forum that solving Problem 5/1/17 was easier than they expected--after they got started.

You should also take into account that the people who registered for Round 1 last year were more dedicated than average, because they managed to find the USAMTS after it moved off the NSA web site. The NSA web site was frozen at the end of Year 15 all the way through Round 1 of Year 16. (The glacial slowness of the bureaucrats who maintain the NSA web site is one of reasons Blair gave the USAMTS over to your care.)

Erin Schram

by Erin J. Schram, Jun 17, 2006, 3:22 PM

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I think you hit the nail on the head here - there were fewer problems than usual (for many students, none) that students could look at and immediately know what to do. This may well have been the decisive factor. I'm not sure exactly how to feel about that - problems that require you to think a while before starting are *good* problems. Perhaps we just need more of a gradient in difficulty, particularly on the first round.

by rrusczyk, Jun 17, 2006, 3:22 PM