Math As We Move Forward

[AKKOLADE]

I was doing some thinking earlier while reading through the BATE set from last year. One thing I noticed they did was ensure that nearly, if not every single, round had a math question. Not a computation question, but a theory question.

Which leads me to proposing that maybe this could help convince coaches who favor math calculation despite its affect on pyramidality. I'd have to think there's enough subject material available, simply because students have a lot of high level math available for them to take.

Do you think this would be successful in helping convert coaches to computation-free sets?

[Deckard Cain]

I would support this. I think math is important enough at the high school level that we can easily justify giving math theory at least one question a game, if not even 1/1, and that there are enough accessible topics available to fill this demand.

[Tanay]

1/1 math seems a bit much, IMO. Maybe you can add it on to science and increase the science distribution by 1 tossup or 1 bonus each round.
So if it was ten rounds, you could have 5/5 math added onto science.

[Matt Weiner]

That's a lot of science. I'd prefer to take a collegiate approach and treat math as a major component of the 1/1 other within the 4/4 science distribution. Guaranteeing it 1 question per game and letting earth science, astronomy, and computer science share the final question would make sense.

[AKKOLADE]

I should have specified this in the first post, but I would favor at least one question a game, with the possibility of going 1/1 but no guarantee.

Edit: Under the science distro, since math is a science.

[Sen. Estes Kefauver (D-TN)]

I think writing one math tossup per game would do a lot more to convert coaches, since it's easy for a bonus to go unasked and for people to forget bonuses.

[kayli]

I like the 1/1 math idea. Math is a very important subject, and I don't see how people can argue that math should get less than one tossup when most tournaments have either a 1/0 or 1/1 trash distribution.

Also, I like to think that science is an applied math. Saying math is a science is like saying English is a book or a sonnet. But that's a technicality.

[Mechanical Beasts]

Also, I like to think that science is an applied math.

For a whole lot of science, this is untrue!

[kayli]

Also, I like to think that science is an applied math.

For a whole lot of science, this is untrue!

I think saying math is science is even more untrue.

[Matt Weiner]

OK, but it's not a metaphysical debate, it's about quizbowl categorization. If you look at who will get those questions, what sort of clues they tend to use, who writes them, etc, then they clearly show an affinity with science questions. Remember, the distribution doesn't exist in order to satisfy some philosophical need; it exists to make the game fair.

[Deckard Cain]

Also, I like to think that science is an applied math.

For a whole lot of science, this is untrue!

Can't help but be reminded of this.

To clarify, I'm not necessarily advocating for 1/1 math, but I don't think it would feel terribly out of place either. Obviously I'm a bit biased here, but I think if we were to examine relative importance and conversion rates between math theory and questions in some other categories that do get 1/1, the math would compare favorably.

[kayli]

I don't see how we can advocate 1/1 trash, current events, and miscellaneous and not advocate for at least 1/1 math. If I remember correctly, math has always been an academic subject whereas trash has not. Personally, I don't see why we don't get rid of trash as a whole. But that's another thread for another time.

[Sen. Estes Kefauver (D-TN)]

Yeah, but eventually you'll run out of math to ask.

[Tanay]

Yeah, but eventually you'll run out of math to ask.

Agreed. For the average high schooler, I don't think there are more than a few dozen askable math terms...

On a side note, does the math canon really expand? I don't see this happening unless kids just start taking harder math courses.

[AKKOLADE]

Having taken Algebra I & II, Geometry, Trigonometry, Pre-Calculus, Calculus I & II and Probability & Statistics during high school, I'd have to think there's a decent size group of answers available to support at least a question a round, but maybe I'm wrong.

[Deckard Cain]

Yeah, but eventually you'll run out of math to ask.

I'm not sure about this, either; I think there are enough valid answers to support at least one question in every round, and probably more. As Fred alludes to, most high school students are exposed to substantial amounts of math, and I, at least, have never had any trouble at all coming up with topics for math theory questions.

[Sen. Estes Kefauver (D-TN)]

I said I agreed with making one tossup per round. I'm saying if it's a full 1/1 for every round of every tournament, things could get scarce to ask about.

[kayli]

If you're talking about vanilla taught only in high school math, then yes. You'll run out of things to write. So, you just ask about stuff not typically covered in a high school class. Geometry in particular would be good things to write tossups about because 1) there's so much to write about 2) all schools offer geometry 3) almost all students would have taken geometry by the time they're sophomores or maybe juniors. Things like areal coordinates, the Euler line, Heron's formula, the Fermat point are all very tossuppable imo.

[Stained Diviner]

First of all, I think that the answer to Fred's original question is No. If you're talking about coaches who expect Math to be on an equal footing with Science, Lit, and History (or Social Studies), then making Math 1/1 (or almost 1/1) is not going to do the trick. (As a side note, despite the way I sometimes come off on this board, I'm not a strict adherent to the idea that computational math needs to be in quizbowl. I take my team to tournaments without computational math and promote tournaments without computational math all the time. There are many coaches who believe more strongly in computational math than I do, and they will be unimpressed with less than 1/1 Math or even 1/1 Math.)

Second of all, if you're talking about just writing good questions for people who like good questions, I think that to some extent variance is acceptable in question distributions, especially on the high school level where there is no gold standard of distributions. For a variety of reasons, writing lots of math questions is difficult. I would think that if a writing team has a person or group that likes to write theoretical math questions and can come up with enough good ones to fill their tournament with 1/1, then that distribution should be reasonable. If you're also going to have 1/1 each of Bio, Chem, and Physics and a little bit of ES, Astro, and CS, then that brings your Science up to 5/4 or 4/5, which I would think could be handled by decreasing Trash to 1/0 or 0/1 or Arts to 3/2 or 2/3. On the other hand, if your writing team is having trouble coming up with enough Math for 1/1, then I would at least aim for half of that and probably leave the Science at 4/4.

[jonah]

I'm guaranteeing one math question per round at New Trier Varsity, which will be split about evenly between tossups and bonuses. I think there's some good justification for having high school distributions based to some extent on curricula, and while high school curricula certainly aren't standardized, I doubt there are any serious ones that eschew math entirely. If it were possible to have as much noncomputational math as science, history, and literature, I wouldn't necessarily be opposed to it, but I'm convinced (and so too, I think, is everyone else) that this is impossible.

We don't need to limit ourselves to math topics studied in most classes, either. We don't do that for lots of other topics. And there are already plenty of math topics that come up fairly often that few high schoolers study in the classroom: Fermat's Last Theorem, say. We should ask about topics that a reasonable number of high school students can learn about independently, too. Lie algebras are probably out of the question; field axioms and vector spaces are probably reasonable for upper-level HS tournaments.

Anyway, I think it's reasonable to make the science distribution a little larger than the literature and history distributions for high school, in order that it include math.

[AlphaQuizBowler]

Things like areal coordinates, the Euler line, Heron's formula, the Fermat point are all very tossuppable imo.

You must have a very loose definition of tossupable.

[at your pleasure]

I'm not sure any of those things other than Heron's Formula are tossupable at regular difficulty.

[Captain Sinico]

I think that guaranteeing 1/1 non-comp. math in addition to whatever other sciences are present per high school round is both possible and reasonable.

MaS

[kayli]

Maybe not immediately, but they should in some point in the evolution of math tossups be included. The canon will probably start out very narrow but I'm just saying that it has a lot of room for expansion. As for those examples, I know many of my friends from math club have heard of them, and I don't think it's a stretch for quizbowlers to learn these simple quirks from geometry.

[New York Undercover]

I would say that I am somewhat decent at math (not at the level of say, Neil but I've done my share of USAMO studying, gone to MOP and other math camps) and I definitely don't think Fermat point or areal coordinates (I'm not even sure what these are). Still I would say that I think 1/1 math theory would be awesome, though I don't know if it would lure any coaches who want computation. There is just too huge of a difference between comp math and math theory, because math theory means you actually have to know a lot more, and in more depth.

[Tanay]

I'm still not sure how the canon will expand in math, unless the average math course taken by members of the quiz bowl community gets more and more complex every year. I totally get that there are terms (like Heron's formula) that are "learnable" without taking some really advanced math course, but I think that, for the most part, canon expansion in math theory at the high school level is currently limited because it's been used so sparsely. That's why I think it makes more sense to have a 1/0 or 0/1 distribution per round and expand gradually, like others have said.

[Matt Weiner]

I think that guaranteeing 1/1 non-comp. math in addition to whatever other sciences are present per high school round is both possible and reasonable.

And making science 5/5 as opposed to 4/4 for the other major categories? That seems unfair. Or do you mean guaranteeing 1/1 math within the 4/4 science?

[Rufous-capped Thornbill]

I think that guaranteeing 1/1 non-comp. math in addition to whatever other sciences are present per high school round is both possible and reasonable.

And making science 5/5 as opposed to 4/4 for the other major categories? That seems unfair. Or do you mean guaranteeing 1/1 math within the 4/4 science?

I think he means a 1/1 math within the 4/4 science. This would make sense to me, and I would like to see this happen as we move forward.

[The King's Flight to the Scots]

I think that guaranteeing 1/1 non-comp. math in addition to whatever other sciences are present per high school round is both possible and reasonable.

And making science 5/5 as opposed to 4/4 for the other major categories? That seems unfair. Or do you mean guaranteeing 1/1 math within the 4/4 science?

I think he means a 1/1 math within the 4/4 science. This would make sense to me, and I would like to see this happen as we move forward.

So no earth science, astronomy, or computer science? Or would you cut down one of the three main sciences?

[Mechanical Beasts]

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts. That's a natural target. Biology deserves 1/1, certainly, at that level.

[AlphaQuizBowler]

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts.

So we're going to take a subject that has a large established canon that may not be entirely taught in the classroom and replace it with one with a very small established canon that is definitely not taught in the classroom?

[Mechanical Beasts]

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts.

So we're going to take a subject that has a large established canon that may not be entirely taught in the classroom and replace it with one with a very small established canon that is definitely not taught in the classroom?

I have written enough high school level chemistry to fill five fifteen round high school tournament sets. I have probably written enough distinct questions with gettable clues all throughout that didn't rely on knowledge of things you don't learn until college to fill two at most. Yay?

Math has a larger potential canon with more question flexibility. I would support invading chemistry a little bit in order to provide more math.

[AlphaQuizBowler]

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts.

So we're going to take a subject that has a large established canon that may not be entirely taught in the classroom and replace it with one with a very small established canon that is definitely not taught in the classroom?

I have written enough high school level chemistry to fill five fifteen round high school tournament sets. I have probably written enough distinct questions with gettable clues all throughout that didn't rely on knowledge of things you don't learn until college to fill two at most. Yay?

If you can write 30/30 (or even 15/15) distinct math theory questions "with gettable clues all throughout that didn't rely on knowledge of things you don't learn until college," I'd be surprised.

Math has a larger potential canon with more question flexibility. I would support invading chemistry a little bit in order to provide more math.

How does math have a "larger potential canon?" And even if you think so, your reasoning that "nobody learns real chem in high school, so let's replace some of it with math" is still ridiculous because of the fact that nobody learns the answers to most math theory questions in high school math classes, either.

[Captain Sinico]

And making science 5/5 as opposed to 4/4 for the other major categories? That seems unfair. Or do you mean guaranteeing 1/1 math within the 4/4 science?

No, I mean having 1/1 math in addition to 4/4 science, or however much science would otherwise have existed. I don't think that's unfair in the least; I guess we disagree. I do think that using the ACF distribution as a hard-and-fast cap on categories is misguided in this case since the contents of high school educations literally everywhere are heavier on math than college ones (and for a variety of other reasons I can get into.) Frankly, math is badly underasked in college relative even to college levels of math study, in which many people will take only one or two per se math classes. Thus, wanting math in high school questions follow the college paradigm, in which it comes up every second or third round, seems misguided.
That said, I would be amenable to having 1/1 math within 4/4 (or however much) science. I think that, in some ways, the college major science categories are possibly overasked at 1/1 per round, so maybe something like .75/.75 each big three and other science with 1/1 math would be okay with me, too, or maybe somewhat less than 1/1 math. I guess what I'm saying here is that I don't think there's single clearly best science/math distribution in my mind, but I do think that math would be underasked at 1 question per round.

MaS

[Captain Sinico]

William, it seems to me that your argument is: "We have to keep asking what's come up before because it's come up before, regardless of any external measure of its difficulty." I disagree there. What quizbowl players currently know is shaped to a large extent by what quizbowl rewards because people study for the game and because people who know the types of things the game asks are most likely to stay around. For that reason and many others, what quizbowlers currently know alone* can't be a good metric for what we should ask. In fact, relying on that exclusively will produce what I view as a poor game, ridiculous as that may seem!
I'd say the fact is that if quizbowl tomorrow shifted to 2/2 super-classroom math, you and everyone else would start studying super-classroom math and people who are good at it would find the game more tractable and more such people would play the game, etc. In other words, on a sufficiently long time scale, the game will adapt to most any small change in the distribution if questions are consistently written in a certain way and there are people who know/can learn what's being written, which is the case for most anything. That doesn't mean that we ought to make any change I or whoever have in mind without a great deal of consideration of the other points at issue; certainly we should not do that. What I am saying, therefore, is that we should carefully examine those points.
I'll also join the chorus of experienced science writers telling you that I think you're overestimating the difficulty of writing non-computational math that people, even now, can answer.

MaS

*Please note that I am not here saying we shouldn't consider whether people know what we're proposing to ask: of course we should and must consider that as writers. What I am saying is that there are many other considerations.

[Mechanical Beasts]

I'll also join the chorus of experienced science writers telling you that I think you're overestimating the difficulty of writing non-computational math that people, even now, can answer.

And underestimating the difficulty of writing other high school science like chemistry that both can be answered and is academic and isn't the same forty questions every tournament.

[AlphaQuizBowler]

William, it seems to me that your argument is: "We have to keep asking what's come up before because it's come up before, regardless of any external measure of its difficulty." I disagree there. What quizbowl players currently know is shaped to a large extent by what quizbowl rewards because people study for the game and because people who know the types of things the game asks are most likely to stay around. For that reason and many others, what quizbowlers currently know alone* can't be a good metric for what we should ask. In fact, relying on that exclusively will produce what I view as a poor game, ridiculous as that may seem!
I'd say the fact is that if quizbowl tomorrow shifted to 2/2 super-classroom math, you and everyone else would start studying super-classroom math and people who are good at it would find the game more tractable and more such people would play the game, etc. In other words, on a sufficiently long time scale, the game will adapt to most any small change in the distribution if questions are consistently written in a certain way and there are people who know/can learn what's being written, which is the case for most anything. That doesn't mean that we ought to make any change I or whoever have in mind without a great deal of consideration of the other points at issue; certainly we should not do that. What I am saying, therefore, is that we should carefully examine those points.
I'll also join the chorus of experienced science writers telling you that I think you're overestimating the difficulty of writing non-computational math that people, even now, can answer.

MaS

*Please note that I am not here saying we shouldn't consider whether people know what we're proposing to ask: of course we should and must consider that as writers. What I am saying is that there are many other considerations.

I wasn't trying to expound any major question writing philosophy, I was really just trying to say that this statement:

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts. That's a natural target.

was illogical. He proposes replacing chem questions with math questions because chem classes have a problem that is even more applicable to math classes. Perhaps we should replace chem with math questions, but this surely isn't the reasoning for it.

[Mechanical Beasts]

At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts. That's a natural target.

was illogical. He proposes replacing chem questions with math questions because chem classes have a problem that is even more applicable to math classes. Perhaps we should replace chem with math questions, but this surely isn't the reasoning for it.

Okay, let me rephrase:
At the high school level, more than half of chem classes consists of learning to do arithmetic problems and memorizing reactivity lists (like in "single-replacement" reactions) and solubility charts, and so if there exists a "natural" high school level chemistry canon, then it is very small. In contrast is the very large range of concepts that you learn about in high school math--even if most of your time doing problems is spent with a calculator--which corresponds to a larger natural canon size, if such an entity exists (and I believe it does).

(By a "natural canon," I mean that there is a finite set of topics in many if not all subjects at the high school level that are accessible enough and widely enough taught or encountered independently to make for reasonable and difficulty-appropriate [leadins | third parts | middle clues | second parts | giveaways | tossup answers | easy parts]. Canon expansion is good at the high school level when it causes the asked-about topics to more closely approach the natural canon.)

[Dresden_The_BIG_JERK]

William, it seems to me that your argument is: "We have to keep asking what's come up before because it's come up before, regardless of any external measure of its difficulty." I disagree there. What quizbowl players currently know is shaped to a large extent by what quizbowl rewards because people study for the game and because people who know the types of things the game asks are most likely to stay around. For that reason and many others, what quizbowlers currently know alone* can't be a good metric for what we should ask. In fact, relying on that exclusively will produce what I view as a poor game, ridiculous as that may seem!
I'd say the fact is that if quizbowl tomorrow shifted to 2/2 super-classroom math, you and everyone else would start studying super-classroom math and people who are good at it would find the game more tractable and more such people would play the game, etc. In other words, on a sufficiently long time scale, the game will adapt to most any small change in the distribution if questions are consistently written in a certain way and there are people who know/can learn what's being written, which is the case for most anything. That doesn't mean that we ought to make any change I or whoever have in mind without a great deal of consideration of the other points at issue; certainly we should not do that. What I am saying, therefore, is that we should carefully examine those points.
I'll also join the chorus of experienced science writers telling you that I think you're overestimating the difficulty of writing non-computational math that people, even now, can answer.

MaS

*Please note that I am not here saying we shouldn't consider whether people know what we're proposing to ask: of course we should and must consider that as writers. What I am saying is that there are many other considerations.

Without analyzing this line-by-line, I agree with this for the most part.

1/1 math should be a bare minimum in high school. This is not the liberal arts skewed college canon, this is high school, and in most places more years of math are required than of science or history. To those who say there is not enough material to establish such a canon, this is absolutely false, and I can only assume that you are not a "math person" (by which I mean no offense; I certainly have subjects I am much less well versed in). Throughout the various disciplines there are hundreds upon hundreds of viable people(Fermat, Descartes, Euler...), terms(vector, polar coordinates, commutative property...), theorems(Fermat's Last, Fermat's Little...) etc. that are askable in a pyramidal h.s. environment. Sure, some of it may not be explicitly discussed in most high school classrooms, but neither is 50%+ of the current literature/history canon. As Mike suggested, this "super-classroom"(love that term btw) info would already be somewhat familiar to those interested in math, and easily studied by the rest.

As to Reinstein's point though, this would not in any way satisfy computational math loyalists. Most (not all) of them are so because their school traditionally produces a powerhouse numbers player that they dont' want to lose the advantage of. Even barring that, they tend to protect it in order to try to tie the canon as strictly to the actual h.s. curriculum as possible. Phasing out comp math and satisfying these folks would have to be a very very gradual process.

[Matt Weiner]

There are a lot of faulty premises at work here. Chiefly:

1) "The high school distribution should be influenced largely. or at all, by a supposed 'high school curriculum'"
2) "The reason that some people say science, history, and literature should be equally weighted is because that's how college quizbowl does it"

Neither of these assumptions stand up to scrutiny, and without them, the whole argument for turning high school quizbowl into Science Bowl II falls apart. IHSA sucks for a lot of reasons; a major one is that if you only know science (math included) and trash, you can dominate it without caring about any other category. It goes against the horizon-expanding, well-roundedness-requiring rationale of normal quizbowl. Let's not turn the rest of the game into that cesspool by upsetting the balance.

For premise #1: This has been addressed in many threads, and suffice to say that unless you are going to tell me why driver's ed and gym should get questions, and why there should be no required questions on art, music, geography, religion, nonwestern history, mythology, philosophy, current events, or any other subject that isn't a commonly required high school class, you don't actually believe it and thus have no business arguing it at all.

For premise #2: It's a straw man. The reason the major categories should be equally weighted is because it's fair, and it requires teams/players to learn all subjects. The fact that ACF learned this a long time ago is a positive for ACF, not a sign that college quizbowl is trying to do something untowards to high school quizbowl. Until someone actually argues that "college quizbowl is inherently good and high school quizbowl should follow its lead for that reason," arguing against such a position is fallacious.

[Dresden_The_BIG_JERK]

There are a lot of faulty premises at work here. Chiefly:

1) "The high school distribution should be influenced largely. or at all, by a supposed 'high school curriculum'"
2) "The reason that some people say science, history, and literature should be equally weighted is because that's how college quizbowl does it"

Neither of these assumptions stand up to scrutiny, and without them, the whole argument for turning high school quizbowl into Science Bowl II falls apart. IHSA sucks for a lot of reasons; a major one is that if you only know science (math included) and trash, you can dominate it without caring about any other category. It goes against the horizon-expanding, well-roundedness-requiring rationale of normal quizbowl. Let's not turn the rest of the game into that cesspool by upsetting the balance.

I agree that the IHSA distribution (and question quality) is not something to model after. However, that doesn't mean that math shouldn't have a place in the distribution. I am by no means advocating math get equal time as some other subjects, but it deserves its own place at the table. The insinuation that math = science is frankly insulting to both disciplines. Just because science sometimes uses numbers does not make it math any more than the fact that literature can be set in historical settings makes it history.

For premise #1: This has been addressed in many threads, and suffice to say that unless you are going to tell me why driver's ed and gym should get questions, and why there should be no required questions on art, music, geography, religion, nonwestern history, mythology, philosophy, current events, or any other subject that isn't a commonly required high school class, you don't actually believe it and thus have no business arguing it at all.

I am not, and will not advocate driver's ed and gym because they are not academic subjects. Math is. With an academic history spanning time and the globe, math has always and everywhere been a scholarly topic, and it's proper to acknowledge that in the distribution.

So no, I am not asking for the distribution to match anyone's high school curriculum. If I did, according to my high school career, we would playing about 2 science, 1 lit, 1 history, 1 French, and 1 math and 1 other. What I am saying is that math, as an academic topic that is mandatory for all students, should be fairly represented.

For premise #2: It's a straw man. The reason the major categories should be equally weighted is because it's fair, and it requires teams/players to learn all subjects. The fact that ACF learned this a long time ago is a positive for ACF, not a sign that college quizbowl is trying to do something untowards to high school quizbowl. Until someone actually argues that "college quizbowl is inherently good and high school quizbowl should follow its lead for that reason," arguing against such a position is fallacious.

As far as this goes, I wasn't attempting to say that the h.s. canon should or should not match college; merely that as it as, it is different. While it has not been explicitly stated, I know that there is sentiment that math is much more of a niche topic academically and in life; the college canon merely reflects this, and I just wanted to establish a jumping off point for standards.

[Captain Sinico]

Matt, I have to disagree with you on these points again. Quizbowl defined without referent to the academy, which is what you propose, is a degenerate, vacuous game without any deeper purpose. It matters very little if one commands the knowledge that quizbowl requires if that knowledge is characterized only by being what comes up because it comes up because it has perpetuated itself in a self-referential game. Surely a universal characteristic of secondary education, i.e. the teaching of mathematics, must have some influence on quizbowl designed for people obtaining such an education, since we're an academic game.
Secondly, I disagree vehemently with your contention that "fair" means "conserving the scoring ratios that exist now among the different Matt-Weiner-defined categories* of players." In fact, I don't see how you can advocate quizbowl's being fair by that definition. It's a fact, as you well know, that any change to the distribution or the way questions are written will change certain players' scoring, yet we've changed both those things many times. Why is it that this change is unfair? Were the others likewise unfair?
On the contrary, I say that changes toward rewarding deeper knowledge in important areas of high school academic study are positive changes, regardless of whose scoring they might impinge upon. To wit, I don't see having 4/4 science and 1/1 non-computational math as unfair in the least. As I've said before, I likewise don't think having somewhat less math or science would be grossly unfair, either; my judgment is that a change to 4/4-1/1 is fairest change we can make at the moment.
Finally, I'll urge you, as many often do, to try not to blow things out of proportion. Even if I accept your premise that adding 1/1 non-computational math to the distribution would greatly privileged science players, however defined, on those 1/1, it doesn't follow that quizbowl has been made "Science Bowl II" or made to have a distribution resembling the IHSA's. Indeed, to get to the IHSA distribution, we'd have to add either 2.5/2.5 or 3/3 (depending on which ratios we want to conserve) math in addition to the 1/1 that you're denouncing. Using that kind of stilted argument will get us nowhere good.

MaS

*You are, in fact, here engaging in the exact same program of strong categorization that you denounced upthread when you denied a claim that math is not science per se. Your claim is the precise converse of that one: that math players are science players because math is science.

[Matt Weiner]

My claim regarding fairness is nothing more or less than "the people who will get math questions are the same people who will get science questions, because empirically this is the case." And to me this is the major point of the distribution. People got NAQT to stop putting geography and trash clues at the end of history and literature questions, because that gave an unfair, undisclosed advantage to geography and trash players. Adding in an additional 1/1 of material that we all know is going to be converted by science players and is written like science questions is, de facto, increasing the science distribution by 20%, whether the case that math is traditionally grouped under science in collegiate distributions is justified or not (and I certainly believe that it is).

[Dresden_The_BIG_JERK]

...the case that math is traditionally grouped under science in collegiate distributions is justified or not (and I certainly believe that it is).

Would you please elaborate this? Perhaps I am biased, but I couldn't possibly disagree more. To what extent are you insinuating math and science are the same?

[Pilgrim]

I agree with pretty much everything that Sorice has written in this thread.

I think Matt's position is pretty silly; even if we accept his argument that players fit into categories of "lit players," "history players," and "science players" and that these groups should get equal parts of the distribution (which I don't agree with), I see no reason why math is more obviously grouped with science than, say, geography is with history or mythology is with literature.

[Deckard Cain]

Perhaps not surprisingly, I find myself in agreement with Mike and dispute Matt's claim that having 1/1 math in addition to 4/4 science unfairly slants the game toward "science players." Math as an academic discipline is distinct enough from biology, chemistry, etc. that players skilled in what quizbowl traditionally refers to as "the big three sciences" do not necessarily have an overwhelming advantage on math questions, and any advantage they do have is really no different than what the game does with other fields. To use a similar distributional situation, whatever advantage "science players" have on math questions is fairly equivalent to any natural advantage "history players" have on geography questions, etc.

edit: I see Trevor has said more-or-less the same thing.

[AlphaQuizBowler]

To those who say there is not enough material to establish such a canon, this is absolutely false, and I can only assume that you are not a "math person" (by which I mean no offense; I certainly have subjects I am much less well versed in). Throughout the various disciplines there are hundreds upon hundreds of viable people(Fermat, Descartes, Euler...), terms(vector, polar coordinates, commutative property...), theorems(Fermat's Last, Fermat's Little...) etc. that are askable in a pyramidal h.s. environment.

While I would not call myself a "math person" per se, I am good at math. I am taking BC Calculus in my junior year; moreover, I really fail to see what that has to do with my argument. I guess the point I'm getting at is this: even if there are many "named things" that could constitute a high school math canon, I don't think there are enough clues. Taking some of your examples:
Fermat and Euler- Sure, you would have a lot of material here. Famous mathemeticians would probably make up a lot of the askable math canon, much like most of the high school econ canon is economists.

vector- A non-transparent tossup on vectors at the high school level would most likely have to resort to near-impossible lead-ins. You have cross-products, dot-products, and maybe some theorems.

polar coordinates- That would be one weird tossup, in my opinion.

commutative property- I will admit to having written a tossup on this. I think that some clues exist (abelian groups), but perhaps not enough.

Fermat's Little, Fermat's Last- Do many people know these? My only contact with these has been through quizbowl.

Sure, some of it may not be explicitly discussed in most high school classrooms, but neither is 50%+ of the current literature/history canon. As Mike suggested, this "super-classroom"(love that term btw) info would already be somewhat familiar to those interested in math, and easily studied by the rest.

This statement ignores the nature of the lit and history canons versus the math canon. In lit, there exists a set of works that (at least most) scholars consider important. Lit is also fairly easy to learn, as one can associate titles with authors and characters with titles more easily than, say, learning the deeper implications of the Goldbach conjecture that would be in a hypothetical math tossup. Moreover, there are many more high school kids who go home and crack open a work of Steinbeck or Hemingway than a math textbook.

With history, I disagree that the quizbowl canon is not taught in high school. If one has taken AP World, one would be familiar with nearly all of the world history topics that come up in varsity-level tournaments. Same with AP US and US history. And, as with lit, I think there are a lot more history buffs (especially military history) than theoretical math* aficionados.

*There may be a significant number of people interested in math in high school, but most of these people do math team type stuff that involves more computation than anything.

[cvdwightw]

People are claiming that the canon of askable math theory is too small to merit 1/1 theory per round. I concur with this, mainly because the "tossupable" ideas in this thread have been supported with the Greg Weinstein "I asked self-proclaimed experts and they thought it was easy" argument and not with any proof that 80-90% of high school teams will actually know them.

That said, I think we need to re-evaluate the science distribution as a whole. Biology and physics have plenty of answers; whether those answers are gettable is an entirely different question (my position is no, because to get a tournament's full representation of biology or physics, you often have to go into the upper echelon of AP Science difficulty, and this makes science players who haven't taken AP Science mad). Chemistry is even worse, because there's only like a semester's worth of real, non-computational answer choices and it's become patently clear that element tossups are difficult to write well and play terribly (Quack Quack Quack FTP Name this element with atomic number 84 and symbol Po).

Still, the Big Three get the Big Three designation of 1/1 per round because that's what most science players (and, really, anyone else who plans to do anything with science in college) take for 3 out of 4 years, and the other year is typically AP Big Three Science (some people take two or three AP Big Three Science courses). Earth Science? Astronomy? Those are for losers who can't pass real science. Computer Science? Maybe if you count "learning how to make Microsoft Word not do things you don't want it to do."

So then there's math. You get 4 years of math in high school, up to 7 if you're one of those geniuses that took Algebra in 6th grade. There aren't too many good answers for any given level of math, but you've got at least seven levels (Algebra, Geometry, Algebra II, Trigonometry, Precalculus, Calculus, Probability/Statistics) that have some real answers.

I also think Matt's attack on the "high school curriculum" is misguided. I'm not at all sure where Matt's reference for "what high schoolers will know" is, but it sounds like "high schoolers will know things that I know they know, because I have seen what they know when I run tournaments." This is an entirely circular argument - there is no reference outside of the game itself; as such, we should expect an entirely new team to know very little (and this is not only patently untrue but dangerous to the game itself). I will agree with his arguments that the distribution should not be beholden to the curriculum, but I disagree with the rest of it. In fact, I will claim that it is the only true reference we have for "what high schoolers will know," since after all, the curriculum exists as an expectation of "things that high schoolers will know."

For a category to merit its place in the academic distribution, it must have academic relevance, it must be possible or at least not difficult to construct the quota of well-written questions in it, and the target audience will know 80-90% of the answers selected in it. I'm convinced that math theory meets all of these points at least as well as chemistry and physics.

[kayli]

Math and science especially at the high school level are very different entities. Biology requires almost no math. Chemistry requires a lot of simple "multiply this and divide that" math. Physics requires a lot of math, but usually requires little geometry and calculus (if one takes AP Physics C). To say that by being good at science means being good at math at the high school level is pretty ridiculous when we're not asking about simple things like taking a derivative. In high school, the study of science often has little to no bearing on true knowledge of math. In contrast, literature often covers mythology, and history often covers some geography. Without studying geometry, there is virtually no way for me to know what the orthocenter is. However, even without studying geography, I would know that Cape Horn is the lowest point in South America from studying about Magellan.

To address the issue of having no askable questions in the math canon: Of course we don't have a lot of askable questions. We haven't begun to write questions about the subjects. Who is going to know that Belgium was lead by the Rexist Party before World War II if no one has asked about it yet? Math has to have a place to start. If it means that we'll have to ask questions that will not get great conversions, then so be it. We have to get through the growing pains. I believe the argument that math questions will have near-impossible lead-ins for the high school level for clues like vector and polar coordinates are extremely faulty. If history questions had lead-ins like
[quote="HSAPQ Round Ten of ACF-style Set 1 Sample Question 12]He was victorious at a battle near Gniew over his cousin Sigismund III in a war that ended with the Treaties of Stzumska Wies and Altmark. He constructed a pontoon bridge over the Lech River to win the Battle of Rain.[/quote]
I would guess that most people would find that impossible too if such a question were never asked before.

There has to be a start somewhere for the math canon. It deserves a place separate from the science curriculum. There are some problems to face, but I believe that it would be beneficial to the game if math were to enjoy a 1/1 distribution. If math becomes marginalized further to the level of earth and planetary science, then I lose all my faith in the game. A game that places more importance on pop culture than math can never be called academic.

[Matt Weiner]

I would like to see your research notes from your study on whether people who support keeping math in the science distribution also support keeping trash at its current level.