Computational Mathematics

[Ciorwrong]

Unrelated, but I was having a discussion with my friend today about the purpose of math and some points made in this thread have made me reconsider my position.

On task....
I can't believe someone who is actually good at math would like computation tossups. As has been said earlier, math tossups primarily ask about topics that are discussed in early high school courses. There are sadly math computation questions in our local league, and most of the questions are Algebra I level. The geometry questions require you to solve for angles, and the trig problems involve memorizing the unit circle (which is actually important to do to succeed in higher level math. It helped me at least.) The only calculus questions involve simple differentiation and integration. What does this stuff test? I am dual enrolled in a Multivariate Calculus course, and I still can't power linear systems problems without a calculator and I consider myself good at mental math (I try to multiply two digit numbers mentally). I may be able to find the derivative of ln(x), but it doesn't help me that I know more math knowledge when Joe Schmoe also knows that the derivative of ln(x) is 1/x.

I actually support people learning mental math shortcuts because there are a lot of mistakes that I have caught because I calculate things mentally (mostly change), and it's a good mental exercise. There is no way it should be asked about in quizbowl. If we discourage buzzer races on titles of novels, why encourage buzzer races on sin(pi/6)?

[Adventure Temple Trail]

Unfortunately, in my understanding, pure memorization is what many conceptual math tossups are down to now. People don't care to understand the concept, they just memorize the clues that come up often.

anyone can remember facts off of quinterest without understanding the material at all.

Pyramidal questions don't prove deep understanding either; you don't need to know anything about calculus to remember that the Weierstrass function is "associated" with derivatives. It is extremely difficult for a writer to find unique clues that are not too obscure to be gettable, so inevitably "fraudulent" knowledge will come up from time to time. Though concepts of computational math can be repeated, one must apply an understanding to arrive at the solution in ALL cases.

These objections are (a) true of every category, not just math and (b) not nearly as big a problem as you seem to think for quizbowl's legitimacy. Using nothing but binary association of keywords to expand one's ability to answer questions is actually not a very effective play strategy, because (i) teams who understand the description before the name is dropped will always buzz earlier (ii) new clues are introduced all the time on which the associations won't work (iii) it results in lots of mistaken negs as soon as a change of context is introduced (Weierstrass made a lot of contributions unrelated to derivatives -- a quick Quinterest search reveals his name as a clue for tossups on "polynomials," "convergence," and "sequences" too, within a small sample of high school tournaments). This is why teams which are better than competent don't rely on binary association alone (or worry much about things being "fraudable," a rather nebulous term which is often just used to mean "knowable"). Instead, they actually look up the clues they hear to understand what they just heard, and flesh out the surrounding contextual information for said clues, so they can prepare to answer questions that get at important material in different ways (i.e. "learn things"). The cynical belief that generating long tables of "X IS ASSOCIATED WITH Y" in one's head is the necessary or even sufficient condition for quizbowl success is actually an incorrect one. It helps, yes. But only to a point.

Will people who don't know a lot about subject matter sometimes (often) internalize words that they buzz on to answer questions on other words? Yes. Is that inevitable? Probably. Is that even a bad thing? Not really -- it's relatively easy to beat or outpace by taking any amount of effort beyond what the mere associators do. And even the most basic internalizations of binary associations, on the level of "Chinua Achebe is from Nigeria" or "derivatives are the inverse of integrals, and both are important to calculus" are actual facts which leave quizbowl players more informed than they were before they came into the game.

Supplementally: What people mean when they say "Computation tossups cannot educate" is this: People might hear the word "Weierstrass" a lot in a conceptual math question and (optionally) choose to say something like "Hmm, I keep hearing about this Weierstrass guy who has a weird mathematical function; I'm curious what makes it so weird." And that opportunity to discover something more about the sweep of human knowledge is a beautiful thing, even if not everyone takes said opportunity. (The spite-laden quizbowl variant, "Hmm, I keep hearing the word 'Weierstrass' and I want to win badly; time to hit Wolfram MathWorld as a means for crushing my enemies!" is also fine.) By contrast, no one is getting an opportunity to broaden their horizons by learning to calculate the areas of regular polygons or estimate the time it takes "Bob" to "paint a fence" -- that's the same basic algebra or geometry done over and over. Computation tossups are therefore inherently far worse at good quizbowl's sub-objective of giving players the chance to expand beyond what they already know.

[merv1618]

(A) The number 2 is an even number.

Statement A is not a fact about reality.

So how'd you end up at that particular conclusion?

[pajaro bobo]

2 isn't real

[ninjaluc79]

There is this perception in our country that "good at computational math = good QB player", but that's probably due to our highly outmoded quiz bowl competition. You see, here in the Philippines, especially in high school QBs, teams with at least one good Comp Math player are almost always assured to be a contender in their region. That's also probably because we're an Asian country, and Asian countries are known to focus more on Comp Math than say, America or Europe IINW.

Well, I do agree that those who are good at computational math are also good at math theory, because how else are you going to know how to compute if you don't know the theory behind it? Of course there's rote memorization of formulas, but that does you no good if you forget them on quiz bowl day. That's where math theory is very important.

I also agree that Comp Math quizzes tend to punish quizzers who are good at math theory but take too long to do calculations. That's why I prefer a multiple category QB since Comp Math specialists can't just rely on their Comp Math strengths alone. I would rather not do away with Comp Math completely though, since that's how QB organizers here measure the players' problem solving skills, and I just can't think of anything else.

Well, I say a Math QB must be organized such that players who are confident enough in their Comp Math skills can play, but at the same time are forced to study more on math theory so they can't just rely on their Comp Math abilities alone.

On a side note, it's a good thing that here in our country, quizzes dealing with pure math are saved for elementary and high school students. The Math Olympiad is something I would save for the Chinese-born students unless our homegrown quizzers can match their mathematical prowess.

So, what is your take on the "good at computational math = good QB player" perception of some people?

[coldstonesteveaustin]

I think the point is that although computational math has some academic merit, comp math tossups have no place in quizbowl, because such tossups are incompatible with a buzzer-system based game, due to the fact that comp math does not test depth of knowledge but speed of calculation. If there's a format that incorporates computational math worksheets into the buzzer-based quizbowl game, that could work, but the benefits are only to those who are good at comp math and educators who think that comp math should occupy a status greater than or equal to conceptual math in the high school curriculum. Therefore, pure quizbowl without attempts to incorporate computational math tossups is the superior format. Computational math bonuses also suffer from the problem that the time that is allowed is often not enough to solve the problem for many teams, resulting in an average lower bonus conversion for those bonuses. Therefore, in the realm of pure ACF/PACE/HSAPQ/other mACF quizbowl, good computational math players who are good at nothing else (including conceptual math) will fail miserably at quizbowl.

Nevertheless, there have been attempts to write pyramidal computational tossups. NAQT used to write them by asking the question, revealing how to solve the problem, and then restating the question. Others have tried to embed multiple problems which all have the same answer within a single tossup, but any single clue may fly past too quickly before the player gets halfway through deciphering that clue, so the player must pay attention to the next, possibly easier clue. In short, people have tried, and no one has worked them into quizbowl seamlessly such that most people are happy, so it's probably impossible.

[ninjaluc79]

I think the point is that although computational math has some academic merit, comp math tossups have no place in quizbowl, because such tossups are incompatible with a buzzer-system based game, due to the fact that comp math does not test depth of knowledge but speed of calculation. If there's a format that incorporates computational math worksheets into the buzzer-based quizbowl game, that could work, but the benefits are only to those who are good at comp math and educators who think that comp math should occupy a status greater than or equal to conceptual math in the high school curriculum. Therefore, pure quizbowl without attempts to incorporate computational math tossups is the superior format. Computational math bonuses also suffer from the problem that the time that is allowed is often not enough to solve the problem for many teams, resulting in an average lower bonus conversion for those bonuses. Therefore, in the realm of pure ACF/PACE/HSAPQ/other mACF quizbowl, good computational math players who are good at nothing else (including conceptual math) will fail miserably at quizbowl.

Nevertheless, there have been attempts to write pyramidal computational tossups. NAQT used to write them by asking the question, revealing how to solve the problem, and then restating the question. Others have tried to embed multiple problems which all have the same answer within a single tossup, but any single clue may fly past too quickly before the player gets halfway through deciphering that clue, so the player must pay attention to the next, possibly easier clue. In short, people have tried, and no one has worked them into quizbowl seamlessly such that most people are happy, so it's probably impossible.

Agreed. Comp Math questions tend to slow down the QB to the extent that when there too many Comp Math questions, the contest is less of a test of knowledge than a test of how fast the players can compute. You know Comp Math sucked when they gave a time limit of like 90-180 minutes. So when anyone could not get the correct answers in ANY of the Comp Math questions, yeah, the scores tend to go down. And Western-style QB's don't work like that, based from what I have observed.

Somehow, I found one QB at our hometown of Davao where there is only one Comp Math tossup per round, or a grand total of only 3 Comp Math questions. If anything, these tossups only served as some kind of bonus points since pretty much no one (save for the best Comp Math players) could give the correct answer anyway. BUT here's the catch. If your team is the only one to get that one Comp Math tossup in the final round, you're pretty much guaranteed to win the contest unless everyone else are like 200-300 points ahead of you.