Computational math

Computational math (or comp math) is a type of math question which asks players to solve a mathematics problem instead of identifying a conceptual answer from verbal clues. These questions are also referred to as "pencil and paper ready" questions, as all NAQT computation questions begin with that phrase - however, this term also refers to questions which require players to write down a list and science questions that require use of a scientific law, formula, other computation to get a numerical answer.

Comp math can be considered the counterpart of "theoretical math".

Theory

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.

Status in modern quiz bowl

College

Computational math is effectively non-existent in college quiz bowl. There are no computational tossups of any kind in any set. There are occasional "pencil and paper ready" science bonuses in both NAQT and housewrites which require some level of calculation to answer correctly, but this is the extent of comp math.

High school

The amount of computational math in the high school game varies significantly from format to format and from state to state. The majority of states which participate in good quizbowl do not have any comp math, the culmination of a steady decline in its popularity that started in the mid-2000s. This means that top teams which do not participate in a state format can go the entire season without playing a computational question.

Many state formats still have significant amounts of comp math. Computational questions comprise up to 20-25% of the entire distribution of the MSHSAA state series. VHSL retains computational math.

By contrast, almost every high school housewrite has zero computational math. PACE does not include any computation questions in their tournament sets and HSAPQ (while it was still extant) did not either. 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.

The HSNCT still uses computation bonuses at the rate of about 1 such bonus per game - computation tossups were eliminated from 2010 forward based on several years of surveys given to attending teams about their preferences.. The Old PACE format for] NSC featured a computation bonus in its "Category Quiz" round until it was phased out in 2010. 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.

Historical status

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.

External Links

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

• A 2004 thread entitled "The Role of Math in High School Quizbowl" was sadly lost during the Great Fuckup of 2004
• Any thread on high school quizbowl in Illinois
• "Computational Math Crisis!"
• "Computational math...Illinois and elsewhere"
• "NAQT High School Math Questions"
• "Format of science questions" (somewhat interestingly, discusses the place of computational science in college quizbowl)
• "Computational math in high school quizbowl"
• "Pyramidal Math Tossups"
• "Yes, it's another thread about math"
• "An Open Letter to NAQT"
• Math Computation, Round 23748234 (contrary to popular belief, the number of times math computation has been discussed remains at most only in the low thousands)
• HSAPQ's policy on math tossups, written in late 2008, in which the company set its policy refusing to write computational math tossups and explained why