Computational math

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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 can also refer to questions which require players to write down a list, or science questions that require use of a scientific law, formula, or 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. This is because there is only a single problem being described by a tossup - the bulk of question consists of simpler rephrasings or hints on the methods required, rather than clues. This objection has largely prevailed over arguments for computation - for a more in-depth look at arguments for and against comp math, see the "Historical" section below.

Computation bonuses have survived longer in ostensibly-good quizbowl sets such as the VHSL sets produced by HSAPQ and NAQT and the HSNCT. In general, though, most sets with a national audience have abandoned computation bonuses simply because 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 computational questions.

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.

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.[1] 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.

State formats

Many state formats still have significant amounts of comp math. Until 2022, computation comprised up to 20-25% of the entire distribution of the MSHSAA state series; it has since been lowered to NAQT's standard 1 tossup and bonus per packet. VHSL also retains computational math.

Historically, the IHSA state series used math questions that were almost exclusively computational. That coupled with occasional computational science questions meant that over 20 percent of all questions were computational. Pressure to adhere to quizbowl standards caused the IHSA to agree to include at least one non-computational math tossup per round (out of the 4 math tossups in each round). Controversy arose in 2012 during a match at the IHSA State Finals between IMSA and Auburn when moderator Tom Egan noted that the packet in use did not meet the set’s Terms and Conditions because all its math tossups were computational. The head editor, Sister John Baricevic, acknowledged the mistake but had no recourse since all the replacement math tossups were also computational. In 2016, Noah Prince served as the math editor for the IHSA and wrote the first state series without computational math tossups. That practice has continued since 2018 under the head editorship of Brad Fischer.

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. Eventually, the growing consensus of players, teachers, and coaches across state lines solidified in their opposition to math computation questions, driving its decline in nationally-oriented formats and tournament sets. Computational math is often controversial in formats that do have it, while it is rarely missed in those that do not.

There are not many legitimate arguments for the existence of computational math tossups. A common tactic of proponents is to employ various forms of avoision: the most common such argument is to accuse those who oppose computational math of being unable to do math. The presence of many math majors, math teachers, and former Mathcounts competitors explaining why calculation tossups are illegitimate does nothing to dissuade this argument.

Here are some major arguments that have been advanced in favor of computational math, with associated rebuttals:

Argument For Argument Against
Because quizbowl is a reflection of what is learned in school and computational math is an important part of that education, it should be included. Other quizbowl subjects that appear in the classroom like history or chemistry are written to focus on important concepts and deemphasize trivia like dates or specific atomic weights. Removing computation from the math distribution is a consistent application of these principles.
It is not feasible to write enough good questions to fill the need for math questions without relying on computational questions.
  • It being difficult to produce quality questions is not sufficient argument - the use of good, pyramidal questions is better than the use of bad, apyramidal questions.
  • There is no reason that there would have to be the same number of math questions after removing computation. In formats without computation, math is given a smaller portion of the distribution as part of other science and there are no problems creating enough good questions to fill it. Even sets with higher fractions of math like Scobol Solo have not run into issues.[2]
Quizbowl can be defined it as an activity that, on a certain minority of questions, includes computation, rather than one that does not. Quizbowl is typically defined as an activity which tests knowledge. Further, "good quizbowl" is defined as quizbowl that preferentially rewards knowledge over other skills. Because computational math requires an additional skill beyond the simple recall of facts and association of facts with an answer, it is not good quizbowl.
Any relevant topic with a single answer that can be quickly judged as "right" or "wrong" can be used in quizbowl - this is true of computational math. The principle underlying pyramidality is that questions should be able to distinguish between players based on their knowledge of a subject. It is not sufficient for a topic to have an answer which can be ruled correct or incorrect to be considered good quizbowl (or even quizbowl).
Computational speed is not the only deciding factor for who answers a computational problem first (assuming they are well written); recall of algorithms and equations also matters and is a form of knowledge.
  • 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.
  • 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.
Giving the answer to a specific computation is less cumbersome than asking for the algorithm or formula used to compute it. This is only true in some sitatuations - there are many ways to write questions asking for algorithms, formulas, or the concepts that underpin them which are no more cumbersome than answering with a number, and which do not require computation.
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. 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. 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.
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. 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.

External Links

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

References

  1. Computation questions and the 2010 HSNCT by Important Bird Area » Fri Jul 10, 2009 7:22 pm
  2. 40 Maths by Stained Diviner » Mon Nov 12, 2012 5:28 am