Computational math

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Computational math questions ask players to solve a given mathematics problem instead of identifying a conceptual answer from verbal clues. Computational math is also used to describe science questions which require using a scientific law or formula to get a numerical answer, because the term "computational science" just isn't as catchy.

All NAQT computation questions begin with the memorable phrase "Pencil and paper ready.", although the phrase occasionally appears on other subjects and serves to warn players to write down a list.

Non-computational questions on mathematics topics, such as the ones in this thread, are often called "theoretical math".

Computational Math in the High School Game

The amount of computational math in the high school game varies significantly from format to format and from state to state. In some formats and states, such as the MSHSAA state series, computational math can take up to 20-25% of the entire distribution.

The general trend has been a steady decline in the prevalence of computational math in good quizbowl circuits from the mid-2000s to the present. Almost every high school housewrite has abandoned the writing of computational math questions, and neither HSAPQ nor PACE includes any computation questions in their tournament sets. NAQT is the sole national question vendor which still sells sets containing computational math tossups, but individual hosts of NAQT sets may choose to skip over the computational questions at their own tournaments.

This state of affairs means that many of the country's best teams, presuming they do not play a less-advanced state format involving computation, can play an entire year's worth of tournaments before nationals without ever lifting a pencil to solve a computation problem within a quizbowl match. The HSNCT still uses computation bonuses at the rate of about 1 such bonus per game, after eliminating computation tossups from 2010 forward; the move came after surveying attending teams about their preferences for several years [1]. The PACE NSC featured a computation bonus in its Category Quiz round until 2010, when the new format eliminated the last computation from the championship. Therefore, it is eminently possible for the best high school team in the country to become a legitimate national champion without focusing on computational math at all.

Most of the objection to computational math comes from the use of computational *tossups*, which are inherently non-pyramidal (all of the text in the question is effectively describing the same single math problem even if there are multiple lines of clues rephrasing it or giving hints). This objection (and others, such as the argument that computational math tossups are uniquely unable to teach players something new, and the truth that top math competitors often lose out on computation questions due to lack of buzzer speed) has largely prevailed over arguments for computation (e.g. "students compute a lot in school, so they ought to in quizbowl as well"). Computation bonuses have survived longer in ostensibly-good quizbowl sets such as HSAPQ's VHSL sets and HSNCT, though most other sets with a national audience have abandoned computation bonuses too, for the reason that it is difficult to solve any non-trivial math problem in 5 or fewer seconds and giving teams more time often delays the game.

The role computational math should play in high school quizbowl has been one of the most hotly debated subjects in the history of the Quizbowl Resource Center forums. However, a growing consensus of players, teachers, and coaches across state lines have solidified in their opposition to math computation questions, a growing trend which has preceded and driven its decline in nationally-oriented formats and tournament sets. Largely, computational math is controversial in formats that have it, while formats that do not have it are happy not to have it.

Because legitimate arguments for the existence of computational math tossups have almost entirely faltered, their proponents often use various forms of avoision to argue for them. A common argument for these tossups accuses those who oppose computational math of being unable to do math. The presence of many math majors, math teachers, and former Mathcounts competitors among the good quizbowl proponents explaining why calculation tossups are illegitimate does nothing to dissuade this argument.

Arguments Against Computational Math

  • Computational math requires an additional skill beyond the simple recall of facts and association of facts with an answer; therefore computational math is not quizbowl and does not belong in quizbowl.
  • Computational math questions rely on a set of memorized "tricks" for answering certain kinds of problems instead of a unique association between a set of clues and its answer; therefore computational math is not quizbowl and does not belong in quizbowl.
  • Pyramidal computation tossups are far more difficult to write, and in the opinion of some are impossible to write; therefore at best computational math is bad quizbowl.
  • Clues in computation questions cannot stand alone; therefore at best computational math is bad quizbowl.
  • The canon of askable computation questions is too small in most formats to adequately differentiate between teams of roughly similar skill levels, and has already expanded to near its maximum; therefore at best computational math is bad quizbowl.
  • Even if it were more universally accepted that answering a computational question is based upon the ability to recall an algorithm, and that it is expedient to give the solution to the problem, rather than the algorithm itself, it is undeniable that computation speed can be considered a factor in the speed at which the question is answered. This creates a situation where questions involving computational math become "different" from other questions, and thus may not be appropriate.
  • Because teams that are very strong in Computational Math can completely dominate the category, it can play a major role in deciding matches even when it is a small part of the distribution.
  • Most people who understand both good quizbowl and math, including math majors and math teachers, oppose computational math and would like to see more questions on math theory instead.

Arguments in Favor of Computational Math

  • Computational math is an important part of a high school education. High school quizbowl should be seen as a reflection of what is learned in a high school education, so computational math should be included. It is difficult to write a large number of good math questions that are appropriate for high school and not computational, so the only way to make the math distribution significant is to use computation.
  • Computational math has a single, uniquely identifying answer, unlike other eschewed parts of a high school education such as "writing an essay" or "debating the effectiveness of a policy". Any relevant topic with a single answer that can be quickly judged as "right" or "wrong" can be used in quizbowl within the flow of the game.
  • It is not universally agreed upon that computational speed is the deciding factor which determines which player will answer a computational problem first; rather it can be the recall of algorithms and equations (ostensibly "facts", though this is far from universally accepted), and the confidence with which one recalls those "facts". To avoid cumbersome answers which are the algorithms or equations themselves, it is preferable for expediency to have the players give the "answer" to the computation, rather than the algorithm itself. This argument assumes that questions will be well-written, since it does not apply to problems in which the most challenging aspect is computation.
  • While it is possible to define quizbowl as something that does not include any computation, it also is possible to define it as an activity that, on a certain minority of questions, includes computation.
  • An argument can be made that the canon of askable computation questions is large enough to be legitimate, especially when you have teams that are used to such questions and recruit strong math students.
  • People who don't like computational math "hate math", are "bad at" math, or are "nerds" who only care about history, science, and art, and don't know anything with applicability to the real world, like the probability of drawing a red ball out of a hat. This is by far the most common "argument" used by computational math proponents.

College

Computational math has largely disappeared from college quizbowl. Occasionally NAQT will throw in a science bonus which requires some thought or familiarity with a formula to obtain the answer (e.g. "if an object exerts a force of 80 Newtons, and its mass doubles, how much force will it now exert?"), but there are no computation tossups and very few computation bonuses in the college game. .

External Links

The following is a non-exhaustive list of discussions and articles about the place of computational math in quizbowl.

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