As a former Mathcounts national champion and USAMO Honorable Mention and prospective math major, I feel that I can't be sour-graped against like other opponents of math computation. I was good at math computation in high school (as anyone who has played against me can tell), and I know a lot of math theory as well. That being said, there are many problems with math computation questions:
1. Too often, they devolve into
Numberwang! questions. For example, one of QG's favorite types of questions is to multiply by 3.14. How does this test math beyond a fourth-grade level. Often times, the computation is harder than the actual math theory, meaning that the person who wins the question can do better arithmetic than their opponent.
2. They are rarely converted and are mystifying and unhelpful for those who aren't already in the inner circle of math computation players. At
New Trier Solo, Algebra and Geom/Trig (the two computational categories) were both in the bottom quartile of question conversion. This means well-written mathcomp tossups go dead a lot of the time, and even moreso bad mathcomp tossups from our favorite question provider. Also, just hearing the answer is unhelpful for someone who doesn't already know how to do the computation. For example, if I were to hear a tossup on Edward Albee and didn't know the answer, I could at least pick up some titles and plot descriptions that may encourage me to learn more about Albee in order to get more tossups or even for personal edification. On the other hand, if I don't know that i^93 = i, learning that isolated fact is not very helpful. It remains a mystery how to solve similar types of problems, since no hints at the actual procedure are given. As a learning activity, I think pyramidal questions in all other subjects reward players for learning and encourages them to learn (for example, I read Achebe's "Things Fall Apart" after hearing several questions on it). Math computation fails in this regard.
3. The math theory canon is way too small and needs expansion. In college, I absolutely enjoy hearing questions on stuff like Legendre symbols, the nine-point circle and Abelian groups. In the high school canon, the limit appears to be much narrower. In literature, high schoolers are expected to have passing familiarity with many works of literature, unlike in math, which appears to be restricted to the standard curriculum. It is a shame, as there are so many answers that would be good answers, and unlike in a mathcomp tossup, not knowing the answer can serve as a guide for learning more instead of as more mystification.
Overall, math computational tossups are bad and I would like to see more math theory tossups. Of course we can't write 25% math, but we can certainly write 1/1 math theory a round and redistribute the extra questions to stuff that is underrepresented (like RMP in Illinois).
--Greg
<div class="editby">Edited by
<a href='http://s4.zetaboards.com/Academic_Compe ... jaguar3</a>, Apr 4 2009, 01:12:20 AM.</div>