Who is really anti-math?

[Matt Weiner]

{Modified from something I posted on another forum a while ago.}

Quite frequently, people come to this board or others and argue on behalf of calculation tossups. One of the arguments that such people use is that "math is important" and thus should be asked, or that people who oppose calculation tossups are "anti-math" with respect to quizbowl or even pedagogy as a whole.

I submit that it is in fact the anti-calculation position which is pro-math, and the pro-calculation position which is anti-math. The reason is that calculation is not math and precludes the inclusion of sufficient questions on math theory, which are in fact actual math. Allow me to expand on this point.

Math is, in fact, very important. It's important enough to be asked in the same way that everything else in quizbowl is asked; that is, fairly, with an eye towards rewarding intellectual curiosity and going beyond the classroom. In biology, in physics, in history, in literature, in art, we ask things that go above the typical high school education, because we're supposed to be rewarding outstanding students who are interested in doing more than the minimum. In math, we get claims that we need to ask questions about drawing marbles out of bags and multiplying numbers quickly because of some ridiculous appeal to what's "in the classroom." Let me tell anyone who is teaching the basics of multiplication to a high school class of any kind (let alone to high school quizbowl players) that you must teach at the worst high school in America. I learned how to do multiplication in third grade. The types of things that excellent high school math students do (trig analysis, calculus, and so on) don't get asked in quizbowl because they aren't reducible to problems that can be done in 10 seconds. As for including something behind the high school horizons in that format...don't even waste my time. A calculation tossup on topology or linear algebra? Good luck. Math calculation is the only category where it's viewed as acceptable to turn quizbowl into a remedial elementary-school exercise instead of a push to actually explore serious academic topics.

Outstanding math students should be encouraged to learn about fields at the collegiate level and above while still in high school, both in their classroom education and in quizbowl. That people who claim to "love math" would deny this opportunity to those students and instead force them to regress to the intellectual level of a horse by doing speed calculation is a complete travesty. Anyone who supports these calculation tossups over real math should be absolutely ashamed of himself for the damage he is doing to the potential mathematicians of the future--you are turning people who may be the next great scholar in a vibrant intellectual field into sideshow attractions, just so you can win bad quizbowl tournaments.

What goes on in mathematics at the university level is not based on being able to calculate quickly, or do arithmetic by hand at all. I'm not talking about the people doing research and publication or grad students here--I mean that when the average college student takes his undergraduate math requirement, he gets to use a calculator the entire time, because concepts and a way of looking at the world, rather than speed at arithmetic, are what is being taught. This is largely the case in high school as well.

I call for the immediate replacement of calculation questions with math questions. Questions that reward, encourage, and communicate knowledge about important academic topics in the field of mathematics, not questions about working together to paint a room that are stolen from someone's 6th grade midterm, and not questions that reduce to who can subtract the fastest.

To support calculation tossups is to be anti-math. To oppose them is to be pro-math.

[rchschem]

I would assume that math calculation also includes specific subject area math calculation like stoichiometry, calculating the velocity of an object falling from height y, etc.? I see no argument that these are justified because you have to know some chemistry or physics to be able to perform them.

[Sen. Estes Kefauver (D-TN)]

I have always seen those listed as science.

[master15625]

I have always seen those listed as science.

But it still involves some aspect of math calculation that makes it a speed race, right?

[Sen. Estes Kefauver (D-TN)]

Of course, but the fact that it's not part of the math distribution seems to be directly relevant to coach Grunden's comments.

[rchschem]

I have always seen those listed as science.

Potato, potato. If mathcomp is bad for math, then it's bad for science, too, for all the same reasons.

[grapesmoker]

I have always seen those listed as science.

Potato, potato. If mathcomp is bad for math, then it's bad for science, too, for all the same reasons.

I don't think anyone is actually disagreeing with this, but yeah, that's exactly right.

[cvdwightw]

I would assume that math calculation also includes specific subject area math calculation like stoichiometry, calculating the velocity of an object falling from height y, etc.? I see no argument that these are justified because you have to know some chemistry or physics to be able to perform them.

I mean, the issue here is twofold:

1. Problems of these types that would be doable in ten seconds need very easy numbers. We use 10 m/s^2 because it's a heck of a lot easier than 9.8 m/s^2 to work with in ten seconds. Accordingly, for two people who recognize what to do at the same time, it becomes a test of multiplying simple numbers really fast. These questions also have at most one clue (calculate "x") and if they're NAQT-"pyramidal," they then spend the next two lines giving you the equation, so someone that can plug and chug really fast can almost always beat someone who knows what the problem is asking for but gets hung up on (1/7) + (1/9).

2. The ability to do these problems is important. All sorts of people in all sorts of fields need to know Ohm's Law. However, the ability to do these problems quickly is not important. It doesn't matter whether I take two seconds or five seconds to solve for V if I = 200 microamps and R = 1 megaohm; what matters is that I know how to solve for V given I and R.

Similarly, there could conceivably be a reason why I want to know the roots of a quadratic equation; for instance, if I'm solving a constant-coefficient second-order differential equation (which begs the question of why solving such an equation would be academic, since it too involves calculation, but let's say I have a legitimate scientific reason like I'm modeling a damped harmonic oscillator). The ability to solve this equation accurately so that the solutions to my differential equation make sense is important and arguably academic (since, after all, I could probably just plug it into the computer once I'm satisfied with the science behind the math). The ability to solve it faster than someone else is not important and certainly not academic. This distinction between doing a problem and doing a problem fast is why I will almost always argue that calculation is an adequate topic for bonuses (which test, "Do you know how to do the problem?") but is never appropriate for tossups (which test, "Can you do the problem faster than other people? If not, we'll tell you how to do the problem and then see if you can plug and chug faster than other people.").

I would conjecture that just about every "scientist" or "engineer" in quizbowl agrees with me: knowing equations in our field is important so we don't have to look them up every time we use them; being able to manipulate those equations and solve them for a specific variable is a conceivably useful skill; being able to solve those equations faster than other people has absolutely no relevance to anything.

[Marble-faced Bristle Tyrant]

This post did a very good job at making me lean more to the no-calculation-questions side. Previously, it was not a subject I'd get too worked up about.

[Down and out in Quintana Roo]

One of the reasons why i was originally a Math Education major in college (yeah, i know, it didn't go so well) is because i really do love math. And i do like "solving for x." I always said that if someone could pay me $50K a year to solve for x, i would quit teaching now because somedays that really is more fun. Lame, i know.

Anyway, what i don't really enjoy is tedious math computation of the problem solving variety, i.e. fast-paced Math League type questions (even though i was in Math League in high school). I hated them when i played quizbowl for CR, i hate reading them now in matches, and i hate seeing the expressions on 75-90% of players when one of those tossups comes up and they hate quizbowl for the next 20 seconds.

But i LOVE math theory. Questions about geometry or linear algebra or Mersenne primes or something are extremely interesting to read and to learn about. These sorts of questions i've been seeing in HSAPQ packets are downright awesome and it's great to see them about once per packet. I think the more than we incorporate them, the more we can get students interested in them and realize that math is indeed important to the quizbowl canon, but only in this appropriate fashion.

[Stained Diviner]

I've made my points in other threads. You'll have to pardon me from this one, since I'm not particularly interested in debating who is pro-math and who is anti-math and how much shame I should feel. Anybody who wants to call themselves more pro-math or less anti-math than me is free to do so.

[vcuEvan]

I've made my points in other threads. You'll have to pardon me from this one, since I'm not particularly interested in debating who is pro-math and who is anti-math and how much shame I should feel. Anybody who wants to call themselves more pro-math or less anti-math than me is free to do so.

I'm more pro-math than you.

[Ben Dillon]

I'm more of an after-math :)

[harpersferry]

Non-computational math has no shortage of answers--just a shortage of answers that are currently tossupable. Computational math has squelched it for so long that the canon for it has not expanded like it has for other subjects over the years.

I can't even tell you how many words I learned in one year of college math that could be asked about if the knowledge were there on the circuit. Quizbowlers could learn many of them very quickly (at least their most common definitions and properties). If we have people studying details of plots of many literary works that they would never study in the high school classroom, there's no reason people can't learn about groups, rings, fields, vector spaces, genus, torus, sphere, ball, geodesic, compact, connected, convex, smooth manifold, open, closed, complete, bijective, surjective, injective, isomorphic, linear maps, inner product, compositions, permutations, transpositions, generators, countable, uncountable, Cauchy sequences, Jordan forms, Gaussian curvature, Hilbert spaces etc. enough to answer questions on them. A lot of this stuff is really interesting, and the intuitive ideas are sometimes very accessible and even beautiful. We can't ask people to do proofs in quizbowl (duh), but we can do what quizbowl does: ask specific questions about things that have names based on their properties. To do that you do not need to take any college math classes or do anything rigorous, just tool around on wikipedia or mathworld for a while. That or read college questions. This stuff already comes up there (although it's not a huge part of the distro). Also notice how you do not need to limit yourself to math history for non-comp math. That's fine too, but in my opinion should have as much weight as science history in science (i.e. some but not excessive).

If current quizbowlers are like I was, if something keeps coming up, you learn it and then you learn some more about related things. The canon for modern math is woefully lacking in high school. Even limiting yourself to calculus is boring. There's so much more out there, and it isn't even all that difficult to get a basic grasp of. You don't need to be able to prove anything about this stuff to answer a tossup on it. It's analogous to being able to answer physics questions on modern topics (like general relativity) that high schoolers simply could never actually learn because it requires heavy mathematical machinery to even approach the rigorous equations.

As far as computation goes: I'm not a fan. Yes, extremely well written math comp questions might be able to test deep understanding of a topic. However, I do not think quizbowl is the correct setting for this type of question. Non-computational questions on topics that are important to modern (and even historical) mathematics which can easily be pyramidal and have specific answers is completely appropriate for quizbowl and should replace computational questions in the distribution. Admitedly the canon expansion for non-comp math is so far behind that writing questions of comparable length and difficulty to other categories at this time would be difficult. My biggest fear, however, is that the inevitable removal of computational math from good quizbowl will leave math shortchanged and a subdistribution of science.

[Adventure Temple Trail]

Now that both high school nationals include no math computation tossups, and one major question provider doesn't use math computation at all while the other is strongly considering reducing it, it would be nice to have theoretical math start showing up in quizbowl more frequently. For all the talk about a potential theoretical math canon, it seems like the vast majority of untimed sets dedicate less than one tossup or bonus a packet to theoretical math, or that math is shoved into "other science" when, at high school, it does have a large askable answer space of its own. I, for one, enjoy pyramidal tossups on math theory subjects, and don't think I'm alone when I say it'd be cool for more high school sets to have at least one tossup or bonus per 20/20 dedicated to math theory. (1/1 out of 24/24 doesn't seem too untenable either.)

Though it's still important not to jump the gun on concepts that are too hard for most high schoolers, I'm pretty sure NAQT (I remember decent tossups on "factorial" and "continuity" in the last two packets of IS-79), HSAPQ (tossups on specific numbers and shapes), and independent writers (Prison Bowl II: tossup on "triangles") have taken the right approach to math theory tossups in the past and can continue to do so in the future, so I'm not too worried. That novice-level tossup on the Fourier transform is still a few years off...

[The King's Flight to the Scots]

Now that both high school nationals include no math computation tossups, and one major question provider doesn't use math computation at all while the other is strongly considering reducing it, it would be nice to have theoretical math start showing up in quizbowl more frequently. For all the talk about a potential theoretical math canon, it seems like the vast majority of untimed sets dedicate less than one tossup or bonus a packet to theoretical math, or that math is shoved into "other science" when, at high school, it does have a large askable answer space of its own. I, for one, enjoy pyramidal tossups on math theory subjects, and don't think I'm alone when I say it'd be cool for more high school sets to have at least one tossup or bonus per 20/20 dedicated to math theory. (1/1 out of 24/24 doesn't seem too untenable either.)

Though it's still important not to jump the gun on concepts that are too hard for most high schoolers, I'm pretty sure NAQT (I remember decent tossups on "factorial" and "continuity" in the last two packets of IS-79), HSAPQ (tossups on specific numbers and shapes), and independent writers (Prison Bowl II: tossup on "triangles") have taken the right approach to math theory tossups in the past and can continue to do so in the future, so I'm not too worried. That novice-level tossup on the Fourier transform is still a few years off...

I agree with this completely.

[Kanye West]

I think that BOTH computational and noncomputational math are important and should be present. But, personally, when facing computational math tossups or bonuses, I know how to do them, but I think we are not given enough time (often 3-10 seconds). With the 15 point math bonuses in PACE format, in which we are given a solid 30 seconds, I have a much easier time answering them, and I have seen other teams have an easier time as well. So, maybe we should be given 30-45 seconds on all math questions? Just my 2 cents.

[jonpin]

I think that BOTH computational and noncomputational math are important and should be present. But, personally, when facing computational math tossups or bonuses, I know how to do them, but I think we are not given enough time (often 3-10 seconds). With the 15 point math bonuses in PACE format, in which we are given a solid 30 seconds, I have a much easier time answering them, and I have seen other teams have an easier time as well. So, maybe we should be given 30-45 seconds on all math questions? Just my 2 cents.

A couple things:
Welcome to the boards.
PACE no longer uses the format it did last year.
Neither PACE NSC nor NAQT HSNCT will have comp math at 2010 nationals.
You'll be expected to defend your declaration that comp math is "important".
Your suggestion will grind matches to a terrible halt for more than half of the players in a game. Thirty seconds on an advanced computation question that you don't know how to do is a looooooooooooooooong time.

[Cheynem]

I am not so much hung up on the "pro-math" or "anti-math" stuff Matt talked about in his initial post. I mean, believe whatever you want about the importance of comp math in my book. Rather, I just think that it's impossible, gallant attempts to prove otherwise notwithstanding, to write a solid, pyramidal computational math tossup. It's the same reason why we don't ask quizbowlers to analyze a poem, do a chemical experiment, or other tasks appropriate for high schoolers. I do think comp math bonuses are fine, although I agree they should place more emphasis on knowledge rather than being able to perform speed tricks (having the proper knowledge to perform an operation but running out of time seems rather frustrating for quizbowl, which is about rewarding knowledge not speed).

[kayli]

Ok, pet peeve here: but there's no denying that math is important. The questions are: Can it can be formatted into a pyramidal question (the concensus best way of asking questions)? And, how much of the distribution does computational math deserve?

[Whiter Hydra]

Ok, pet peeve here: but there's no denying that math is important. The questions are: Can it can be formatted into a pyramidal question (the concensus best way of asking questions)?

It already has been. It's known as non-computational math.

[kayli]

Ok, pet peeve here: but there's no denying that math is important. The questions are: Can it can be formatted into a pyramidal question (the concensus best way of asking questions)?

It already has been. It's known as non-computational math.

Agreed.

[Jesus vs. Dragons]

Couldn't computational math be pyrmamidal? I am sure this is going to be refuted, but couldn't you simply have an answer space of n, and lead in with [insert level appropiate hard math here] and progress through them? While I am in no way a supporter of comp math, this seems to be a fairly pyramidal setup.

Note: I am sure this has been proposed elsewhere, but it does in fact seem to mesh together comp math and math theory. Most quizbowlers know what a derivative is, but a smaller percentage know how to actually calculate them. Isn't this the aim of a pyramidal tossup?

[Auroni]

Computational math includes a set of background information, leading to the question (like the ages of three people, and the question is, how old will person y be in a few years). In this sense, there are no "clues" for this question other than the basic question itself, so all of the background information to the problem is useless on its own.

Hence, you can't create a multi-clued pyramidal tossup if the question is the closest thing to a uniquely identifying clue.

[Mechanical Beasts]

Couldn't computational math be pyrmamidal? I am sure this is going to be refuted, but couldn't you simply have an answer space of n, and lead in with [insert level appropiate hard math here] and progress through them? While I am in no way a supporter of comp math, this seems to be a fairly pyramidal setup.

It's not intuitive to me that it should be easy to construct such a beast; you'd have to find multiple clues for the same answer that are near-instant calculations but conceptually of different levels of familiarity. At that point, you could just as easily write a non-comp tossup, and you'd be almost bound to do a better job.

Note: I am sure this has been proposed elsewhere, but it does in fact seem to mesh together comp math and math theory. Most quizbowlers know what a derivative is, but a smaller percentage know how to actually calculate them. Isn't this the aim of a pyramidal tossup?

There's a terribly small percentage of quizbowlers who knows what a derivative is but doesn't know how to use the definition of a derivative to, well, find a derivative. I don't know how productive it would be to test quizbowl's ability to quickly apply shortcuts in finding derivatives or why that's not as well or better tested by a novice-level tossup on "derivative."

[kayli]

It's impossibly hard to make a good pyramidal computational math problem. Let's say a good pyramidal tossup has 7 clues going from hardest to easiest. To make computational math pyramidal, you'd have to get 7 computations in decreasing difficulty; and to make it so this one question doesn't take 3 minutes to read, the clues can't have any pauses in between them so people can work on them. Thus the computations have to be near instantaneous to be viable. Either that or you'd have to reduce the amount of clues which is rarely a good idea. Additionally, such a case would produce quite the dilemma. If you know how to do the first (hardest) problem, should you tank through that problem or should you wait for the problem two clues down? After all, the time it would take for you to solve the hard problem might be greater than the time it would take for the reader to read two more clues and figure out the easy problem. In these ways, math is a lot different than other subjects.

As Andrew says, you're better off trying to make a non-computational math tossup. Less painful. Better question.

[Monk]

quizbowl, which is about rewarding knowledge not speed

...Really? Never feels like that to me.

It would really be nice if there was a good way to write comp math questions - there is a player on my team who mainly comes for comp math. Even someone as clueless about math as I has realized that it doesn't seem practically possible at the current moment, but maybe quizbowlers in the year 2050 will solve the problem.

[Kwang the Ninja]

quizbowl, which is about rewarding knowledge not speed

...Really? Never feels like that to me.

Good quizbowl rewards knowledge. Bad quizbowl rewards speed.
Which is why computational is usually considered a hallmark of bad questions-- in its current form, it reduces to a race between two people to do a problem faster.
EDIT: Forgot to post my point.

[Mechanical Beasts]

maybe quizbowlers in the year 2050 will solve the problem.

People generally find me irritatingly impractical for my willingness to leave comp math this out, because I'm willing to believe that in our imperfect wisdom there's actually a way to do it that we're unaware of.

But we have to write 2010 questions with 2010 technology.

[jdeliverer]

This has probably been brought up before, but computational math is like trash - it's not a real test of academic knowledge, but you keep it around because it allows bad/new teams to see that quiz bowl can be fun and encourages them to stick around and learn enough to compete with more academic material. Perhaps it could be reduced to 1/1 per game, like trash, and especially have it reduced at the varsity level, but I know there are people (like me) who wouldn't be playing good academic quiz bowl if there hadn't been comp math to keep me interested at the beginning.

[Cheynem]

My problem with this is that trash, as non academic as it is, can still be written in a pyramidal way which rewards knowledge. Computational math (in a tossup form) cannot. People might stick around for spelling questions or grammar speedchecks, but these have no place in good quizbowl either. There comes a time in which as nice as it is to attract and retain new people, the very nature of the game shouldn't be compromised to do so.

[Monk]

have it reduced at the varsity level

Already happened.

[Tanay]

Perhaps it could be reduced to 1/1 per game, like trash, and especially have it reduced at the varsity level, but I know there are people (like me) who wouldn't be playing good academic quiz bowl if there hadn't been comp math to keep me interested at the beginning.

The issue here is that 1/1 is still an excessive amount (it would actually be an increase over what most "good quiz bowl" formats currently have), and if you put comp math in the same category as trash, then you are saying that the game will be 2/2 "trash", or about 10% trash overall. That is enough to make an appreciable difference in a competition that is supposed to stress academic knowledge. Furthermore, it limits the ability to run an effective timed format and will ultimately disappoint people who join quiz bowl for the comp math, only to see it eliminated later. It will also disappoint people who see a trade-off, because every question that is used for comp math will be a question detracted from another, more legitimate field of study.

[Kanye West]

I think that BOTH computational and noncomputational math are important and should be present. But, personally, when facing computational math tossups or bonuses, I know how to do them, but I think we are not given enough time (often 3-10 seconds). With the 15 point math bonuses in PACE format, in which we are given a solid 30 seconds, I have a much easier time answering them, and I have seen other teams have an easier time as well. So, maybe we should be given 30-45 seconds on all math questions? Just my 2 cents.

A couple things:
Welcome to the boards.
PACE no longer uses the format it did last year.
Neither PACE NSC nor NAQT HSNCT will have comp math at 2010 nationals.
You'll be expected to defend your declaration that comp math is "important".
Your suggestion will grind matches to a terrible halt for more than half of the players in a game. Thirty seconds on an advanced computation question that you don't know how to do is a looooooooooooooooong time.

Thanks.
I am aware, I should have clarified, "old PACE".
Aww darn.
No thanks.
30 seconds isn't terribly long.

[Sen. Estes Kefauver (D-TN)]

No thanks.

Then enjoy us refusing to engage you further and refusing to listen to your opinion on math computation.

[Jesus vs. Dragons]

Couldn't computational math be pyrmamidal? I am sure this is going to be refuted, but couldn't you simply have an answer space of n, and lead in with [insert level appropiate hard math here] and progress through them? While I am in no way a supporter of comp math, this seems to be a fairly pyramidal setup.

It's not intuitive to me that it should be easy to construct such a beast; you'd have to find multiple clues for the same answer that are near-instant calculations but conceptually of different levels of familiarity. At that point, you could just as easily write a non-comp tossup, and you'd be almost bound to do a better job.

Note: I am sure this has been proposed elsewhere, but it does in fact seem to mesh together comp math and math theory. Most quizbowlers know what a derivative is, but a smaller percentage know how to actually calculate them. Isn't this the aim of a pyramidal tossup?

There's a terribly small percentage of quizbowlers who knows what a derivative is but doesn't know how to use the definition of a derivative to, well, find a derivative. I don't know how productive it would be to test quizbowl's ability to quickly apply shortcuts in finding derivatives or why that's not as well or better tested by a novice-level tossup on "derivative."

I agree with this, and this would be a better alternative to me, but if comp math is going to be around, shouldn't it at least be attempted to make it as pyramidal as possible? While this most likely not the easiest/best way to go about it, it is a viable option. While a tossup on "derivative" would be more pyramidal, it would not be comp math and would fall into some other distribution (assuming that there is no math theory subdistribution).

It's impossibly hard to make a good pyramidal computational math problem. Let's say a good pyramidal tossup has 7 clues going from hardest to easiest. To make computational math pyramidal, you'd have to get 7 computations in decreasing difficulty; and to make it so this one question doesn't take 3 minutes to read, the clues can't have any pauses in between them so people can work on them. Thus the computations have to be near instantaneous to be viable. Either that or you'd have to reduce the amount of clues which is rarely a good idea. Additionally, such a case would produce quite the dilemma. If you know how to do the first (hardest) problem, should you tank through that problem or should you wait for the problem two clues down? After all, the time it would take for you to solve the hard problem might be greater than the time it would take for the reader to read two more clues and figure out the easy problem. In these ways, math is a lot different than other subjects.

As Andrew says, you're better off trying to make a non-computational math tossup. Less painful. Better question.

I also agree with this, and I am again not arguing for comp math, but NAQT is the only set that contains comp math that I have played, and most of their questions do not contain 7 clues. With questions containing 3-4 clues, a pyramidal comp math tossup the way I proposed would be plausible.

[Important Bird Area]

I also agree with this, and I am again not arguing for comp math, but NAQT is the only set that contains comp math that I have played, and most of their questions do not contain 7 clues.

This is a bug, not a feature. More of our questions should contain at least 7 clues. The shorter character limit for A-series means that we have to get by with 5-6 clues sometimes, but 3-clue tossups are obviously a bad idea (math comp or otherwise).

[Kanye West]

No thanks.

Then enjoy us refusing to engage you further and refusing to listen to your opinion on math computation.

ok.

[Down and out in Quintana Roo]

No thanks.

Then enjoy us refusing to engage you further and refusing to listen to your opinion on math computation.

ok.

Then why are you even here if you're now saying that you don't feel like explaining why you think math comp is "important" to good quizbowl games? That's like the entire point of this thread. Practically everyone (of significance and influence) disagrees with you. But maybe you have a point that we haven't thought of yet. Defend your argument and it could be a worthwhile discussion.

[Stained Diviner]

If Ashu has finally realized that this thread should be left for dead, then I call on all members of the community to join me in agreeing with him on this matter.