Math Question Discourse: From "An Open Letter to NAQT"

Dormant threads from the high school sections are preserved here.
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Re: An Open Letter to NAQT

Post by yisun »

There's still no good argument as to why we need to go through all these contortions to include (still entirely hypothetical) "good" math calculation at all. Sorry if this is going around in circles, but..there just isn't. It doesn't need to be there, it's not quizbowl, and collegiate quizbowl and the tournaments in high school that don't use calculation are doing just fine without it. If your school is not good at quizbowl, then get better, don't recruit your math team and demand that their game be played for 1/5 of the round.
I imagine that tournaments would do just fine without philosophy as well, yet this isn't an argument for not including philosophy in the distribution. If you remove computation, you reduce the "math" to either math history or a very small answer space. Computation is what high school math (mostly) is, and it's the best way at this level to test *knowledge* of math (is this not what quiz bowl is about?).

As for pyramidality, it's designed to make sure that the player with the *most knowledge* will answer the question first. I claim that as long as the questions are sufficiently hard, this is exactly what will happen.
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Re: An Open Letter to NAQT

Post by theMoMA »

Philosophy can be written without compromising the core tenets that make good quizbowl good quizbowl. Math computation, for the most part, cannot. Some things are academic and can be ranked in a competition but just don't fit the format of the game. We don't ask teams to write essays, debate each other, or solve complex economic problems, which are all academic activities that people do compete in. But those activities (just like math computation) aren't quizbowl.
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Re: An Open Letter to NAQT

Post by Mechanical Beasts »

Another issue is that you can't really solve the computation problem by making the problems harder, or longer, or ten rephrasings of the same problem. First, as Yi pointed out, it's still about a skill. Second, these tossups go dead. A lot. Or teams just neg them, guessing nice answers like 6, or double their opponent's answer. Reading at the HSNCT, I think we saw three or four computation questions answered all day--by the end of the tossup. These teams are the teams that WANT to participate on NAQT format questions, meaning that they don't hate computation too much; moreover, they're at a national tournament--one with a big field, but still.

I'm sure you could have tossups that begin "It is the base seven discrete logarithm of fifteen modulo forty-one" and end the tossup with "FTP, give the integer that follows two and precedes four," and then they'd be pretty damn pyramidal. But: first, nonetheless computation speed would be what matters, in the (relatively) common case of equal knowledge of how to do such a problem; second, it would never be answered on the early clues, wasting time; third, without an absurd giveaway it probably would never be answered at all.

NAQT, here's a challenge: release conversion statistics for computation questions. Let's see how they stack up.
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Re: An Open Letter to NAQT

Post by Captain Sinico »

yisun wrote:I imagine that tournaments would do just fine without philosophy as well, yet this isn't an argument for not including philosophy in the distribution.
Right, but that's not the argument against computational math tossups; it's a proximate cause due to which the argument isn't moot. There's nothing entitatively essential about any quizbowl subject. However, only computational math unavoidably tests knowledge convolved with a not-essentially related skill (and therefore requires concomitant changes in game mechanics, etc.)
yisun wrote:If you remove computation, you reduce the "math" to either math history or a very small answer space.
yisun later wrote:Computation is what high school math (mostly) is, and it's the best way at this level to test *knowledge* of math (is this not what quiz bowl is about?).

As for pyramidality, it's designed to make sure that the player with the *most knowledge* will answer the question first. I claim that as long as the questions are sufficiently hard, this is exactly what will happen.
These arguments are inconsistent. If enough players know the "hard" concepts underlying "hard" computation tossups in order to make asking them feasible (as you're implicitly claiming,) then the cannon of askable non-computational answers is not as limited as you initially claim (since all such concepts themselves can be asked about.) Conversely, if not enough people know these "hard" concepts, then the computation questions you propose are insolvent as questions (will go dead much more often than other questions, etc.)

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Re: An Open Letter to NAQT

Post by Mechanical Beasts »

ImmaculateDeception wrote:Conversely, if not enough people know these "hard" concepts, then the computation questions you propose are insolvent as questions (will go dead much more often than other questions, etc.)
And they are! However, I've solved the problem.

QUESTIONS THAT START WITH WHY MAKE GOOD TOSSUPS.

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Re: An Open Letter to NAQT

Post by Stained Diviner »

My answer does not fit within the 6000 word constraint of this board.
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Re: An Open Letter to NAQT

Post by pray for elves »

everyday847 wrote:"All elliptic curves with integer coefficients correspond to weight-two modular forms. Why?"
It is obvious from the definitions.
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Re: An Open Letter to NAQT

Post by Ike »

An acquaintance of mine from this board told me if you are right and you compromise to make a change, you still end up wrong. This is all I have to say here.
I won't argue with there; my ideas were thrown out hopefully to "ease" the computation problem, not utterly destroy it (although Id love to see that)
it's not quizbowl
One problem is that many people in the HS quizbowl community (and out of it for that matter) interpret Quizbowl as a reflection of what is taught at the HS school curricula level; such an interpretation leads to this argument for math distributions - it would really help if coaches and teams recruiting that they mention Quizbowl and HS Academics overlap on the edges - and not to expect HS academics. (I mean who wants more HS?)
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Re: An Open Letter to NAQT

Post by yisun »

theMoMA wrote: Philosophy can be written without compromising the core tenets that make good quizbowl good quizbowl. Math computation, for the most part, cannot. Some things are academic and can be ranked in a competition but just don't fit the format of the game. We don't ask teams to write essays, debate each other, or solve complex economic problems, which are all academic activities that people do compete in. But those activities (just like math computation) aren't quizbowl.
I don't understand this comparison to writing essays or debate. As far as I understand it, the core tenet of quizbowl is to test knowledge in a pyramidal manner so that people with more knowledge will get questions first. I think, done properly, math computation should accomplish both of these goals; is there some other aspect that makes computational math inherently not quizbowl?
everyday847 wrote: First, as Yi pointed out, it's still about a skill.
I think it's not really entirely clear how to differentiate knowledge and skill at the high school level of math. Take trigonometry, for example. If someone can solve a problem with the correct application of a trig identity, is that knowledge or skill? I claim that for a lot of problems, knowledge is a bigger factor assuming some minimal baseline of math abilities.
ImmaculateDeception wrote: These arguments are inconsistent. If enough players know the "hard" concepts underlying "hard" computation tossups in order to make asking them feasible (as you're implicitly claiming,) then the cannon of askable non-computational answers is not as limited as you initially claim (since all such concepts themselves can be asked about.) Conversely, if not enough people know these "hard" concepts, then the computation questions you propose are insolvent as questions (will go dead much more often than other questions, etc.)
The problem here is that not all math concepts are easily named. Consider trig again. I think most people would agree that there is more to know about the subject than {sine/cosine/tangent, law of sines/cosines/tangents, double/half angle formula}. But one can't really write a tossup on "that identity that goes like sin^2(x) + cos^2(x) = 1" or the fact that the area of a triangle is (1/2)ab sin C, though these still remain widely known facts.
everyday847 wrote: Another issue is that you can't really solve the computation problem by making the problems harder, or longer, or ten rephrasings of the same problem. First, as Yi pointed out, it's still about a skill. Second, these tossups go dead. A lot. Or teams just neg them, guessing nice answers like 6, or double their opponent's answer. Reading at the HSNCT, I think we saw three or four computation questions answered all day--by the end of the tossup. These teams are the teams that WANT to participate on NAQT format questions, meaning that they don't hate computation too much; moreover, they're at a national tournament--one with a big field, but still.
I haven't seen this happen personally while playing, but I agree that it is a problem if teams are unable to answer harder computation questions. If this is because there is not enough time, I don't see the real issue with giving a small amount of extra time (~10 s) for computation; this might cause complications within NAQT timing, but computation questions are likely to be shorter on a whole. Adding this much time should probably be enough (conversion rates for similar questions at Science Bowl, which has essentially these rules, are quite high). If, on the other hand, it's because not enough teams know how to solve the problems at HSNCT, I'm confused. Throughout the thread, several people have argued that the questions are too formulaic and easy, leading to computation/buzzer races. One example below, there are others:
Matt Weiner wrote: I find that at the HSNCT level, you pretty much always have people racing to complete the arithmetic on the first statement of the problem, and there is no time to start over when you get the new "method." The "pyramidal" restatements are just so much filler to maybe give people a chance at power when the original question is easy enough.
So my question is, which is it? If the questions are too hard, we should get the desired scenario by making them easier. Otherwise, we can make them harder. Or maybe they are just hard if you don't know math and too easy if you do. Then the problem is that teams aren't good enough at math, and I don't see the issue with making them learn some. In comparison with the lit or history questions at HSNCT, I think the math is far easier (in terms of amount of time necessary to learn how to do it -- there was an earlier post that claimed that 1 day of studying was sufficient). But it seems like there are far more people entirely incapable of doing computational math than people entirely incapable of answering an American history question, and I think that can and should be changed.
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Re: An Open Letter to NAQT

Post by Matt Weiner »

yisun wrote:is there some other aspect that makes computational math inherently not quizbowl?
The fact that it's doing a math problem and not answering a question about factual knowledge?

Also, the fact that the "canon" of doable-in-ten-seconds computational math is about 30 items wide, making it a race every time between teams who prepare?
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Re: An Open Letter to NAQT

Post by cdcarter »

Here is the issue. Computation is not recall. Quizbowl is a game of recall. Not a game of applying anything but factual recall. This is why tossups on theoretical math is fine. Because it is recall. Of facts. Canonical computational math is something I personally hate, because even though I know how to do the problems, how to boil them down, I can't easily multiply or divide like the kid across the table from me. If the issue was I didn't know it, I would be fine with it there, I don't know 4/5 of the canon. But if I know what they want, but can't tell you what 13 mod 2 is in 10 seconds, I am going to be angry. Keep quizbowl as recall.
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Re: An Open Letter to NAQT

Post by Sen. Estes Kefauver (D-TN) »

Exactly. I've used this exmple before, but my teammate Grant always get math because he can calculate quickly, not necessarily because he knows more about the concepts (I almost always got our team's theoretical math questions, and quite often I would figure out the problem the question wants one to answer as quickly as him, or even beat him). The reason he would always get the calculation is because he is very good at a skill, not because he knows more. The reason someone should be getting tossups is because they know more than the other person.
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Re: An Open Letter to NAQT

Post by Matt Weiner »

I think "quizbowl is about recall" might be a little too simplistic (see viewtopic.php?p=27675#p27675 for one reason why) but it is getting at the basic issue, which is that *doing* something is not the point here, and if we have that in math we should start doing it in every category.
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Re: An Open Letter to NAQT

Post by Mechanical Beasts »

Matt Weiner wrote:I think "quizbowl is about recall" might be a little too simplistic (see viewtopic.php?p=27675#p27675 for one reason why) but it is getting at the basic issue, which is that *doing* something is not the point here, and if we have that in math we should start doing it in every category.
So you could rephrase it as "putting the facts you hear in the context of all the knowledge in your head" and figuring out what are possible answers given any inconsistencies ("well, it sure couldn't have been written in the 1200s because it seems to namedrop Isaac Newton"). But the mechanic is recall plus, like, some logic as to figuring out what a clue means as to what information in your head is relevant.

The reason math doesn't make sense is because you can't buzz after having done all the knowledge-activities; you still have to do some calculations. Once I've determined "the clues thus far have given me a triangle and three of its six defining measures and asked me to find its area" I can't just buzz and give a method for finding the area with the given information. The knowledge process has ended, since I've eliminated the ways to find a triangle's area (let's be charitable and assume that there are thousands so that this doesn't have the other problem of having a tiny answer space from the start) that don't work. I'm still required to do something else, and that something else is not quiz bowl.
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Re: An Open Letter to NAQT

Post by cvdwightw »

Warning: this is yet another one of those rambling, theoretical posts that I like to write, so if this isn't your cup of tea, skip it.

People who argue against computational math rightly point out that computation goes beyond what is necessary and sufficient for quizbowl, and typically use the example of "writing an essay" as something else that is done in the classroom but not in quizbowl, whereupon proponents of computational math either get completely lost or counter-argue that writing an essay and doing a math problem are not the same thing. Where the confusion lies, I believe, is in the idea that there is no right or wrong answer on an essay, but there is a single unique answer (or set of answers) for a computational math problem. People who argue for the inclusion of computational math in quizbowl often use the fact that "there's a unique answer" as a justification for including computational math; these people conveniently ignore that "answer" is only half of a quizbowl question and that they must also look at the question itself.

Quizbowl, stripped down to its bare essentials, tests who can recall a specific set of information ("clues") and associate it with the answer faster. This is exactly why list memorization (though inferior to other forms of studying) works - at the fundamental level of quizbowl, players buzz due to having created a cognitive map in which clue A maps uniquely to answer B. If a clue comes up that indicates that the answer was the 16th president of the United States, or the question gives that chestnut about being the only American president to have been issued a patent, I'm sure as heck going to buzz in with Abraham Lincoln. Maybe you don't know that clue, but I buzz off that clue and maybe you remember "hey that clue maps directly to Abraham Lincoln". Obviously there is not a perfect correlation - many players additionally rely on contextual clues to narrow the possible answer space, but still each clue maps to a specific answer; the narrowing of the possible answer space merely allows one to be in the correct general area when a clue comes up that one recognizes (e.g. if I'm thinking "Scandinavian writer" based on clues that I don't uniquely recognize and "When We Dead Awaken" shows up, I'm buzzing a lot faster with Ibsen than if I have no idea where the question is going, and therefore I'm a lot less likely to lose a buzzer race).

On the other hand, if a question begins by noting that "John has 5 red sticks and 12 blue sticks", this cannot possibly map to any unique answer because I don't know what to do with those numbers - maybe he wants to make a right triangle, maybe he wants to draw a red stick, maybe he wants to continue to collect red sticks until he has half as many red sticks as blue sticks, the point is, I don't know, and there's no context to help me. Similarly, if I am told that "Kwame wants to build a rectangular fence that encloses as much farmland as possible", this cannot possibly map to any unique answer because I don't have any numbers to plug in - I know that I divide the amount of fence by 4 and square it to find the maximum area, but once I recognize this clue I need another clue to tell me what the answer is (unless, of course, I buzz in with "divide the amount of fence by 4 and square it", but the idea behind computation is that those kinds of answers are never right). Using this line of logic, it can be debated whether computational math is a subset of quizbowl; however, what cannot be debated is that the "clues" in a computational math problem cannot possibly stand alone (and are therefore bad clues).

However, now that we have associated computational math with "bad quizbowl" because of the inherent non-existence of good clues, I believe we can go further in separating computational math from quizbowl. One of the major tenets of quizbowl is that the player(/team) who recalls the correct answer first shall be the one rewarded with points - this is a fundamental law of quizbowl and any competition that does not adhere to this law must necessarily be distinguished from quizbowl (there is some inherent randomness related to "buzzer speed", but generally the player who recognizes the right answer before anyone else will usually win the buzzer race if it comes down to that). Computational math does not abide by this law, because there is a non-random lag between recognition of a clue (or set of clues) and pressing the buzzer to give an answer. Obviously there is some non-randomness in quizbowl, but a lot of this has to deal with where one is thinking the answer might lie - if we have both narrowed it down to "Scandinavian writer" and I have a hunch it's Ibsen but you have a hunch it's Strindberg, then obviously only one of us is right, and if When We Dead Awaken shows up I'm going to be buzzing faster than you because you have to first recognize that your hunch is wrong, then recognize the right answer, whereas I must only recognize that my hunch is right. But generally this non-randomness is on the order of probably hundredths of a second and comparable or slightly greater than the random component of the recall -> buzz model; furthermore, neither of these causes a significant delay in transmission of the answer. In computational math, however, this non-randomness is usually on the order of seconds, and therefore clearly dominates the random component of the recall -> buzz model to the point where the random component is essentially insignificant. I don't have a "hunch" that the answer is 6 or 12 or pi/3 or whatever; the non-randomness does not come about from changing answers once a clue is recognized. The non-randomness comes from, as Andy said, from doing "something else" that interferes with the recall -> buzz paradigm.

I had some sports analogy lined up, but I'm going to use chemistry instead. In most "quizbowl reactions", we have a reactant "I recall the answer" turning into a product "buzzing". In "computational math reactions", there is this gigantic rate-limiting step we call "doing computation" that completely dominates the rate at which one goes from recalling the answer to buzzing. Therefore, the amount of time it takes to "recall the answer" is completely insignificant because the time it takes to buzz is completely dependent upon the computation time. Therefore the player who recalls the answer first does not necessarily earn 10 points, and while we would expect that a small percentage of the time this does not happen in normal quizbowl, the probability that this happens in computational math is far out of the realm of randomness because the non-random component (which is not based at all on recall) dominates. So, computational math violates a fundamental law of quizbowl and therefore cannot be quizbowl.
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Re: An Open Letter to NAQT

Post by yisun »

For all those who hate arithmetic -- what if all numbers in computational math problems were replaced by variables? This non-random gap after realizing how to do the problem is now narrowed, and you can actually answer with things like "the area is sqrt(s (s - a)(s-b)(s-c))," as in Andy's example.
Matt Weiner wrote: Also, the fact that the "canon" of doable-in-ten-seconds computational math is about 30 items wide, making it a race every time between teams who prepare?
So my last 3 posts have focused on the need to expand the canon greatly to make this viable. Somehow I wonder if you are reading them, since all your replies seem like form replies to arguments I am not making. In addition, I challenge you to write down a list of 30 viable math answers at the high school level; here by viable I mean both gettable and possible to have a 6 line tossup written on them in a pyramidal fashion.
cvdwightw wrote: Similarly, if I am told that "Kwame wants to build a rectangular fence that encloses as much farmland as possible", this cannot possibly map to any unique answer because I don't have any numbers to plug in - I know that I divide the amount of fence by 4 and square it to find the maximum area, but once I recognize this clue I need another clue to tell me what the answer is (unless, of course, I buzz in with "divide the amount of fence by 4 and square it", but the idea behind computation is that those kinds of answers are never right).
Suppose instead that the question begins: "Kwame wants to enclose as much farmland as possible with his rectangular fence..." If you are really familiar with this type of thing, you immediately have several candidate answers that pop into your head after "to enclose." Then when you hear rectangular, you should be able to buzz immediately (assuming reasonable numbers, which is certainly possible).
cvdwightw wrote: the narrowing of the possible answer space merely allows one to be in the correct general area when a clue comes up that one recognizes (e.g. if I'm thinking "Scandinavian writer" based on clues that I don't uniquely recognize and "When We Dead Awaken" shows up, I'm buzzing a lot faster with Ibsen than if I have no idea where the question is going, and therefore I'm a lot less likely to lose a buzzer race).
This is exactly what I'm talking about above. The thing about computation is that the way to be fast is to know how to do the question before the question is finished. Plugging in actual numbers is more or less an automatic process; if you talk to anyone who has done high school math competitions, the calculation is the trivial part, and using your knowledge to find how to solve the problem is the heart of the issue. So if calculation is actually dominating (I can't tell if this is true, as some people claim that compmath questions go dead frequently, while others are saying that they all get buzzer-raced.), the questions need to get harder.
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Re: An Open Letter to NAQT

Post by cdcarter »

yisun wrote:
Matt Weiner wrote: Also, the fact that the "canon" of doable-in-ten-seconds computational math is about 30 items wide, making it a race every time between teams who prepare?
So my last 3 posts have focused on the need to expand the canon greatly to make this viable. Somehow I wonder if you are reading them, since all your replies seem like form replies to arguments I am not making. In addition, I challenge you to write down a list of 30 viable math answers at the high school level; here by viable I mean both gettable and possible to have a 6 line tossup written on them in a pyramidal fashion.
I'm not even going to bother talking about the rest of your points. Someone else will do so more competently. But the idea of making the HS math canon harder is completely flawed. As Matt said, the number of problems that are computable in 10 seconds number below 50. If we make the canon harder, we either need more time, or more tossups will go dead unless there is a math expert. When you have a limit of (effective) answer space, you don't just add more and hope it works out. You use harder clues. But you need each clue to be something easily computable so there isn't a benefit to just sit through the leadin and buzzer race at the end. But those easily computable clues also need to be hard enough that they actually differentiate between top teams. Do you see how this would be a problem, even if math comp had a place in quizbowl?
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Re: An Open Letter to NAQT

Post by Tegan »

Yisun,

I think you are going to be on the losing end of this argument, but that isn't to say that there aren't people who don't agree with you up to a certain extent.

To some people, computational problems are a skill, and therefore generally outside the bounds of what this activity entails. However, I contend that math specialists, for the most part, have roughly equal computation speeds; and if there is a difference, it is do to uncertainty, in much the same way two people who know Newton wrote the three laws may not hit the button at the same time because one is more sure about themselves. The person who computes faster does so because they are more sure about knowing the facts of computation. I could here the argument that computation is unique in that it generally requires a cascade of facts to be known (call that an algorithm), and that it requires a totally different thinking process than simply recalling >>fact<<, but my view is that what we call solving an algorithm is simply recalling sets of facts.

We could ask a question like "What process would you use to solve >>insert problem<<, but it is highly impractical, because there are multiple ways to word the various steps in the process. It is simply easier to ask for the solution.

I don't agree with those that claim computational math is so radically different that it is to be shunned like lepers, but I also see that it does utilize somewhat different thinking than the other strict recall, or even the "lateral thinking" type synthesis questions, and I can see where some think that if it is so different, why include it?
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Re: An Open Letter to NAQT

Post by Stained Diviner »

Do the questions in this thread do anything to address the problems in Dwight's 'rambling' thread?

There are clues that stand alone, so they are not bad in the same way you describe. Also, computation is not always the major bottleneck in solving them.
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Re: An Open Letter to NAQT

Post by yisun »

cdcarter wrote: As Matt said, the number of problems that are computable in 10 seconds number below 50.
This is just completely false. If you go look at the middle school MathCOUNTS countdown round, there are on the order of 100 questions each year, each of which is answered in much less than 10 seconds. And that's ignoring high school material.
But you need each clue to be something easily computable so there isn't a benefit to just sit through the leadin and buzzer race at the end.
So shouldn't using variables instead of numbers solve this issue? If there's no computation to do, you can't possibly be beaten to it.
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Re: An Open Letter to NAQT

Post by cdcarter »

yisun wrote:
cdcarter wrote: As Matt said, the number of problems that are computable in 10 seconds number below 50.
This is just completely false. If you go look at the middle school MathCOUNTS countdown round, there are on the order of 100 questions each year, each of which is answered in much less than 10 seconds. And that's ignoring high school material.
I have not seen these rounds. How often do they test the same skills? Are they all figure out the problem type questions, or more pure "what is X div Y?" style questions? (Disclaimer, I don't actually know, I'm just wondering).
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Re: An Open Letter to NAQT

Post by Matt Weiner »

yisun wrote:For all those who hate arithmetic -- what if all numbers in computational math problems were replaced by variables? This non-random gap after realizing how to do the problem is now narrowed, and you can actually answer with things like "the area is sqrt(s (s - a)(s-b)(s-c))," as in Andy's example.
Then you're not even pretending to ask pyramidal questions anymore, you're just doing buzzer-race on "remember the formula."
So my last 3 posts have focused on the need to expand the canon greatly to make this viable. Somehow I wonder if you are reading them, since all your replies seem like form replies to arguments I am not making.
What?
In addition, I challenge you to write down a list of 30 viable math answers at the high school level; here by viable I mean both gettable and possible to have a 6 line tossup written on them in a pyramidal fashion.
It's not answers, it's problems. There are a few problems you can do within the length limits and time limits of a tossup. There are even fewer when you need things that can be done in multiple ways to satisfy the delusional pseudo-pyramidality that NAQT has convinced itself exists when you ask about questions with decreasingly difficult trick methods to solve. As a result of having barely enough types of problems to cover a single set, the tricks NAQT uses are the same in every NAQT set. Some teams memorize them, others don't. When two teams who have memorized them (like two elite teams playing for finish at the HSNCT) encounter each other, it reduces to a one-clue number-crunching race. This is not the case for real quizbowl topics, where you can make the start of the pyramid arbitrarily hard by finding new information about the topic. There is no new information about calculating the probability of drawing a red marble, and there never will be. The idea of encouraging people to expand their horizons from the high school curriculum and keep ahead of the learning arms race is completely destroyed on math questions. Introducing harder questions will only make this roadblock occur at a higher level of the educational path, not solve the problem.
Suppose instead that the question begins: "Kwame wants to enclose as much farmland as possible with his rectangular fence..." If you are really familiar with this type of thing, you immediately have several candidate answers that pop into your head after "to enclose." Then when you hear rectangular, you should be able to buzz immediately (assuming reasonable numbers, which is certainly possible).
Uh, no, you still have to crunch-race with the other team when the numbers come up. There is no answer to "Kwame wants to enclose as much farmland as possible with his rectangular fence."
This is exactly what I'm talking about above. The thing about computation is that the way to be fast is to know how to do the question before the question is finished.
Which three TJ players and two Charter players knew, and were racing to do the arithmetic on. You cannot overcome the pyramidality problem here because the one math question always comes at a discrete time, as opposed to the real quizbowl tossup which can actually be pyramidal.
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Re: An Open Letter to NAQT

Post by yisun »

Matt Weiner wrote: Then you're not even pretending to ask pyramidal questions anymore, you're just doing buzzer-race on "remember the formula."
Well that's only if my question is something stupid like "given a triangle with sides a, b, and c, what is its area?" I can make this better by asking for the length of one of the altitudes or medians something of the like. There aren't formulas for things like this, nor should there be (well in theory you could make formulas and memorize them, but that's just stupid).
So my last 3 posts have focused on the need to expand the canon greatly to make this viable. Somehow I wonder if you are reading them, since all your replies seem like form replies to arguments I am not making.
What?
I've been arguing that we should expand the canon of askable computation questions; your response is that computation is not feasible because the canon is too small. I don't see how this is relevant.
There is no new information about calculating the probability of drawing a red marble, and there never will be. The idea of encouraging people to expand their horizons from the high school curriculum and keep ahead of the learning arms race is completely destroyed on math questions. Introducing harder questions will only make this roadblock occur at a higher level of the educational path, not solve the problem.
There is plenty of new information about probability. For example, consider the following problem: "There are 3 red marbles and 3 blue marbles in a jar. They are drawn out one by one in succession, without replacement. What is the probability that, at any time, the number of red marbles drawn is at most equal to the number of blue marbles drawn." There are two ways to do this: (1) Recognize the Catalan numbers (big knowledge points here), and the problem is automatic. or (2) Recognize that you can list out the small number of possibilities and see which work. This is much much slower, and anyone in group 2 will definitely lose to anyone in group 1. This is definitely incentive to learn about the Catalan numbers.
Which three TJ players and two Charter players knew, and were racing to do the arithmetic on. You cannot overcome the pyramidality problem here because the one math question always comes at a discrete time, as opposed to the real quizbowl tossup which can actually be pyramidal.
OK, so this problem was too easy for the finals of the HSNCT. So let's make it harder. How? There are 50 questions here (the AMC 12 A and B for 2005): http://www.mathlinks.ro/resources.php?c ... &year=2005. I claim that at least 30-40 of them can be done quickly, and not all of these reduce to a formula. Math is not about formulas.
I have not seen these rounds. How often do they test the same skills? Are they all figure out the problem type questions, or more pure "what is X div Y?" style questions? (Disclaimer, I don't actually know, I'm just wondering).
They are all figure out the problem type questions. Here's an example: http://www.mnspe.org/mathcounts/2007tes ... ntdown.pdf This is a bit easier than what I was thinking of (it's the first round of the competition, the state and national rounds get much harder.)
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Re: An Open Letter to NAQT

Post by Matt Weiner »

Every problem at those links still separates players into only two classes: "knows how to do it" and "doesn't know how to do it," with members of the first class subsequently racing to finish the arithmetic. The fundamental issue with math tossups being non-pyramidal and non-quizbowl-like is not solved at all. Real questions sort people into a continuous spectrum based on, at a minimum, which fact they know, often with some ability of deduction shading it even further.
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Re: An Open Letter to NAQT

Post by yisun »

"There are 3 red marbles and 3 blue marbles in a jar. They are drawn out one by one in succession, without replacement. What is the probability that, at any time, the number of red marbles drawn is at most equal to the number of blue marbles drawn." There are two ways to do this: (1) Recognize the Catalan numbers (big knowledge points here), and the problem is automatic. or (2) Recognize that you can list out the small number of possibilities and see which work. This is much much slower, and anyone in group 2 will definitely lose to anyone in group 1. This is definitely incentive to learn about the Catalan numbers.
This problem quite clearly gives at least 3 gradations. I could argue for more based on how fluent people are with the Catalan numbers or combinations and things like this.
Every problem at those links still separates players into only two classes: "knows how to do it" and "doesn't know how to do it," with members of the first class subsequently racing to finish the arithmetic. The fundamental issue with math tossups being non-pyramidal and non-quizbowl-like is not solved at all. Real questions sort people into a continuous spectrum based on, at a minimum, which fact they know, often with some ability of deduction shading it even further.
I'm not sure what you mean by "knows how to do it" and "doesn't know how to do it." Many of these problems have several possible solutions; the easier ones take less time. This gives pyramidality. Another example of this: Consider the problem "Compute sqrt(3! * 3!), where for a positive integer n, n! = n * (n - 1) * .. * 1" This is #44 from the second link slightly modified. Solving this this requires 3 steps: (1) for any positive real x, sqrt(x*x) = x, (2) for a positive integer n, n! = n * (n - 1) * .. * 1, (3) either computing 3! = 3 * 2 * 1 = 6, or just knowing this outright. At each step, you can either know it outright, or not. If not, you will take extra time or not solve the problem. This spectrum seems just as continuous to me as, say, for a college math theory tossup.
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Re: An Open Letter to NAQT

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I think you're misinterpreting Matt's response. Computation questions are not feasible because the canon is too small. Your potential remedy for this is to "expand the canon" of askable computation questions. I (and I believe Matt) posit that the canon of askable computation questions is already at its limit. I mean, let's face it, is your average high school math player going to know Catalan numbers? No. Is your average high school math player going to know even simple differential equations like y' + y = 0? No. Is your average high school math player going to know Pythagorean triples? Yes. I might be completely wrong on this, but I would expect that any math that goes (at any point) beyond one-dimensional integral calculus is not going to be accessible to the average quizbowl math player.

Regarding MathCounts questions: Middle school kids get 45 seconds to do these problems. They often take more than 10 seconds to do them, and I hate to say it but as kids get interested in other parts of quizbowl and other parts of math they're not focusing on improving that time. I dunno, maybe someone like Greg Gauthier would be like "oh yeah I can do every problem in that pdf in 5 seconds or less per problem", but as most people in Illinois will attest not every team has a Greg Gauthier.

Regardless of whatever you say about the answer space, you cannot turn the above questions (and these are the "longer" ones) into a question that has any vestige of pyramidality. There's either "you know the trick" or "you don't know the trick"; NAQT tries to remedy this somewhat by giving you the trick, but this doesn't help - there's essentially two clues in the entire question - "the problem" and "this is how you solve the problem", and no one can make a pyramidal question out of that.

Let me clarify that while I do not think that computational math = quizbowl, I do not have a problem with this stuff showing up in bonuses because bonuses need not have pyramidality, and accordingly if the numbers are easy enough to work with these kinds of questions are able to test "knowledge" without suffering from the pitfalls of computation tossups. I'm sure Matt and others are going to hate me for this, but I would have no problem with a bonus like this:

Bonus: John has 3 green socks, 2 blue socks, and 4 red socks in a drawer, and he cannot see the color of any sock when pulling it out of his drawer. For 10 points each:
[10] What is the probability that John draws a green sock OR a blue sock? Give your answer as a fraction in simplest form.
Answer: 5/9
[10] John draws a green sock, puts it back in his drawer, and draws a green sock again. What is the probability that this happens? Again, give your answer as a fraction in simplest form.
Answer: 1/9
[10] Let Event A be the event "John draws a green sock". What is the probability of the complement of Event A?
Answer: 2/3

This would test whether the team understands the ideas of independence and mutual exclusivity and knows what a complement is, and if you can't work with those numbers in 10 seconds then yeah you probably were hung up on the "what the heck do I do here?" part of the problem. However, in a bonus you are not competing against the other team - if you can do the problem in 10 seconds you get the points; it matters not how quickly you recall and compute but THAT you recall and compute, similarly it doesn't matter if it takes me 2 seconds or 4 seconds to come up with Kreutzer Sonata, I'm going to get the points if the answer's Kreutzer Sonata. In a tossup, knowing the answer is not what matters - what is important is how quickly you know the answer, and even figuring out what is 2+2 is going to take an extra "jump" that the other tossups don't. Sure, competitively computing what is 2+2 went out of style in 2nd grade, but the point is that on a tossup you are "penalized" (in that you don't get the points) for not being able to do the problem faster than some other person while in a bonus you are "penalized" only if you can't do the problem in a certain time limit, which is almost certainly because you don't know what to do (and therefore you lack the knowledge; I mean how hard can 3/9+2/9 be?).
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Re: An Open Letter to NAQT

Post by Matt Weiner »

I think calculation bonuses are an acceptable compromise when you have people who really demand math questions, but you don't want to include the nonsense that is calculation tossups. I wouldn't have edited all these PACE tournaments with calculation bonuses if I found them so odious.
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Re: An Open Letter to NAQT

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Re: An Open Letter to NAQT

Post by theMoMA »

Anyway, you're confusing "rewarding academic exercise that can be tested for in competition" for "what quizbowl should be." There are plenty of things in the former category that just don't work in the latter.
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Re: An Open Letter to NAQT

Post by AKKOLADE »

everyday847 wrote:This is the problem.
This looks more like the solution to me.
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Re: An Open Letter to NAQT

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everyday847 wrote:This is the problem.
An awesome sport.
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Re: An Open Letter to NAQT

Post by OctagonJoe »

I really wanted to avoid posting here, but this seems endless and I want to try to stop it. I think a reading of the QBWiki article on Pyramidality should really help end this discussion. The first line sort of says it all.
QBWiki wrote:Pyramidality is a concept in tossup-writing that states that clues should be arranged in descending order of difficulty, with the hardest information first and the easiest at the end, after the "For 10 points."
I mean, Yi Sun has consistently said that 'it's pyramidal because the solving method is the key to speed', which is clearly not what the definition of a pyramidal tossup is. If you want to be really stubborn, you could argue that "harder" clues can be given for some certain answer, but it's still not the right idea behind what a quizbowl tossup should be. Looking at other parts of the article, it's even near-to-completely impossible to write a "transparent" or "anti-pyramidal" math computation tossup unless you're an idiot, while on a normal canonical subject this happens all too often. Internal pyramidality is also not something I see as possible if you have to give everyone all the necessary pieces pretty much in one go, and I'm sure, especially to a "good" math player, the order isn't all that important. As you should be able to tell, I just went through all the parts of an article that describes how a tossup should or should not be written, and seemingly not one bit of it applies to a math computation tossup. So please, read the article, think about it, and then post if you really see some way how any part of that could apply to computation tossups.
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Re: An Open Letter to NAQT

Post by evilmonkey »

Arg, I'm away with out internet for 2 DAYS without internet (at Mathfest, strangely enough), and this argument happens again.
Ugh.
Computation bonuses = good.
Computation tossup = could be good, but only if used in exceedingly rare situations (so as not to use the entire 35 question canon in a single year).
Math Theory tossup = outstanding, but canon needs some serious expansion, and in creative ways to account for the fact that MATHCOMP is all that is really taught in highschool
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Re: An Open Letter to NAQT

Post by Gautam »

evilmonkey wrote:canon needs some serious expansion
Can we please stop calling for "serious expansions" of the canon? I don't remember whether I've argued for hardcore canon expansion of math theory in hs quiz bowl, but if I have, assume that I have nullified those arguments, and that I'm starting afresh by saying this is a really dumb idea.

I practiced some "canon expansion" last year when I wrote tossups on things like "finding the root of a polynomial" and "pi" but I realized that other than a couple of math aficionados, none were able to get those tossups until it got to the giveaway. I also think that even if the same tossup is read to an average high school student some 5 years from now, it's probably not going to be gotten until the giveaway. I don't see any reason why the average highschool quizbowl player's knowledge base is going to be so deep as to convert points from the new information that can be accommodated by this serious expansion of the math theory canon.

Personally, I feel the high school chem canon is too narrow. I say this because almost all the askable chemistry stuff in high school can be found in the average College Freshman Chemistry book/lab manual. Also, I have been writing several questions on this subject for the last month or so, and I find it difficult to be creative in the rather narrow answer space. However, I don't see any reason to start writing tossups on the Diels-Alder reaction for high school sets, regardless of how difficult the set is intended to be. The average player is just not going to be able to answer those questions!

There are clever ways to do canon expansion. For instance, in a bonus part of magnetic potential (perhaps the hard part of a bonus), one can mention the Aharonov-Bohm effect. However, I think it would be shameful of us to expect people to come up with Aharonov-Bohm effect as an answer.

Serious expansion can be done at CO, but not at PACE NSC/HSNCT. There is a world of difference between canon expansion in college, and canon expansion in HS, and I really don't see canon expansion as a solution to any of the problems being discussed here. I wrote some questions for MUT and NSC last year which shouldn't really have been questions at all, but I've learned from that mistake.

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Re: An Open Letter to NAQT

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gkandlikar wrote:
evilmonkey wrote:canon needs some serious expansion
Can we please stop calling for "serious expansions" of the canon? I don't remember whether I've argued for hardcore canon expansion of math theory in hs quiz bowl, but if I have, assume that I have nullified those arguments, and that I'm starting afresh by saying this is a really dumb idea.
Yeah, I think calling for "serious expansion" of the canon is more an expression of "argh I can't write tossups on things I want to toss up to high schoolers" or at least "argh this 5/5 chem I'm writing is not proceeding too well." You can't really call for something like that; it's something that happens in a passive and undirected way. Though in some sense the writers of side tournaments could be interpreted as a cabal that assembles and says "hee hee hee now finally I can toss up Section: Rock Drill at ACF Fall," I think that interpretation would have little to do with reality. Canon expansion (as per Andrew Hart's excellent guide) happens gradually and undirectedly, more a question of "hey, it'd be neat to mention Hart Crane in a modernism bonus and maybe eventually he'll be canonical" than "this IS-A packet really needs a tossup on The Bridge." You don't take things that don't get mentions and turn them into answers. You never, ever do that.

The other issue is this: it's not like the trend of high school players getting a whole lot better over the past like five years (and more, as the game in general has improved) can improve indefinitely. Fifteen months ago I was a senior in high school and had been on the earth for almost exactly eighteen years. I had eighteen years to study. Even as high school players get more and more serious about the game, and Hunter's impressive seventh graders become Hunter's impressive third graders, they'll be limited by the fact that at birth, they start at zero, and a hundred years from now high schoolers will probably still not have the math background for us to toss up the Sylow theorems. Math canon expansion will even happen particularly slowly, since while a friend of mine in high school would have been content for the high school law canon to cover most of the material from an average constitutional law curriculum, and another friend would have been happy for the history canon to cover minor engagements in Central European military history, it's pretty uncommon for high school students to have a desperate interest in tossupable math. There are MathCounts stars and IMO participants, obviously--but not only aren't there many of them playing quizbowl, I think that there's a difference between being really good at math and having a high-level academic exposure to math, which would expose you to the appropriate theorems etc. that you might need to buzz on in a hypothetical expanded canon.
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Re: An Open Letter to NAQT

Post by Matt Weiner »

everyday847 wrote: Even as high school players get more and more serious about the game, and Hunter's impressive seventh graders become Hunter's impressive third graders, they'll be limited by the fact that at birth, they start at zero, and a hundred years from now high schoolers will probably still not have the math background for us to toss up the Sylow theorems.
Also, how good the nationally elite teams are getting has absolutely nothing to do with answer selection, only with strengthening the first few clues in tossups at the more competitive tournaments. The average player is still the average player and the end-of-question difficulty needs to be pretty much the same as ever.
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Re: An Open Letter to NAQT

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Matt Weiner wrote:Also, how good the nationally elite teams are getting has absolutely nothing to do with answer selection, only with strengthening the first few clues in tossups at the more competitive tournaments. The average player is still the average player and the end-of-question difficulty needs to be pretty much the same as ever.
Right; I guess I'm saying that there's also a limit to how good those elite teams are likely to get, as well. Like, it's very possible that we'll never have to include the Sylow theorems as a clue to distinguish between the teams that have REALLY deep knowledge of theorems about subgroups and those that will get it on Lagrange's theorem (the poor things!).
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Re: An Open Letter to NAQT

Post by Captain Sinico »

yisun wrote:The problem here is that not all math concepts are easily named.
I argue that this presents no significant difficulty to a creative question writer. The answer to a question doesn't have to be the concept itself. I could very easily write (and, in the second case, have written) non-computational questions that test knowledge of the concepts you've cited; for example, I could write a question on triangles or the cosine function.
Also, you've failed to address my first point. Computational questions are fundamentally different from other quizbowl questions because they do not test knowledge per se, but rather only knowledge convolved with computation ability. Further, in my experience, it is necessarily the case that computational ability (in the form of speed at arithmetic) dominates the outcomes of computation tossups. Other people here are saying similar things. What do you say to that?

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Re: An Open Letter to NAQT

Post by Mechanical Beasts »

ImmaculateDeception wrote: Further, in my experience, it is necessarily the case that computational ability (in the form of speed at arithmetic) dominates the outcomes of computation tossups. Other people here are saying similar things. What do you say to that?
Yeah, this is probably the most important thing. Whereas the vast majority of teams have microdifferentations in history knowledge substantial enough to buzz on facts of two different obscurities about Pope Gregory VII or whatever, I'd say that you can't do that with your combinatorics example. I'd say that the use of Catalan numbers is important to one in five hundred teams, and the amount of teams who simply have to add up a bunch of different cases is maybe one in ten. But the chance that you have a math dude on your team--particularly for a format where you know there will be math, but it won't be all math--who can do combinatorics but doesn't know these Catalan number things is pretty high. If at least 89% of teams know how to do it the medium-speed way, doesn't it boil down to computational speed in like 80% of matches? (Not to mention the one percent of the time that the kids just add up some numbers or, worse, guess, and the tossup goes dead.)

Of course, you're saying that there exist hypothetical math tossups where computational speed per se doesn't matter. And sure, you could use variables; sure, you could pretty easily determine a question that requires you to figure out how to recombine them, and where familiarity with abstract algebra allows you to recombine them more quickly than someone who took some high school linear algebra more quickly than someone who's taken algebra II. But ultimately, you're trying to do SOMETHING quickly, and quicker that someone else--something other than buzz, which is unavoidable until we have a truly magical buzzer device that taps into your brain. And that's not quiz bowl. Quiz bowl would be saying "why, I know the name of the thing that helps you solve that kind of problem!"
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Re: An Open Letter to NAQT

Post by yisun »

Regarding MathCounts questions: Middle school kids get 45 seconds to do these problems. They often take more than 10 seconds to do them, and I hate to say it but as kids get interested in other parts of quizbowl and other parts of math they're not focusing on improving that time. I dunno, maybe someone like Greg Gauthier would be like "oh yeah I can do every problem in that pdf in 5 seconds or less per problem", but as most people in Illinois will attest not every team has a Greg Gauthier.
At the actual competition, most questions are converted in far less than 10 seconds. The 45 seconds are a maximum.
Yeah, I think calling for "serious expansion" of the canon is more an expression of "argh I can't write tossups on things I want to toss up to high schoolers" or at least "argh this 5/5 chem I'm writing is not proceeding too well." You can't really call for something like that; it's something that happens in a passive and undirected way. Though in some sense the writers of side tournaments could be interpreted as a cabal that assembles and says "hee hee hee now finally I can toss up Section: Rock Drill at ACF Fall," I think that interpretation would have little to do with reality. Canon expansion (as per Andrew Hart's excellent guide) happens gradually and undirectedly, more a question of "hey, it'd be neat to mention Hart Crane in a modernism bonus and maybe eventually he'll be canonical" than "this IS-A packet really needs a tossup on The Bridge." You don't take things that don't get mentions and turn them into answers. You never, ever do that.
I agree, you don't do that. However, I challenge you to write down 30 askable answers to math tossups. Things that you can write a 6 line, pyramidal tossup to without filling the first 3 with things high schoolers have *no* chance of answering. I pretty much can't do it, even with resorting to what I think is the very annoying (not the writer but the player) method of writing tossups like, "hey, there are a lot of things in math all with 'triangle' in their names." And I don't think this is true of all answers at the high school level; there are definitely books I've never heard of that come up, and I'm fine with that.
As you should be able to tell, I just went through all the parts of an article that describes how a tossup should or should not be written, and seemingly not one bit of it applies to a math computation tossup. So please, read the article, think about it, and then post if you really see some way how any part of that could apply to computation tossups.
So the point of pyramidality is to ensure that the player with the most knowledge pertaining to a particular tossup answers the tossup first, in theory. If this goal is somehow accomplished otherwise, what's the problem?
Arg, I'm away with out internet for 2 DAYS without internet (at Mathfest, strangely enough), and this argument happens again.
Funny, I'm currently at Mathfest.
I practiced some "canon expansion" last year when I wrote tossups on things like "finding the root of a polynomial" and "pi" but I realized that other than a couple of math aficionados, none were able to get those tossups until it got to the giveaway.
This is ridiculous. I just looked at the sample HSNCT packet on the NAQT website. Of the answers, I have no knowledge of Orpheus in the Underworld and Saint Gregory the Great, and no knowledge that the first even exists. But somehow this is okay because many high school players know these. Of course lots of people actually know these offhand and I have no problem with that, but I think some knowledge of pi and solving polynomial equations is pretty basic, just as those answers probably are (I've no idea.)
Math canon expansion will even happen particularly slowly, since while a friend of mine in high school would have been content for the high school law canon to cover most of the material from an average constitutional law curriculum, and another friend would have been happy for the history canon to cover minor engagements in Central European military history, it's pretty uncommon for high school students to have a desperate interest in tossupable math. There are MathCounts stars and IMO participants, obviously--but not only aren't there many of them playing quizbowl, I think that there's a difference between being really good at math and having a high-level academic exposure to math, which would expose you to the appropriate theorems etc. that you might need to buzz on in a hypothetical expanded canon.
So your argument is more or less: "People currently playing quizbowl aren't interested in math (probably because it's not really covered), so we shouldn't change that." Also, I don't think your average good literature student would know hardly any of the literature in the canon, so this is not really a great metric. Of course, I'm not a proponent of asking anything about the Sylow theorems (personally I find them very very boring), but there are many other things that don't involve taking advanced math classes that could be asked (actually difficult Euclidean geometry theorems, elementary number theory, combinatorics). These are common things that high school kids interested in math learn or see on their own and don't have too much intersection with first year college math.
I argue that this presents no significant difficulty to a creative question writer. The answer to a question doesn't have to be the concept itself. I could very easily write (and, in the second case, have written) non-computational questions that test knowledge of the concepts you've cited; for example, I could write a question on triangles or the cosine function.
While I agree that these questions are pyramidal if done well, I find that they largely reduce to "here are a list of things in math that all have this word attached to them. guess the word." This really doesn't reward knowledge but having heard the name of a lot of things; I personally benefit from this a lot, but it's pretty annoying [why learn anything about Alexander-Lefchetz duality when you can get a tossup on "duality" off it in the first line? (this happened at EFT last year)].
Of course, you're saying that there exist hypothetical math tossups where computational speed per se doesn't matter. And sure, you could use variables; sure, you could pretty easily determine a question that requires you to figure out how to recombine them, and where familiarity with abstract algebra allows you to recombine them more quickly than someone who took some high school linear algebra more quickly than someone who's taken algebra II. But ultimately, you're trying to do SOMETHING quickly, and quicker that someone else--something other than buzz, which is unavoidable until we have a truly magical buzzer device that taps into your brain. And that's not quiz bowl. Quiz bowl would be saying "why, I know the name of the thing that helps you solve that kind of problem!"
In response to Mike, my point is that well-written questions shouldn't rely on this speed aspect, and, to accomplish this, the math needs to be made a bit harder.

I'm not sure what this "do something" argument is saying. If the computations can boil down to things like.. "what is 3 * 4?" (after solving the problem), it's unclear how much "faster" someone can do this than someone else. And if you really can't do this in a reasonable time period (I've seen this argued in one of the previous threads)... sure you technically are being slow at doing it, but you can also view it as being slow in remembering your times tables.
Yeah, this is probably the most important thing. Whereas the vast majority of teams have microdifferentations in history knowledge substantial enough to buzz on facts of two different obscurities about Pope Gregory VII or whatever, I'd say that you can't do that with your combinatorics example.
I don't see the deal here. I have no knowledge of Pope Gregory VII, and a typical AP Euro class probably imparts minimal knowledge about him (I took one and don't remember anything about him appearing). Your argument is that the history people on typical teams might have such a difference in knowledge. Other than the fact that the status quo is like this, do you have any arguments that math people should not?
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Re: An Open Letter to NAQT

Post by Irreligion in Bangladesh »

yisun wrote:So the point of pyramidality is to ensure that the player with the most knowledge pertaining to a particular tossup answers the tossup first, in theory. If this goal is somehow accomplished otherwise, what's the problem?
It's a problem if the goal is accomplished in a different manner because continuity between all tossups in a match is absolutely key to quizbowl. By playing a certain number of tossups by one set of rules, then playing a certain number of tossups by a different set of rules, you create a hybrid of two games. This is not fair to teams that excel in either one of the games alone. Those teams should play their strength by itself - the quizbowl teams should play quizbowl, and the math teams should play (insert your particular flavor of math competition here).

Here's a good scenario...the summer that I graduated from high school, I played MASQUE, the open HSNCT mirror in Minnesota. Thanks to Illinois' use of computational math (20% of the distribution), I was a good computational math player in high school, and thanks to Illinois' non-use of pyramidal questions at the time, I was not up to par on the tough clues of pyramidal questions.* My team won 6 games that day. Of those wins, we won the game of "quizbowl in every subject except math" 3 times and lost 3 times. We also won the game of "computational math" 6 times, because I was the only person in the building who was trained on how to do it. 3 of the overall wins were legit, but 3 of them were won because I was good at the "other set of rules."

*My philosophy - you practice what you play. If you don't like what you play, by all means work to change what you play, but, generally speaking, keep playing in the meantime.

Now, one could easily parse this differently. My team wasn't very good at science. In those 6 wins, we won "quizbowl in every subject but science" some number of times, lost "science," and therefore lost the game. The difference between science (or any other subject) and computational math is illustrated by this next quote.
...Ultimately, you're trying to do SOMETHING quickly, and quicker that someone else--something other than buzz, which is unavoidable until we have a truly magical buzzer device that taps into your brain. And that's not quiz bowl. Quiz bowl would be saying "why, I know the name of the thing that helps you solve that kind of problem!"
yisun wrote:I'm not sure what this "do something" argument is saying. If the computations can boil down to things like.. "what is 3 * 4?" (after solving the problem), it's unclear how much "faster" someone can do this than someone else. And if you really can't do this in a reasonable time period (I've seen this argued in one of the previous threads)... sure you technically are being slow at doing it, but you can also view it as being slow in remembering your times tables.
Here's what the "do something" argument is saying: quizbowl is about taking a clue, figuring out what the answer is in terms of that clue, and buzzing in, while computational math is about taking a problem, establishing the formula needed to solve the problem, computing the answer, and then buzzing in. I don't care how long or short that computing step takes. It doesn't matter how far you boil the "doing it" step down, whether you're working with big numbers or small numbers or variables or anything. That extra step is still there, and that's not fair from a continuity standpoint.
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Re: An Open Letter to NAQT

Post by Sen. Estes Kefauver (D-TN) »

Whether or not you've never heard of Pope Gregory the Great (hint: he is known for a namesake chant) ofr Orpheus in the Underworld, the source of the Can Can, doesn't make them any less relevant and askable. I would contend that both of these have their place in the canon well earned.
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Re: An Open Letter to NAQT

Post by Mechanical Beasts »

yisun wrote: I agree, you don't do that. However, I challenge you to write down 30 askable answers to math tossups. Things that you can write a 6 line, pyramidal tossup to without filling the first 3 with things high schoolers have *no* chance of answering. I pretty much can't do it, even with resorting to what I think is the very annoying (not the writer but the player) method of writing tossups like, "hey, there are a lot of things in math all with 'triangle' in their names." And I don't think this is true of all answers at the high school level; there are definitely books I've never heard of that come up, and I'm fine with that.
No, believe me: I think writing math theory can be hard as balls. I don't know how these people do it. So I can't meet your challenge--but "x is extremely hard" isn't necessarily an argument for "do y, which has been used as a substitute but isn't quite one and has negative side-effects."
yisun wrote:So the point of pyramidality is to ensure that the player with the most knowledge pertaining to a particular tossup answers the tossup first, in theory. If this goal is somehow accomplished otherwise, what's the problem?
Because in reality, it's not a question of "buzz when you know how to solve it because you've been exposed to the material;" it's a question of "buzz when you know how to solve it and then have solved it." Which you admit:
yisun wrote:I'm not sure what this "do something" argument is saying. If the computations can boil down to things like.. "what is 3 * 4?" (after solving the problem), it's unclear how much "faster" someone can do this than someone else. And if you really can't do this in a reasonable time period (I've seen this argued in one of the previous threads)... sure you technically are being slow at doing it, but you can also view it as being slow in remembering your times tables.
The fact that you must not only know how to solve the problem but also solve it makes this not quiz bowl. I suppose the language many people have been using is a little imprecise: we don't just mean computational speed as in "speed at which one can evaluate arithmetic:" it's the speed at which one can do some kind of manipulation on something. One must solve the problem faster. And I'd argue that there are people with more knowledge about a subject in math who are not capable of solving the problem faster.
yisun wrote:This is ridiculous. I just looked at the sample HSNCT packet on the NAQT website. Of the answers, I have no knowledge of Orpheus in the Underworld and Saint Gregory the Great, and no knowledge that the first even exists. But somehow this is okay because many high school players know these. Of course lots of people actually know these offhand and I have no problem with that, but I think some knowledge of pi and solving polynomial equations is pretty basic, just as those answers probably are (I've no idea.)
What he's saying, I think, is that with the tossups he wrote, almost no one would be able to buzz before the giveaway, so that sort of canon expansion is bad. Whereas just because you don't know Orpheus in the Underword doesn't mean that many high school players would be able to get it on the second to last clue, and some on the leadin, and...
yisun wrote:So your argument is more or less: "People currently playing quizbowl aren't interested in math (probably because it's not really covered), so we shouldn't change that." Also, I don't think your average good literature student would know hardly any of the literature in the canon, so this is not really a great metric. Of course, I'm not a proponent of asking anything about the Sylow theorems (personally I find them very very boring), but there are many other things that don't involve taking advanced math classes that could be asked (actually difficult Euclidean geometry theorems, elementary number theory, combinatorics). These are common things that high school kids interested in math learn or see on their own and don't have too much intersection with first year college math.
I mean, kind of? But not really: high schoolers are never going to be able to answer tossups on Alexander-Lefchetz duality, whatever that is, ever ever ever. Because they'll never know jack about it, because that sort of information is simply inaccessible to the immense majority of high school students. But everyone can read a book, so nothing prevents them from learning quiz bowl lit to the point where they can one-line tossups on it. But even if you made math something that you absolutely had to dedicate one student to, in a game with 25% theoretical math, you'd just get a lot of math guys who wouldn't be able to answer a lot of the really hard tossups.

I wouldn't consider Menelaus's theorem, for example, to be inappropriate canon expansion. That'd be just fine. In some sense, it certainly could be part of the canon already for top teams, like at NSC. But it doesn't belong in an IS set.

yisun wrote:I don't see the deal here. I have no knowledge of Pope Gregory VII, and a typical AP Euro class probably imparts minimal knowledge about him (I took one and don't remember anything about him appearing). Your argument is that the history people on typical teams might have such a difference in knowledge. Other than the fact that the status quo is like this, do you have any arguments that math people should not?
That's precisely what I'm arguing, since one writes questions for the "typical" team attending your tournament. If you're going to toss up rotation matrices somehow to a bunch of eighth grade junior bird players, the players who are good at inventing answers will get it off "FTP, identify these mathematical objects that aren't movies about Neo that can rotate shit." Whereas you can toss up an important pope because you will have teams who know different amounts about him.
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Re: An Open Letter to NAQT

Post by Gautam »

yisun wrote:
I practiced some "canon expansion" last year when I wrote tossups on things like "finding the root of a polynomial" and "pi" but I realized that other than a couple of math aficionados, none were able to get those tossups until it got to the giveaway.
This is ridiculous. I just looked at the sample HSNCT packet on the NAQT website. Of the answers, I have no knowledge of Orpheus in the Underworld and Saint Gregory the Great, and no knowledge that the first even exists. But somehow this is okay because many high school players know these. Of course lots of people actually know these offhand and I have no problem with that, but I think some knowledge of pi and solving polynomial equations is pretty basic, just as those answers probably are (I've no idea.)
Hey look, I don't know what your idea of high school quiz bowl is, but in my world, people like to get tossups. Some are gotten early, some are not gotten early. People like getting tossups early. We have whole mechanisms set up to reward them with powers if those tossups are gotten early. That said, we should not write tossups that are designed for the chosen few to be gotten early and either go until the giveaway or just go dead for the other teams. That's not what should happen with these tossups.

Also, can you please stop implying this "I don't know this therefore it's too hard, or I know this, therefore it's too easy" idea?
So your argument is more or less: "People currently playing quizbowl aren't interested in math (probably because it's not really covered), so we shouldn't change that." Also, I don't think your average good literature student would know hardly any of the literature in the canon, so this is not really a great metric. Of course, I'm not a proponent of asking anything about the Sylow theorems (personally I find them very very boring), but there are many other things that don't involve taking advanced math classes that could be asked (actually difficult Euclidean geometry theorems, elementary number theory, combinatorics). These are common things that high school kids interested in math learn or see on their own and don't have too much intersection with first year college math.
Look dude, I think your idea of "high school kids interested in math" is somewhat different from what we have. I don't mean to say this is bad, but it probably just a result of your exposure to other students like you. I know that you have done a lot of math (you're the same 2006 IMO medalist, right?), and what you have been exposed to far outshines what I am exposed to (I could never get past the AIME), which in turn is probably much higher than what the average quiz bowler is exposed to. The fact that they are "common things" to you is in stark contrast with the fact that they may be profound ideas for some people out there.

It is sad that the math canon is small, but there is relatively little we are going to be able to do about it, unless we find that the average person's exposure to math increases. If we start writing hard IS set tossups that become indistinguishable from ACF Fall/EFT level tossups, I think we have come to a bad state in quiz bowl.
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Re: An Open Letter to NAQT

Post by Tegan »

I am bit curious as to how this discussion has turned, because just when I think I have heard it all, something new comes up.

The recent issue that seems to be debated (and correct me here if I am misunderstanding):

-- there should be more computational math
-- there is a limited canon in acceptable math problems under the current format.
-- make the math questions more difficult.
-- these questions would go dead, because the average good/bad/indifferent quizbowl player is not adept at math.
-- I (et.al.) do not know many things that are common in quizbowl, so this argument is non sequitor.
-- the non-math things you claim not to know are very common and deserving a place in the canon, wether you know them or not. A majority of the quizbowl world would not know the math you are suggesting, so it does not belong.


On one level, I see that this is a bad argument against math .... a lot of people I know don't know it ... I likely don't know it, therefore it should be kept out. That sounds like the "our school doesn't teach British Lit" excuse I heard years ago (note: it is not the same, because those schools were pretty bad; I said "sounds like", not "is"). There will certainly be some (former) math people who will say "I was good at math, and it should be kept out". OK, but that still doesn't mean that I am seeing the merit of just saying "most people don't know, it, therefore it is out" ... there is a distinct parallel to those who do say "the Napoleonic Wars are too tough, so they should not be covered".

But .... in the end, what defines something as being canonical (I'm talking high school here)? I suppose that if you were to look up and down the ranks of players and honestly ask "is this something that we are going to know, should know, have had history of knowing ... yadda yadda" and there is a resounding "no, this is above our heads" or "we don't really have a good access to learning this", etc. then I could see that this becomes a good argument. I mean, I know there are more than a few high schools out there who teach diffeycue, but I would think that any of those question popping up at this time would be rightfully chastised. From that standpoint, you could argue that tougher math is beyond the high school canon. Without the difficult math (or a change in format, which I am not advocating), I see that there is a severe limit placed on what can be done in math. It is not so much to say that it is "out of canon" as to say "does not fit format".
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Re: An Open Letter to NAQT

Post by theMoMA »

Sir Walter British wrote:Whether or not you've never heard of Pope Gregory the Great (hint: he is known for a namesake chant) ofr Orpheus in the Underworld, the source of the Can Can, doesn't make them any less relevant and askable. I would contend that both of these have their place in the canon well earned.
Just for clarity, Gregory VII is not Gregory the Great (aka Gregory I); he's the dude that Henry IV went barefoot at Canossa to appease.
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Re: An Open Letter to NAQT

Post by Matt Weiner »

Tegan wrote:On one level, I see that this is a bad argument against math .... a lot of people I know don't know it ... I likely don't know it, therefore it should be kept out.
The argument is that adding things that people don't know solely to preserve something that doesn't need to be there in the first place is a crazy way of going about this. Yisun is putting forth the argument that all the fundamental problems with math calculation questions can be solved by asking harder calculation questions, when of course this solves none of the problems and adds a new one (dead tossups).

I find the turn this thread has taken kind of bizarre. "You want quizbowl to look like Mathcounts" and "you don't know anything except how to do arithmetic so you just want more arithmetic in quizbowl" are used as insults in these discussions, normally. They are extreme characterizations of the pro-math position that may even be unfair ad-hominem attacks to use in many circumstances. Except, Yisun seems to unironically believe them and is loudly proclaiming them? This is bordering on satire.
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Re: An Open Letter to NAQT

Post by Tegan »

Matt Weiner wrote:The argument is that adding things that people don't know solely to preserve something that doesn't need to be there in the first place is a crazy way of going about this.
Acknowledged .... as I (personally) was reading the argument it was this statement minus the words between "know" and the second "is". All I'm saying is that using the "we don't know it, ergo it should not be in quizbowl" can be dangerous when discussing broad categories. Especially for newbies, it can come across as a couple of blowhards dictating accepted policy because they like it to be a certain way, rather than policy being based on a strong rationale (which it is).
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Re: An Open Letter to NAQT

Post by Ike »

I just would like to point out that even if there were a way to do a pyramidal math tossup in which some pyramidal trick could be used (eg the aforementioned Catalan numbers or something) it comes down to "subliminal quizbowl." or what someone else dubbed "metaphysical."

This year's 2008 HSNCT had a tossup on Leopold Bloom in round 17. It mentions that while he is at the national library, he navigates between two men arguing about Aristotle, fleeing Barney Kieran's pub as a man throws a biscuit, blind with rage, and men acting like swine.
Aside from the fact of the Irish pub causes huge transparency problems, all you have to really know is that Ulysses parallels the Odyssey, put two and two together, and bam, Leopold Bloom. I don't like clues that are like subliminal messages permeating the whole question.

I see this to be a problem. Lets say someone does know Catalan numbers, but they have too much pressure or whatever reason to recognize those as instant Catalan numbers instantly, or they just know the definition and can't recognize them as Catalan numbers, is it fair to penalize them because they were so supposed to subliminally recognize they are Catalan numbers? I doubt that.

Without pyramidality, computation is finding a way + computation.
With pyramidality, you're entering into a new ground with many quizbowl problems.

Bottom Line in my opinion, computation should be cut completely, maybe PACE math can stay.
If there is to be a compromise, refer back to my cyclic and step pyramidality post.
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Re: An Open Letter to NAQT

Post by yisun »

I mean, kind of? But not really: high schoolers are never going to be able to answer tossups on Alexander-Lefchetz duality, whatever that is, ever ever ever. Because they'll never know jack about it, because that sort of information is simply inaccessible to the immense majority of high school students. But everyone can read a book, so nothing prevents them from learning quiz bowl lit to the point where they can one-line tossups on it. But even if you made math something that you absolutely had to dedicate one student to, in a game with 25% theoretical math, you'd just get a lot of math guys who wouldn't be able to answer a lot of the really hard tossups.
So the Alexander-Lefchetz duality thing was my example of a bad math question using a common-link sort of deal and has nothing to do with HS difficulty. It was the first line of a tossup in my room at EFT and I got buzzer-raced out of it (by Harvard A) because both me and the guy who answered had taken a class that vaguely mentioned this existed. But there's no need for any real knowledge when the tossup mentions Alexander-Lefchetz, which is really the case for most such tossups.

Also, there are such things as math books (note that everything I'm proposing are things usually studied before or during the first year of college).
The fact that you must not only know how to solve the problem but also solve it makes this not quiz bowl. I suppose the language many people have been using is a little imprecise: we don't just mean computational speed as in "speed at which one can evaluate arithmetic:" it's the speed at which one can do some kind of manipulation on something. One must solve the problem faster. And I'd argue that there are people with more knowledge about a subject in math who are not capable of solving the problem faster.
So in the case of, say, the fundamental theorem of calculus, is your argument more or less: "there exist people, Alice and Bob, so that Alice 'knows more' about the FTC, but Bob can solve calculus problems involving the FTC faster. in this case, Alice needs to get the tossups, rather than Bob." It seems like this makes it an issue of semantics, since one could say that we're testing the knowledge of how to solve the problem.
Here's what the "do something" argument is saying: quizbowl is about taking a clue, figuring out what the answer is in terms of that clue, and buzzing in, while computational math is about taking a problem, establishing the formula needed to solve the problem, computing the answer, and then buzzing in. I don't care how long or short that computing step takes. It doesn't matter how far you boil the "doing it" step down, whether you're working with big numbers or small numbers or variables or anything. That extra step is still there, and that's not fair from a continuity standpoint.
Okay, so do you accept that "establishing the formula needed to solve the problem" is legit? Because if so, at least on some level, easy computation can be memorized. (the multiplication tables, the basic rules for multiplying variables, etc). Strangely, this would be similar to a math competition in quite few ways.
Whether or not you've never heard of Pope Gregory the Great (hint: he is known for a namesake chant) or Orpheus in the Underworld, the source of the Can Can, doesn't make them any less relevant and askable. I would contend that both of these have their place in the canon well earned.
I'm not challenging this. There are a lot of things in the canon I don't know about, and it doesn't bother me that those who do answer those questions instead of me.
Also, can you please stop implying this "I don't know this therefore it's too hard, or I know this, therefore it's too easy" idea?
What I'm saying is that the relation between Orpheus and the Underworld/Gregory the Great and what the typical high school student learns in high school is more or less the same as the relation between a second fact about pi and the high school math curriculum.
Look dude, I think your idea of "high school kids interested in math" is somewhat different from what we have. I don't mean to say this is bad, but it probably just a result of your exposure to other students like you. I know that you have done a lot of math (you're the same 2006 IMO medalist, right?), and what you have been exposed to far outshines what I am exposed to (I could never get past the AIME), which in turn is probably much higher than what the average quiz bowler is exposed to. The fact that they are "common things" to you is in stark contrast with the fact that they may be profound ideas for some people out there.

It is sad that the math canon is small, but there is relatively little we are going to be able to do about it, unless we find that the average person's exposure to math increases. If we start writing hard IS set tossups that become indistinguishable from ACF Fall/EFT level tossups, I think we have come to a bad state in quiz bowl.
So I generally go by what the interested kids at my high school would know. I agree that many things would not be okay at the high school level under any circumstance. And by "common" I mean, "these are accessible things that a student interested in math would go to outside the standard high school curriculum." It seems like the literature and history canons are very far divergent from the corresponding high school curriculum, so I don't see why this is not possible for math (of course not immediately but at some point).
Yisun is putting forth the argument that all the fundamental problems with math calculation questions can be solved by asking harder calculation questions, when of course this solves none of the problems and adds a new one (dead tossups).
I believe that I've addressed all your arguments against what I claim to be the helpful effects of harder questions. If I've missed any or you disagree, feel free to challenge my position. But it's a bit hard for me to really argue against these nebulous "fundamental problems." Also, I've asked a couple times whether there are indeed buzzer races, as some have claimed, or many dead tossups. Which is it? You seem to have argued the former before, so I'm a bit confused:
Matt Weiner wrote: Which three TJ players and two Charter players knew, and were racing to do the arithmetic on. You cannot overcome the pyramidality problem here because the one math question always comes at a discrete time, as opposed to the real quizbowl tossup which can actually be pyramidal.
I find the turn this thread has taken kind of bizarre. "You want quizbowl to look like Mathcounts" and "you don't know anything except how to do arithmetic so you just want more arithmetic in quizbowl" are used as insults in these discussions, normally. They are extreme characterizations of the pro-math position that may even be unfair ad-hominem attacks to use in many circumstances. Except, Yisun seems to unironically believe them and is loudly proclaiming them? This is bordering on satire.
So a large part of my point is that arithmetic can be kept to more or less a minimum that is equivalent to "can you remember your multiplication tables." So I fail to see how your second point is in any way accurate. And what's wrong with Mathcounts, seriously? It does have questions that involve too much computations, but that doesn't mean the entire competition revolves around it. They can more or less be taken out by making the numbers nicer.
It seems that only one side of this argument is considering such a claim (eg, Gregory the Great, Orpheus in the Underworld)? I know perfectly well how to do math..
I was worried when I brought those examples up that I would be accused of making this argument. My argument is that most high school students (independent of quiz bowl) don't know these things, yet they are part of the canon. So saying that most high school students don't know some things about math is not really an argument against its inclusion.

I guess what I'd like to see is an argument for why things currently in the canon are there besides "everyone knows them" and "they are important" (so are a lot of things), since these seem to be being used a lot against harder math.
I see this to be a problem. Lets say someone does know Catalan numbers, but they have too much pressure or whatever reason to recognize those as instant Catalan numbers instantly, or they just know the definition and can't recognize them as Catalan numbers, is it fair to penalize them because they were so supposed to subliminally recognize they are Catalan numbers? I doubt that.
I agree that such subliminality is bad and is currently a feature of many of the computation questions. In this particular case though, if they just know the definition, they should probably lose to someone who has deeper knowledge of the Catalan numbers and knows the many types of places where they come up. This is actually one of the canonical examples used to introduce Catalan numbers that someone who just learned about them would probably know.
Yi from Harvard
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