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Math in High Quality Quizbowl

Math is an important subject and rightfully has its place in quizbowl, in the form of questions based on math theory, and not in the form of computational questions.

This idea may seem radical to players and coaches who are used to MSHSAA format, which contains a 20% share of math almost entirely consisting of computation questions. Matt Chadbourne, a graduate of Missouri S&T with bachelor's and master's degrees in applied mathematics, explains why math computations are not appropriate for use in high quality quizbowl.

The goal behind high quality quizbowl is to reward the player who knows the most about the subjects at hand. Math computation questions, however, boil down to who can crunch numbers fastest, not whose knowledge is best. As I have learned in my studies of mathematics, "who can crunch numbers fastest" and "who has the best grasp of the concepts involved" are often not the same person. In fact, the player with best knowledge quite often is not the player who has the most innate computational speed, and is thus not rewarded with points. Since math computation questions reward players with raw speed over players with deep knowledge, they are not appropriate for use in high quality quizbowl.

Math is an important part of the distribution, and should consist of questions involving math theory. Theory questions can be pyramidal, while computational questions by and large cannot. Pyramidal math theory questions, unlike computational questions, do reward the player with the best knowledge of mathematical concepts, and therefore should be used instead of questions focusing on computation.

MOQBA recognizes the prevalence that math computation has traditionally held in Missouri quizbowl, and therefore its presence in a tournament will not automatically preclude MOQBA certification, provided the other standards are met. However, tournament directors are highly encouraged to use questions that exclude or greatly minimize the presence of math computation in favor of math theory.

Comparison of the two question types

To illustrate the difference between computation and non-computation math questions, consider two questions that test knowledge of the same concept. First, a theory-based question ("Tossup 1"):

One form of this mathematical operation uses its namesake's concept of measure and is known as the Lebesgue variety, while a generalization of its normal variety using partitions is named after Stieltjesa. Fubini's theorem states that multiple instances of them can be done in any orderb, and ones involving products of functions are often performed "by parts."c Usually represented as the area under a curve,d For ten points, name this operator, the inverse function of differentiation.e

ANSWER: integration

Compare this to a computation question applying the concept ("Tossup 2"):

Calculate the integral from 0 to 2 of 3x2 + 2x.f You have 15 seconds.


These two tossups both test knowledge of integration, but tossup 1 is better than tossup 2 for this purpose. Players with deep knowledge of calculus have roughly five areas to buzz - somewhere before (a), somewhere between (a) and (b), somewhere between (b) and (c), somewhere between (c) and (d), and somewhere between (d) and (e). Tossup 2, however, offers a good player only one realistic place to buzz if he hopes to receive points - immediately after (f). Any good math player will buzz on tossup 2 exactly at that point, as the resulting computations can easily be done in the three seconds you are given to answer. Therefore, tossup 2 cannot hope to differentiate between levels of knowledge, since all of the good players will be buzzing at the exact same time.

Ultimately, the computation tossup is the equivalent of asking a one-line tossup, like this one-line version of the first tossup ("Tossup 3"):

What is the inverse function of differentiation?

ANSWER: integration

The computation tossup is equivalent because it offers exactly the same opportunity as this one-line tossup for good players to be rewarded with points by being able to buzz earlier - that is, none at all. Tossup 3 is clearly inferior to tossup 1, yet tossups 2 and 3 are pretty much equivalent in their ability to tell which player knows the most. Therefore, tossup 1 (the pyramidal, non-computation tossup) is superior to tossup 2 (the computation tossup).