Math Computation, Round 23748234

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Re: Math Computation, Round 23748234

Post by Deviant Insider » Thu Jun 18, 2009 2:33 pm

Guy,
While it is true that other quizbowl subjects test factual knowledge while computational questions test applied knowledge, I don't think that should disqualify them from consideration. Practically speaking, the primary requirement of a quizbowl question is that it can be read by moderators who may not understand it, answered in a relatively short amount of time, and have its answer be judged right or wrong by the same moderators who may or may not understand it. Legitimately speaking, the primary requirement of a quizbowl question is that most of the time it will get answered by the competitor in the room who understands it best. In my opinion, computational questions meet these criteria, though they do take a little bit longer than recall questions and their consistency in differentiating understanding probably is worse than recall questions. (That is, if you were to take a history question and a computational question at a tournament and figure out what percentage of the teams that "understand" history and math better than their opponents answered those questions correctly in each match, it would be between 50-100% in each case and probably closer to 100 in the case of the history question, though that's not something we'll ever know for sure.)

Other types of applied knowledge cannot be considered for quizbowl because they do not meet the practical requirements I mentioned above. You're never going to be able to arrange a situation where some parent volunteer can within thirty seconds determine that one team's literary analysis is more deserving of ten points and a shot at the bonus than another team's, so it's never going to be a part of quizbowl, but that parent volunteer can determine which team was the first to correctly answer a math question.

As far as defending my statement that students learn from computational questions, my opinion may be biased by the fact that I'm a math teacher. My team and I often discuss computational questions that come up, and there often is something interest in it. I remember us talking about something that came up in I think HSNCT Round 12, so if somebody can post the comp tossups from that round I can try to remember whatever it was. While kldaace's polynomial example probably would make a better bonus part than tossup, Vieta's Formulas contain interesting mathematics. I also think that it is good for students to be exposed to Geometry and Probability after completing those topics in class, since they are important in various ways even though, because they don't relate well to Calculus, many students don't see them at all as junior or seniors, just like quizbowl does a good job of keeping students actively thinking about US History even though they may not be studying it all in school during a particular year.

Matt,
You do make some good points, though of course I don't agree with the characterization that those questions are nonsense. Quizbowl competitions which include a significant amount of computational math have a special obligation to cut out crap so that there can be significant literature, history, and fine arts. Those three humanities categories in IHSA combine for at most 43% of the distribution, and I am unhappy about that. We could get those three humanities categories above 50% by eliminating Miscellaneous and cutting back on Geography/Government, and I wish we would do it. Similarly, it would be very easy for NAQT to keep its 7% math and increase the humanities by cutting back on all of its miscellaneous categories, and they should do it.
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Re: Math Computation, Round 23748234

Post by Important Bird Area » Thu Jun 18, 2009 2:51 pm

Shcool wrote:something that came up in I think HSNCT Round 12, so if somebody can post the comp tossups from that round I can try to remember whatever it was.
2009 HSNCT round 12 wrote:Pencil and paper ready. Ellen wants to find the sum of the first 11 positive multiples of 11; that is, the sum of the first 11 positive integers that are evenly divisible by 11. Those numbers form a sequence whose first and last elements are 11 and 121 to which she can apply a trick similar to the one Gauss used as a schoolchild. Ellen finds that the sum of the first 11 multiples of 11 is --for 10 points--what number?

Pencil and paper ready. A country has a monetary system wherein 1 silver coin equals 5 copper coins, and 1 gold coin equals 8 silver coins. Neville has 3 gold coins and 1 silver coin and wants to buy as many pieces of gum priced at 3 copper coins as possible. Neville figures the easiest way is probably to convert his money to copper, divide by 3, and discard any remainder. For 10 points--how much gum can he buy?
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 3:16 pm

bt_green_warbler wrote:
Shcool wrote:something that came up in I think HSNCT Round 12, so if somebody can post the comp tossups from that round I can try to remember whatever it was.
2009 HSNCT round 12 wrote:Pencil and paper ready. Ellen wants to find the sum of the first 11 positive multiples of 11; that is, the sum of the first 11 positive integers that are evenly divisible by 11. Those numbers form a sequence whose first and last elements are 11 and 121 to which she can apply a trick similar to the one Gauss used as a schoolchild. Ellen finds that the sum of the first 11 multiples of 11 is --for 10 points--what number?

Pencil and paper ready. A country has a monetary system wherein 1 silver coin equals 5 copper coins, and 1 gold coin equals 8 silver coins. Neville has 3 gold coins and 1 silver coin and wants to buy as many pieces of gum priced at 3 copper coins as possible. Neville figures the easiest way is probably to convert his money to copper, divide by 3, and discard any remainder. For 10 points--how much gum can he buy?
Both of those questions, from my perspective, were frightfully stupid. The first one asks you to compute the product of eleven times (1+...+11) = eleven times sixty-six = 726. If you don't start calculating after the first clue and solve the problem faster or slower than the other team based on computation speed alone, I don't know how to help you. The second question has the terrible problem of being unbuzzable until "3 copper" is read; moreover, the rest of the question teaches you how to divide; if you didn't know how to divide going into HSNCT, I also can't help you. But really, how is this nontrivial arithmetic or even remotely interesting to your team? 3g+1s is 25s, you multiply by five, you get 125, you divide by three, you get forty-one. If any of the steps in this question besides the speed arithmetic are remotely interesting, please tell me because evidently I've been missing out on the excitement hidden in tying my shoes, too.
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Re: Math Computation, Round 23748234

Post by magin » Thu Jun 18, 2009 3:31 pm

Shcool wrote:Legitimately speaking, the primary requirement of a quizbowl question is that most of the time it will get answered by the competitor in the room who understands it best. In my opinion, computational questions meet these criteria, though they do take a little bit longer than recall questions and their consistency in differentiating understanding probably is worse than recall questions.
Actually, as I understand it, the contention is that computation tossups reduce to "here is a problem: how fast can you solve it?" instead of presenting a series of clues arranged from hardest to easiest. Basically, once the problem is presented, either you know how to do the problem or you don't, and since often times both teams will have at least one player who knows how to solve the problem, it comes down to buzzer speed, not understanding. So, such tossups are reducible to two steps: knowing how to solve the problem and speed. It seems to me like there is no real pyramidality in the first step, since either you know how to solve the problem (or a trick to solve the problem the fastest way, but I don't think such tricks represent deep understanding of math) or you're clueless, and no real pyramidality in the second step (since computational speed often allows fast players to outbuzz players with a deeper understanding of math). Am I misunderstanding the nature of computational tossups? Because if not, computational tossups are clearly much less pyramidal than "recall" tossups, and necessarily worse at rewarding understanding of math.
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 3:37 pm

Shcool wrote:Guy,
While it is true that other quizbowl subjects test factual knowledge while computational questions test applied knowledge, I don't think that should disqualify them from consideration.
As was pointed out in this very thread earlier, you don't find it unfair that only one form of applied knowledge is tested? What about all the people who are good at writing essays or composing poetry? Why should one form of applied knowledge be favored over any other?
Legitimately speaking, the primary requirement of a quizbowl question is that most of the time it will get answered by the competitor in the room who understands it best. In my opinion, computational questions meet these criteria, though they do take a little bit longer than recall questions and their consistency in differentiating understanding probably is worse than recall questions. (That is, if you were to take a history question and a computational question at a tournament and figure out what percentage of the teams that "understand" history and math better than their opponents answered those questions correctly in each match, it would be between 50-100% in each case and probably closer to 100 in the case of the history question, though that's not something we'll ever know for sure.)
OK, so you're admitting that computational questions are worse in determining who knows more about the subject at hand than other, well-written, pyramidal questions. Why keep using subpar questions when a perfectly acceptable alternative—theoretical math—is out there? This criterion alone has been used to weed out plenty of subpar questions in the past, and is the basis of the modern game. (Why don't we see FAQTP out there anymore, for example?) Any type of question with this thus needs serious justification for its continued inclusion; I don't really see anything that you've said that meets this. "Hey, these questions do the same thing as theoretical math questions with a result slightly less in tune with an integral aspect of quizbowl itself" does not convince me.
I also think that it is good for students to be exposed to Geometry and Probability after completing those topics in class, since they are important in various ways even though, because they don't relate well to Calculus, many students don't see them at all as junior or seniors, just like quizbowl does a good job of keeping students actively thinking about US History even though they may not be studying it all in school during a particular year.
Prison Bowl II round 9 wrote:4. The Erdős [EHR-dish]-Mordell inequality applies to these entities, and in one of these, the Nagel point is the isotomic conjugate of the Gergonne point. Kimberling also cataloged the Spieker center and the Feuerbach point for one of these. The de Longchamps point for one lies on the Euler line, along with the nine point center, orthocenter, and circumcenter. Their area can be calculated using Heron’s formula, and in non-Euclidean geometries, the sum of their angles differs from the usual 180 degrees. In ones with a right angle, the side-lengths can be calculated with the Pythagorean theorem. For 10 points, name these three-sided polygons.

ANSWER: triangles [LC]
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Re: Math Computation, Round 23748234

Post by Geringer » Thu Jun 18, 2009 3:42 pm

I am infinitely disappointed that I missed this discussion up until now. Why didn't anyone shine the MathSignal into the cloudly sky?

To avoid around 8 yellow boxes, let me sum up my argument as succinctly as I can addressing specific people when required.

First of all, in response to a Dees post, trophy whoring is an excuse for everything. While this is completely irrelevant to the topic at hand, I want to throw some props at the dude without the signature for being so ballsy as to request to keep computational math so he could keep on winning.

Watkins- I don't mean to offend, but find me some third-graders that can do this math in 30 seconds. Maybe there's one or two in the galaxy, and I bet they're both on Vulcan...or maybe Bynaus (but they'd be working in pairs). Under the aforementioned assumption that the high school canon should in some part descend from curriculum, math seems to be a logical part of quiz bowl. (Comp vs theory will be addressed below)

Okay, time to be serious.

Watkins- As most players wouldn't know the Shoelace theorem, it shouldn't be tossed up. Just as the one German music question as PACE was too obscure for high school, Shoelace wouldn't be included. I think Mr. Reinstein has given plenty of examples of good comp math question templates, plus my own possible addition of permutation questions.

To all- It seems to me that some of the arguments against math computation do not involve intrinsic error, but rather just poor question writing. Assuming distribution is limited to one question or so per game, writing good comp math tossups is possible. Coupled with an appropriate amount of math theory, math can be a legitimate category. While I think that the IHSA's math-heavy distribution is preposterous, it would be foolish to do away with it altogether. Seemingly, tournaments are often short math questions and instead of sitting down and writing legitimate questions, they throw some numbers together and create something horrible like that fruit stand question.

I will sum up my argument as such- with a limited distribution (like 1/1 for all math) and good question writing, comp math works.
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 3:46 pm

SaveComputationalMath wrote:To all- It seems to me that some of the arguments against math computation do not involve intrinsic error, but rather just poor question writing.
Perhaps it is more germane to address those that do involve intrinsic error, then.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 3:50 pm

Well, I do agree that those tossups in Round 12 were a little on the easy side.

But I just want to know, what is wrong with having a couple of math tossups, sometimes zero, that appear in a round of quizbowl. I mean, there are going to be like 18 others that people can still answer and can learn information from.

I agree with Andy that these problems can be solved with just one technique and you are done. But what about a question like this, which involves more than one technique/concept of solving the problem.

Pencil and paper ready. You want to find the area of the region within one unit of a square with sides of length 4. You know that this can be done by determining the boundary of the region. You see that this is bounded on the inside with a square and on the outside by circular arcs and straight segments. Knowing that you can split the figure into rectangles and sectors of circles, you see that this area will be in the form of a+b*pi. (*)For ten points, what is the area of that locus?

Answer: 28+pi

This question isn't really greatly written, but it is challenging.

I mean, I believe that for this question, you can't just use any "tricks" to solve this problem. Anyone in high school quizbowl should be able to understand what this question is asking, and should be able to apply what they've learned in school to solve such a problem. It also isn't as easy as just adding a bunch of numbers. You actually have to think about what the area is going to be, and notice that it won't just be the simple area of a rectangle you have to worry about. If someone can get this question pretty quickly upon hearing it, they should deserve the points, because the question isn't a joke. And there are multiple concepts involved in this figure as you need to not only determine what you have to find the area of, but also find the area for it.

Many of NAQT's math questions are a joke, but I do believe that if they can get more complex, then people would agree that the computational tossups could still be important, which they should be, as not only math theory is important, but also applying the skills you learned in school to solve problems.
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Re: Math Computation, Round 23748234

Post by Geringer » Thu Jun 18, 2009 3:53 pm

Sir Thopas wrote:
SaveComputationalMath wrote:To all- It seems to me that some of the arguments against math computation do not involve intrinsic error, but rather just poor question writing.
Perhaps it is more germane to address those that do involve intrinsic error, then.
I meant to say, the concept of computational math isn't necessarily bad, but rather the question writing often sucks worse than :chip:
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 3:58 pm

Shcool wrote:Legitimately speaking, the primary requirement of a quizbowl question is that most of the time it will get answered by the competitor in the room who understands it best.
So brain-teasers are good questions? Decode this Caesar cipher is a good question? You have thirty seconds to do the following physical challenge involving while I explain the mechanical principles behind it. There are all kinds of further qualifications we make to the above principle.
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Re: Math Computation, Round 23748234

Post by DumbJaques » Thu Jun 18, 2009 4:42 pm

These discussions always seem to range out into the abstract very, very quickly, and I don't totally understand why. Of the non state-level entities who currently produce pyramidal questions, there's only one that I know of currently writing computation tossups for their sets. If everyone on here magically agreed that theoretically computation could be great quizbowl, it still wouldn't change the fact that computation questions adapted as part of the normal quizbowl game fall unbelievably short of doing this.

To meet this criteria, one would need to construct a relatively short prompt (particularly in NAQT) that takes just over 10 seconds to solve once the information is presented. As people have said, you're not going to find that kind of thing on any math tests, but the reason is not just theoretical (ie nobody cares about testing computation speed). It's also practical - there's an incredible limit to what kind of math problem you can construct that's solvable in that time frame.

That limits the pool of what can theoretically be computed already, and then you have to consider that in order to meet our basic criteria, the question has to present some semblance of pyramidal information or restatement. Even if you accept that this is truly possible to the degree that it is with other subjects (something that, despite 23748234 math threads, we're still waiting on), you still have to accept that it further limits what kind of problem you can ask.

But even if you can meet those two conditions, and you construct a "challenging" question or whatever that involves some sort of application of mathematical logic and negligible calculation to solve a matrix equation or find the area of a circle in part of a square, you're still presenting this information as a tossup - that means it's going by at absolutely breakneck speed if it's NAQT (and, remember, it's the real world and that's where those questions live), and even if you manage to accurately recreate the diagrams that ANY sensible math test would provide for you, you've spent precious time doing that and barely have moments to solve this hypothetical pyramidal math question that involves the application and understanding of key math concepts.

Tossups are not presented like material on academic assessments. You aren't given diagrams and cannot be given the time (and really, it's got to be a minute or something minimum) to apply real understanding and solve a mathematical solution. Panasonic would give handouts, calculators, and anywhere from 1-3 minutes to work on computation problems, but no one could argue that those retained any semblance of pyramidality or were analogous to other questions.

Perhaps you think that computation is an important skill and questions on triangles, even if they involve legit math knowledge, are imperfect to cover the math distribution because they do not involve the vital act (and assuredly it is vitally central to mathematics) of calculation. But that's the world we live in - in fact, all quizbowl questions are like that! We cannot test understanding of imagery in Dubliners , we cannot test the ability to interpret a political cartoon or label and explain the significance of each feature on a map of the Battle of Gettysburg, cannot test the ability to play music. We could try to do all those things, and maybe we could come as close as the people who really have put in effort to do so with math calc questions, but we'd still be forcing it for no particular reason. Quizbowl involves testing knowledge of something and we try to construct questions to reward the most legitimate and complex knowledge of the given subject. I maintain that you just can't do that with math calc, but even if you think it can be done, the fact is that it hasn't been and you just get the same NAQT calc questions year after year. At this point why is the burden still on detractors to prove it can't theoretically be done and have the questions finally retired, rather than on the defenders to prove it can be done meaningfully in reality and bring the questions back?
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 4:44 pm

master15625 wrote:But I just want to know, what is wrong with having a couple of math tossups, sometimes zero, that appear in a round of quizbowl. I mean, there are going to be like 18 others that people can still answer and can learn information from.
Well, since you've already admitted that math questions are often unanswerable and do not teach, then no, I don't see why there should be any. Every question counts; zero questions should be subpar.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 5:15 pm

Sir Thopas wrote:
master15625 wrote:But I just want to know, what is wrong with having a couple of math tossups, sometimes zero, that appear in a round of quizbowl. I mean, there are going to be like 18 others that people can still answer and can learn information from.
Well, since you've already admitted that math questions are often unanswerable and do not teach, then no, I don't see why there should be any. Every question counts; zero questions should be subpar.
I never said that math questions are often unanswerable. I actually think that math questions are the easiest questions that can be answered, as they are often a joke. I do agree though that the math computation questions do not teach, but I do still feel that if the math computational questions got harder, without any tricks needed and could be solved by anyone, then they would do a good job in distinguishing teams.

Math theory tossups are also not necessarily the best way to replace math computation questions. For instance, I have seen so many questions that often have the same answer with clues that are "supposed to be obscure", yet are still common in all the questions. With these types of questions, teams can just memorize these clues, and essentially when the clue is heard it will be a buzzer race. For instance, determinant has come up so many times, and many teams know that. So they memorize the clues of the determinant, and it ends up being a buzzer race there.

Also, math theory tossups at the high school level, in my opinion, do not achieve their goal of achieving pyramidality. consider the question that Guy posed above.
4. The Erdős [EHR-dish]-Mordell inequality applies to these entities, and in one of these, the Nagel point is the isotomic conjugate of the Gergonne point. Kimberling also cataloged the Spieker center and the Feuerbach point for one of these. The de Longchamps point for one lies on the Euler line, along with the nine point center, orthocenter, and circumcenter. Their area can be calculated using Heron’s formula, and in non-Euclidean geometries, the sum of their angles differs from the usual 180 degrees. In ones with a right angle, the side-lengths can be calculated with the Pythagorean theorem. For 10 points, name these three-sided polygons.
This one does not achieve pyramidality. For instance, Erdos-Mordell is a famous inequality that people who participate in math contests see come up often. The Nagel Point and the Gergonne Point do as well. Kimberling and de Longchamps do not come up that often, and are more obscure than the aforementioned examples. So, math theory tossups also do not do a good job in achieving pyramidality. Just because these things seem obscure, doesn't mean you can put it in any order and say it does a good job pyramidally.

For these reasons, I fear that people will start to complain about math theory tossups as they do with computational tossups, as they will in the end be buzzer races or that people get the math theory tossups early because they are well acquainted with the subject. People deserve to get the math theory tossups early especially if they are acquainted with the topic. And these buzzer races happen in any area of quizbowl, including literature and science.
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Re: Math Computation, Round 23748234

Post by jonah » Thu Jun 18, 2009 5:18 pm

master15625 wrote:For instance, I have seen so many questions that often have the same answer with clues that are "supposed to be obscure", yet are still common in all the questions. With these types of questions, teams can just memorize these clues, and essentially when the clue is heard it will be a buzzer race. For instance, determinant has come up so many times, and many teams know that. So they memorize the clues of the determinant, and it ends up being a buzzer race there.
How is this different from any other topic ever?
master15625 wrote:This one does not achieve pyramidality. For instance, Erdos-Mordell is a famous inequality that people who participate in math contests see come up often. The Nagel Point and the Gergonne Point do as well. Kimberling and de Longchamps do not come up that often, and are more obscure than the aforementioned examples. So, math theory tossups also do not do a good job in achieving pyramidality. Just because these things seem obscure, doesn't mean you can put it in any order and say it does a good job pyramidally.
There's a massive difference between "this question on Topic X isn't great" and "topic X can't be written about well".
master15625 wrote:For these reasons, I fear that people will start to complain about math theory tossups as they do with computational tossups, as they will in the end be buzzer races or that people get the math theory tossups early because they are well acquainted with the subject. People deserve to get the math theory tossups early especially if they are acquainted with the topic. And these buzzer races happen in any area of quizbowl, including literature and science.
So...what the heck is your point?
Last edited by jonah on Thu Jun 18, 2009 5:20 pm, edited 1 time in total.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 5:19 pm

jonah wrote:
master15625 wrote:For instance, I have seen so many questions that often have the same answer with clues that are "supposed to be obscure", yet are still common in all the questions. With these types of questions, teams can just memorize these clues, and essentially when the clue is heard it will be a buzzer race. For instance, determinant has come up so many times, and many teams know that. So they memorize the clues of the determinant, and it ends up being a buzzer race there.
How is this different from any other topic ever?
But that is like math computational tossups, and people seem to be complaining about that aspect of math computational tossups.
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Re: Math Computation, Round 23748234

Post by jonah » Thu Jun 18, 2009 5:21 pm

master15625 wrote:
jonah wrote:
master15625 wrote:For instance, I have seen so many questions that often have the same answer with clues that are "supposed to be obscure", yet are still common in all the questions. With these types of questions, teams can just memorize these clues, and essentially when the clue is heard it will be a buzzer race. For instance, determinant has come up so many times, and many teams know that. So they memorize the clues of the determinant, and it ends up being a buzzer race there.
How is this different from any other topic ever?
But that is like math computational tossups, and people seem to be complaining about that aspect of math computational tossups.
I edited in a lengthier response to your post right after you submitted that post but before I saw it; sorry for that confusion. Anyway, my answer to that is contained in the second part of my post above.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 5:33 pm

jonah wrote:
master15625 wrote:This one does not achieve pyramidality. For instance, Erdos-Mordell is a famous inequality that people who participate in math contests see come up often. The Nagel Point and the Gergonne Point do as well. Kimberling and de Longchamps do not come up that often, and are more obscure than the aforementioned examples. So, math theory tossups also do not do a good job in achieving pyramidality. Just because these things seem obscure, doesn't mean you can put it in any order and say it does a good job pyramidally.
There's a massive difference between "this question on Topic X isn't great" and "topic X can't be written about well".
The problem is, I haven't seen that happen yet. Like, I mean, this problem has been going on for a while, so why hasn't it been fixed yet? I would want to see this fixed.
jonah wrote:
master15625 wrote:For these reasons, I fear that people will start to complain about math theory tossups as they do with computational tossups, as they will in the end be buzzer races or that people get the math theory tossups early because they are well acquainted with the subject. People deserve to get the math theory tossups early especially if they are acquainted with the topic. And these buzzer races happen in any area of quizbowl, including literature and science.
So...what the heck is your point?
Its just that both of these things have on commonality, math. It seems like that math might have to go away all together if people complain about both, which I believe would be just bad if it happens. I fear that people complaining about both math theory tossups and math computational tossups would cause people to think that math is a bad topic to have in quizbowl, when it really is not.
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Re: Math Computation, Round 23748234

Post by cvdwightw » Thu Jun 18, 2009 5:34 pm

I think part of Chris's post hits the nail on the head.

In order to do something people generally agree is important (understanding a mathematics word problem and solving it given numbers), one typically needs time on the time scale that quizbowl does not provide. I might have said this before, or I might have deleted it in revision, but MathCounts gives students 45 seconds per problem in the Countdown Round and (IIRC) over a minute average per problem in the two written rounds. I'm going to estimate that even a really good math student is going to need 15 minutes to complete a 25-question exam (that's 36 seconds per question on average). Understanding and solving math questions is just not feasible on the time scale presented in quizbowl. Instead, what we have is students learning mathematical tricks and/or doing middle school (or lower) arithmetic, regardless of whether or not they actually understand the concepts being applied.

A good math exam question will test both the knowledge and application of the concepts involved. For instance, an Algebra I exam might say something like, "I have ten coins, some of which are dimes and some of which are quarters. I have a total of $2.90. How many dimes do I have?" So the student has to set up two equations in two variables, and solve for the variable corresponding to the number of dimes. Usually students get partial credit if they set up the equations correctly and then do something stupid like write the number of quarters instead.

Here is where quizbowl deviates from a good math exam:
1. The question on the test does not need to be pyramidal. The student is tested on whether he can perform the necessary calculations within the given time, not on whether he can perform the calculations faster than someone else.
2. In order to give the quizbowl question some appearance of pyramidality, the question will often spend two lines talking about how to solve the problem. Therefore, teams that do not understand the concept "hey I need to set up two equations in two variables" can still answer this question based purely on the computation skills necessary. In a worst-case scenario, the team that does understand what to do immediately makes a calculation error, and the team that has no understanding of what's going on picks up the points.
3. A student can get partial credit on the test for setting up the equations correctly. A quizbowler cannot get partial credit for any intermediate steps.
4. The time frame is significantly different. Students are asked to complete the exam, all the questions, in a specified time frame that even for the good students typically ends up being over 30 seconds a question. Instead, we're asking students to do this in ten seconds.
5. The test question is printed directly on the page. Therefore, if a student misremembers a number, it is back in the statement of the problem. In quizbowl, if a student misses or misremembers a number (which is not at all uncommon), the student has no chance of solving the problem correctly.

To me, the most egregious of these problems are (2) and (4). (2) because in all other subjects, a student who has no knowledge can only get points through a random guess. However, in "pyramidal" math calculation, a student who has no idea how to do the problem can just wait to be told how to do the problem, and then employ basic arithmetic skills to get points. In short, "pyramidal" math calculation is just an excuse for trying to increase conversion numbers. (4) because the additional time crunch means that the student is much more likely to make lots of stupid mistakes, and also that the student must usually use some kind of "trick" (instead of conceptual understanding) to solve the question within the time period.

We can then do one of four things with a math calculation tossup:
1. We can make it a simple one-line question like "Calculate the area of a circle inscribed in a square of side length 4." This does not at all test anything but "do you know the concept" and "can you square half of four really fast?" This is a bad question.
2. We can make it a "pyramidal" question like NAQT uses. This divides teams into three tiers: "teams that know the concept, hear all the numbers, and can do the arithmetic really fast," "teams that hear all the numbers and can do the arithmetic really fast," and "teams that misheard the numbers or can't do the arithmetic really fast." Note that there is no fourth category: even if a team understands the concept, they get no benefit from that if they are too slow on the arithmetic or missed a number because an NAQT moderator was speed-reading, and a team that has zero understanding of the concept but hears the numbers and how to do the problem can beat them. This is a bad question.
3. We can make it a series of one-line common-link questions on a number. This removes many of the bad things associated with math computation, but introduces two additional constraints: first, the number of such answers is impossibly small (no one is going to write a good question on 91, for example), and second, each of the one-line questions must be computable in about a second, otherwise someone who recognizes what's going on early can get beaten by someone who's faster at arithmetic from a slightly later clue. Such questions may be able to blend theoretical and computational math. For instance, the lead-in could be a couple of sentences on theoretical use of the number, while the giveaway could be a computational clue. This is not necessarily bad question, but it is very difficult to execute well and near-impossible to execute consistently well over a set of tournaments.
4. We can increase the time used to solve the question. Again, once teams are divided into "those that know how to do the problem" and "those that must be told how to do the problem," this becomes a measure of computation speed. Especially with longer, more complex problems, a fast team can easily make up the extra "how to do the problem" time. This is a bad question.

Again, I am not averse to bonuses that test computational knowledge, because the test is now not one of computational speed but "do you know how to do the problem?" (if you do, then you will do it in the allotted time; if not, you'll have to guess or you won't get points). In particular, if there are scientific or mathematical concepts that can only or better be tested using computation, then I would advocate putting such computation questions as bonus parts, so long as the arithmetic is trivially easy (that is, the bulk of the points come from understanding the concept and not from doing the math). I believe there are several others in the anti-computation camp that feel the same way.

ADDENDUM: This showed up while I was writing this reply:
master15625 wrote:(Stuff that doesn't come up in high school is too easy; "stuff I haven't heard of is too hard;" therefore, this tossup is not pyramidal)...So, math theory tossups also do not do a good job in achieving pyramidality. Just because these things seem obscure, doesn't mean you can put it in any order and say it does a good job pyramidally.
Really, I have no idea what this is arguing. Maybe this inequality thing that Dennis Jang thought obscure enough to be the lead-in at noted good college novice tournament EFT III is so easy that high schoolers are going to be all over it. I, and I'd guess everyone else in this thread, seriously doubt that. I'd like to think that Lily Chen has some idea of what's hard for high school and what isn't, and given that I read that Prison Bowl set and teams didn't seem to be complaining that the question was too easy, nor did teams at the other sites feel that the question was terrible, I'd like to think it is you who are in the wrong. Perhaps I can direct you to the Fundamental Difficulty Error, as that's clearly what's going on here?

Oh, also, there's that other error that I can't remember the name of, you know, the one where you take a single instance of that's completely fine for the difficulty level, claim that the single instance does not do a good job of doing what it (more-or-less) does, and then decide that the single instance you've cited is entirely representative of everything in the entire category. I think this is analogous to the "ACF IS IMPOSSIBLE" argument? In any case, even if there were something ridiculous like "Pythagorean theorem applies to these geometrical entities" in the lead-in, that still lends zero (0) support for your claim. Like, no good question writer I know says, "Hey I have these three third-tier William Dean Howells novels, I can just throw them in whatever order I want." Good question writers try to arrange good clues in descending order from "least likely to generate a correct buzz" to "most likely to generate a correct buzz."
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Re: Math Computation, Round 23748234

Post by DumbJaques » Thu Jun 18, 2009 5:36 pm

This one does not achieve pyramidality. For instance, Erdos-Mordell is a famous inequality that people who participate in math contests see come up often. The Nagel Point and the Gergonne Point do as well. Kimberling and de Longchamps do not come up that often, and are more obscure than the aforementioned examples. So, math theory tossups also do not do a good job in achieving pyramidality. Just because these things seem obscure, doesn't mean you can put it in any order and say it does a good job pyramidally.
You just noted that a question *might* have its first two lines pyramidally reversed. It is unclear to me how you think this can possibly be a logical argument against math theory tossups being pyramidal (let alone an argument in favor of computation tossups being so). Besides, an editor can look at that question and switch the clues if they're out of order. The problems with calculation questions are systemic and cannot be remedied in this way.


EDIT:
The problem is, I haven't seen that happen yet. Like, I mean, this problem has been going on for a while, so why hasn't it been fixed yet? I would want to see this fixed.
Uh, what? Are you saying you've never seen a pyramidal math theory question? That is almost impossible to believe and if it's really true, than you have not done sufficient research into available packets to really be able to understand the debate. We're not talking about the Easter Bunny here - go open a collegiate packet, you'll find some. You don't even need to do that, though - your post claiming that the triangle question was not a good, pyramidal math theory tossup relied on the fact that the first two and second two clues were out of order. This logically implies that by switching these things you could easily fix it, so I remain unclear why you doubt the possibility of creating a good theory tossup.
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Re: Math Computation, Round 23748234

Post by Cheynem » Thu Jun 18, 2009 5:39 pm

Man, I had a good post going and then Dwight Wynne trumps it.

Let me basically say that I'm not sure how you extrapolate "People might complain about math theory tossups" to "Math should be eliminated in general from quiz bowl." I'm sure there will be any number of complaints about math theory tossups, just as people complain about every category in quiz bowl. The difference is that people are complaining about established elements of quiz bowl ("misplaced clues," fraud, etc.). Complaints about computational math tend to be holistically different ("I don't know how to do it," "I can't do it this quickly," "I made a mistake in my calculations").
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Re: Math Computation, Round 23748234

Post by Geringer » Thu Jun 18, 2009 5:53 pm

master15625 wrote:This one does not achieve pyramidality. For instance, Erdos-Mordell is a famous inequality that people who participate in math contests see come up often.
Neil,

People who frequent math contests SHOULD power this one. As they are experts on math, their superior knowledge gets them 15.

You, sir, are an even worse troll then me. Your reasoning for computational math, including "not having buzzer races" and "there are still 18 other questions," is quite frankly idiocy and fails harder than Land of the Lost.

Your logic is so bad, it makes me want to eliminate computational math too.

I am so insulted, I henceforth demand my name be changed to something better and less cumbersome.
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Re: Math Computation, Round 23748234

Post by Auks Ran Ova » Thu Jun 18, 2009 5:55 pm

SomethingBetterAndLessCumbersome wrote:I am so insulted, I henceforth demand my name be changed to something better and less cumbersome.
Your wish is my command.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 5:56 pm

OK, fine I agree that the math theory tossups can be fixed now and all that. I was trying to say that there are still some math theory tossups that although can be fixed, when the questions are asked at a tournament, it seems that the math theory tossups do not convey pyramidality. I am all in for having math theory tossups, I want that to happen.

But I still believe that math computational tossups must stay. With regards to Cheynem's post, math computational tossups can be written with some difficulty in the questions asked and yet people can solve them pretty quickly without any tricks.
And mistakes in thinking are part of any quizbowl topic, so we can't include making computational errors as part of the reason why math computational questions should be eliminated.
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 5:56 pm

master15625 wrote:
jonah wrote:
master15625 wrote:For instance, I have seen so many questions that often have the same answer with clues that are "supposed to be obscure", yet are still common in all the questions. With these types of questions, teams can just memorize these clues, and essentially when the clue is heard it will be a buzzer race. For instance, determinant has come up so many times, and many teams know that. So they memorize the clues of the determinant, and it ends up being a buzzer race there.
How is this different from any other topic ever?
But that is like math computational tossups, and people seem to be complaining about that aspect of math computational tossups.
No; math computation tossups have one clue. That clue is the problem, once it has been properly stated. I suppose you could construct a tossup, theoretically, that is complicated enough that a significant fraction of people wouldn't have any clue of how to do the calculation off the initial statement of problem, and subsequent clarifying clues (for example, where NAQT says "if you want, you can line up the numbers so that one of them is above the other on the page and add the digits from right to left, carrying a digit when the sum is greater than nine") are actually helpful. But chances are, you won't be able to simplify it enough that 85% of teams will convert it at the end. If you can produce a tossup that meets these criteria, great; if you can't (I've never seen one), too bad.

Your argument suffers from a misunderstanding about the problem with buzzer races. There'd be a problem if I give a vague description of The Conspiracy of Claudius Civilis and then say the words Night Watch, generating a buzzer race. If team X and team Y know all of the clues in a tossup on determinants, then good for both of you, and I hope you don't play each other that round. If you do, that sucks, but look: we're writing the tossups for a field, not a pair of teams. It might take a thousand-line determinants tossup to differentiate you; that's not anyone's business. That buzzer race isn't a problem unless the tossup is too short or the clues are out of order or something. But an otherwise good tossup on determinants having two teams buzzing on the same clue: no problem with that here.

And after all, your premise is that computational tossups can test knowledge, right? So that means that team X and Y would be able to start solving the computational tossup on the same clue, and then the faster-computing team would buzz first, thereby not testing knowledge and being no better than the buzzer race. (Indeed, instead of being a random result, like the other buzzer races that match might contain, computational speed would be consistently rewarded, so there'd be no way for these knowledge-races to cancel properly like we hope buzzer races might over the course of a match between two good teams.)
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Re: Math Computation, Round 23748234

Post by Auks Ran Ova » Thu Jun 18, 2009 5:58 pm

master15625 wrote:But I still believe that math computational tossups must stay. With regards to Cheynem's post, math computational tossups can be written with some difficulty in the questions asked and yet people can solve them pretty quickly without any tricks.
Adopting your opponents' arguments as support for your own is certainly a novel strategy. By, uh, agreeing with everyone, you do nothing to weaken the correct claim that mathcomp tossups reduce to computational speed and lack any sort of of pyramidality. Try again!
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Re: Math Computation, Round 23748234

Post by Geringer » Thu Jun 18, 2009 6:01 pm

Ukonvasara wrote:
SomethingBetterAndLessCumbersome wrote:I am so insulted, I henceforth demand my name be changed to something better and less cumbersome.
Your wish is my command.
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Re: Math Computation, Round 23748234

Post by kayli » Thu Jun 18, 2009 6:14 pm

What's up with people against tricks? Do people really like doing things the nitty gritty way?

I think that it'd be difficult to write computational math problems that required the normal type of pyrimidality. So... maybe we should exile math comp to the bonuses? At least until someone finds out how to write good math comp questions.

Also, a good math comp question doesn't necessarily have to boil down to computational speed math. Show me eight kids on two teams who only need use speedrithmetic to compute the sums of the cubes of polynomial, and I will show you Philips Exeter.


So, my opinion (it's changed since my first post): Math comp should be part of bonuses, and math comp should test more outside of the core math curriculum so knowledgeable teams can be distinguished from the rest.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 6:17 pm

Ukonvasara wrote:
master15625 wrote:But I still believe that math computational tossups must stay. With regards to Cheynem's post, math computational tossups can be written with some difficulty in the questions asked and yet people can solve them pretty quickly without any tricks.
Adopting your opponents' arguments as support for your own is certainly a novel strategy. By, uh, agreeing with everyone, you do nothing to weaken the correct claim that mathcomp tossups reduce to computational speed and lack any sort of of pyramidality. Try again!
But I don't believe I was agreeing with everyone. I was making a reply to Cheynem's post.

Obviously mathcomp tossups in QuizBowl require computational speed. Quizbowl inherently requires speed when answering a question, and math computation tests computation.

But I am saying that it is possible to write a good math computation question that people can learn from without being pyramidal.

I really can't say anything much. But honestly, I just want QuizBowl to run more smoothly so that the problems can be fixed, and hopefully we can focus on the mistakes in other topics as well other than just math.
Last edited by master15625 on Thu Jun 18, 2009 6:33 pm, edited 1 time in total.
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Re: Math Computation, Round 23748234

Post by Auks Ran Ova » Thu Jun 18, 2009 6:32 pm

master15625 wrote:But I don't believe I was agreeing with everyone. I was making a reply to Cheynem's post.

Obviously mathcomp tossups in QuizBowl require computational speed. Quizbowl inherently requires speed when answering a question, and math computation tests computation.

But I am saying that it is possible to write a good math computation question that people can learn from without being pyramidal.
Yeah, that was kind of my point. You unwittingly said things everyone else has been using to oppose computational math, but you incorrectly assumed they supported your point.

Further, statements of obvious facts aside, you've still done nothing to support your argument. You're supposed to be arguing against the idea that these questions do something to separate levels of understanding and knowledge of math other than reduce to "who can compute things fastest".

Support for your third point is quite lacking as well. Wishing something was so does not make it so, and apyramidal exercises in calculation are fundamentally at odds with what the community holds to be good quizbowl.
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 6:32 pm

kldaace wrote:What's up with people against tricks? Do people really like doing things the nitty gritty way?
No, the problem with tricks is that they do not in any way signify actual mathematical knowledge and understanding, merely trivial shortcuts.
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 6:36 pm

master15625 wrote:Obviously mathcomp tossups in QuizBowl require computational speed. Quizbowl inherently requires speed when answering a question, and math computation tests computation.
No, dude! That's a completely different kind of speed; if you don't understand the difference between quickly pressing a buzzer and quickly doing a computation, then pressing a buzzer, then I don't know how to clarify that. Moreover, we don't want to test computation speed, since that's an idiotic aim. In no real, important, academic environment is anyone required to multiply two numbers or find the area of a region; if you know some doctoral student whose research is about finding the area of a region really quickly, please refer me to his research. If you had said "math computation tests math," then you'd be presenting an appropriate motivation for including those questions, at least, if you could show that it tests math at least as well as noncomputational math does, but the problem is you haven't (and, I claim, won't).
master15625 wrote:But I am saying that it is possible to write a good math computation question that people can learn from without being pyramidal.
Thus ruining the actual purpose of writing the question. Moreover, write such a question, then we'll talk. You haven't done it yet.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 6:44 pm

Ukonvasara wrote:
master15625 wrote:But I don't believe I was agreeing with everyone. I was making a reply to Cheynem's post.

Obviously mathcomp tossups in QuizBowl require computational speed. Quizbowl inherently requires speed when answering a question, and math computation tests computation.

But I am saying that it is possible to write a good math computation question that people can learn from without being pyramidal.
Yeah, that was kind of my point. You unwittingly said things everyone else has been using to oppose computational math, but you incorrectly assumed they supported your point.

Further, statements of obvious facts aside, you've still done nothing to support your argument. You're supposed to be arguing against the idea that these questions do something to separate levels of understanding and knowledge of math other than reduce to "who can compute things fastest".

Support for your third point is quite lacking as well. Wishing something was so does not make it so, and apyramidal exercises in calculation are fundamentally at odds with what the community holds to be good quizbowl.
I don't want to argue anymore, as I understand what I say will not change anyone's beliefs.

But isn't it possible to make a math computation tossup that has like several clues that have the same answer? In a way, like you can create like four questions that have teh same answer, and you can make four clues such that the first clue said is like one that can literally be solved by people who know their stuff, until the fourth clue which can be solved by anyone.
That would certainly make it more pyramidal, as one would ahve to deal with four different questions, rather than just one.

And I know that the first clue will probably be made so that it will be difficult to answer it immediately after the question is asked, and can also be made so that people can learn something from the clue. Learning from this clue is of utmost importance. Granted the first clue might actually be a combination of math theory and math computational, but it is possible to combine computation with theory and still make the question pyramidal.
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 6:49 pm

Here's another thing. Let's say that Neil succeeds in producing an appropriate computational math tossup; let's even suppose that he proves that an entire set of computational math tossups is 100% awesome for quizbowl and tests knowledge, etc. etc. Whatever. I don't think he will meet this burden, since it's a tough one to meet.

That means that the world contains one (1) competent computational math writer. If Neil wants to write two million such tossups a year to satisfy the needs of everyone else, great. If he doesn't, then somehow we need to convince everyone else that whatever they do, they're not doing it well, and they need to imitate Neil. Which will probably result, whatever we do, in a lot of people continuing to fail to write good questions because they're not as awesome at writing these questions as Neil may demonstrate that he is. We don't go around recommending to everyone that they shoot apples off their children's heads for the marginal benefit it may produce in father-son bonding because most of the time it will result in pain. Similarly, we need to act pragmatically: empirical data tells us that even if we find that Neil can find it within himself to produce great questions, very few other people ever will or will learn from him, and as a result there will be a lot of pain.

Advocates against computational math say: spare us the pain; even if noncomputational math is a slightly inferior alternative (and we don't think it is), we still know that it's not worth the fuss and bother and blood and guts.
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Re: Math Computation, Round 23748234

Post by Auks Ran Ova » Thu Jun 18, 2009 6:51 pm

master15625 wrote:I don't want to argue anymore, as I understand what I say will not change anyone's beliefs.

But isn't it possible to make a math computation tossup that has like several clues that have the same answer? In a way, like you can create like four questions that have teh same answer, and you can make four clues such that the first clue said is like one that can literally be solved by people who know their stuff, until the fourth clue which can be solved by anyone.
That would certainly make it more pyramidal, as one would ahve to deal with four different questions, rather than just one.

And I know that the first clue will probably be made so that it will be difficult to answer it immediately after the question is asked, and can also be made so that people can learn something from the clue. Learning from this clue is of utmost importance. Granted the first clue might actually be a combination of math theory and math computational, but it is possible to combine computation with theory and still make the question pyramidal.
I only had ten seconds to perform the necessary computation, so my numbers might be a bit off, but variations on this idea have been proposed roughly eight thousand times. The objections generally take the same form:

1) These questions are very hard to write, at least in such a way that the early clues don't consist of useless and/or overly-complicated problems that no one will be able to benefit from hearing (because waiting for an easier problem that can be solved more quickly is more likely to pay off)
2) Even were someone to, savant-like, develop the ability to write these questions, there are a very limited number of questions of this style that can be written without running into the exact same problems.
3) This only sort of addresses the pyramidality argument, and does nothing to address any of the arguments about the questions reducing to individual computation speed or being about an applied skill rather than factual recall.

(Yeah, basically what Andy said.)
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 6:51 pm

master15625 wrote:But isn't it possible to make a math computation tossup that has like several clues that have the same answer?
I will allow that these are generally the least poisonous of math computation questions. But your canon is pretty small (how many possible answers?), computation speed still matters (two teams buzzing off knowledge of the same clue will buzz at different times based on speed), and this exhausts the very small number of problems that you can test in a short time even faster (since you're including four, rather than one, per question).
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Re: Math Computation, Round 23748234

Post by theMoMA » Thu Jun 18, 2009 6:52 pm

Neil, I think most people are fine with questions like that. In fact, HSAPQ has had a few of them appear on their sets. The problem is that the clues quickly exhaust themselves, since generally you're writing on an answer like "four" and you can only say so many things about it without devolving into trivial calculations like 18-14 or whatever. Most people who write these questions tend to stock them with clues like "this is the number of members in the smallest non-cyclic group, named for Klein," or "According to the Abel-Ruffini theorem, this is the highest number of degrees of a polynomial for which a general equation to find the roots exists" instead of the aforementioned trivial calculations. There just aren't enough of those clues to write more than a couple of these tossups per set, even if they are good tossups.

There are probably easy-to-do calculations exemplary of certain rules or theorems that could be worked into these questions, but it's a hard balancing act between making those meaningful or having them devolve into triviality.

For what it's worth, I'm quite fond of these as a good compromise between calculation and theory, and I try to work them into high school sets I'm editing.
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Re: Math Computation, Round 23748234

Post by Important Bird Area » Thu Jun 18, 2009 7:04 pm

kldaace wrote:math comp should test more outside of the core math curriculum so knowledgeable teams can be distinguished from the rest.
I think making math comp harder and adding content "outside the core math curriculum" are bad ideas. They won't serve the goal of appropriately distinguishing teams with deep knowledge, because (as Charlie pointed out above) conversion rates for math comp tossups are generally substandard right now.*

*(Not at all speaking for NAQT, other than "I believe this in part because I've seen a lot of NAQT conversion statistics.")
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 7:07 pm

everyday847 wrote:Here's another thing. Let's say that Neil succeeds in producing an appropriate computational math tossup; let's even suppose that he proves that an entire set of computational math tossups is 100% awesome for quizbowl and tests knowledge, etc. etc. Whatever. I don't think he will meet this burden, since it's a tough one to meet.

That means that the world contains one (1) competent computational math writer. If Neil wants to write two million such tossups a year to satisfy the needs of everyone else, great. If he doesn't, then somehow we need to convince everyone else that whatever they do, they're not doing it well, and they need to imitate Neil. Which will probably result, whatever we do, in a lot of people continuing to fail to write good questions because they're not as awesome at writing these questions as Neil may demonstrate that he is. We don't go around recommending to everyone that they shoot apples off their children's heads for the marginal benefit it may produce in father-son bonding because most of the time it will result in pain. Similarly, we need to act pragmatically: empirical data tells us that even if we find that Neil can find it within himself to produce great questions, very few other people ever will or will learn from him, and as a result there will be a lot of pain.

Advocates against computational math say: spare us the pain; even if noncomputational math is a slightly inferior alternative (and we don't think it is), we still know that it's not worth the fuss and bother and blood and guts.
I am sorry for making it sound that I would be successful at creating such questions. I was just being hypothetical in saying how it can be written pyramidally, etc.

I do not in any way think that I can make a good math question anytime soon, and I do not want to write two million tossups on this trust me.

I also am sorry that I made it sound like the earlier quizbowl question that I mentioned lacked pyramidality was bad because it lacked pyramidality. I know that it is of utmost importance that it teaches someone something rather than pyramidality, so I will avoid making such comments again.

I guess the only reason why I support computational math is that I feel that is the way we usually get some of our points. I know really realize the grand scheme of what quizbowl is all about, to learn from the questions. I also now do not support computational questions either, especially if like 1 of them shows up every one half; but I do believe that some there should exist a computational math tossup but really sparingly. Nonetheless, I'd rather answer good math questions at math contests than answer math questions at quizbowl in any case.

Thanks for all your comments
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Re: Math Computation, Round 23748234

Post by Cheynem » Thu Jun 18, 2009 7:35 pm

I know that it is of utmost importance that it teaches someone something rather than pyramidality
Wait...you make it sound like that's mutually exclusive!
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 7:41 pm

master15625 wrote:I am sorry for making it sound that I would be successful at creating such questions. I was just being hypothetical in saying how it can be written pyramidally, etc.

I do not in any way think that I can make a good math question anytime soon, and I do not want to write two million tossups on this trust me.
No need to apologize; I'm just saying that SOMEONE (and since you were proposing their creation, I used you as an example) is going to have to be successful at creating them; if someone says "surely there exists x," we have to see x to believe it.
master15625 wrote:I also am sorry that I made it sound like the earlier quizbowl question that I mentioned lacked pyramidality was bad because it lacked pyramidality. I know that it is of utmost importance that it teaches someone something rather than pyramidality, so I will avoid making such comments again.
I think you missed the point of what we were saying about it. If it's true that the first clue's more famous than the second and third, then you're correct to criticize it for not being pyramidal. But your argument seemed to infer from that example that math theory tossups are necessarily not pyramidal or something, which is silly; the above fix in fact makes the tossup pyramidal if you're right that the first clue is the most famous. (Whereas we were saying that computational math tossups are necessarily not pyramidal because you're only solving one problem in all but a few almost-never-encountered cases.)
master15625 wrote:I guess the only reason why I support computational math is that I feel that is the way we usually get some of our points. I know really realize the grand scheme of what quizbowl is all about, to learn from the questions. I also now do not support computational questions either, especially if like 1 of them shows up every one half; but I do believe that some there should exist a computational math tossup but really sparingly. Nonetheless, I'd rather answer good math questions at math contests than answer math questions at quizbowl in any case.
It's good to hear this; it's pretty understandable to be biased towards what you're good at, and it's good that you're looking at the big picture now re: what's fair rather than what supports your own team.
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Re: Math Computation, Round 23748234

Post by Mechanical Beasts » Thu Jun 18, 2009 7:44 pm

everyday847 wrote:
master15625 wrote:I am sorry for making it sound that I would be successful at creating such questions. I was just being hypothetical in saying how it can be written pyramidally, etc.

I do not in any way think that I can make a good math question anytime soon, and I do not want to write two million tossups on this trust me.
No need to apologize; I'm just saying that SOMEONE (and since you were proposing their creation, I used you as an example) is going to have to be successful at creating them; if someone says "surely there exists x," we have to see x to believe it.
master15625 wrote:I also am sorry that I made it sound like the earlier quizbowl question that I mentioned lacked pyramidality was bad because it lacked pyramidality. I know that it is of utmost importance that it teaches someone something rather than pyramidality, so I will avoid making such comments again.
I think you missed the point of what we were saying about it. If it's true that the first clue's more famous than the second and third, then you're correct to criticize it for not being pyramidal. But your argument seemed to infer from that example that math theory tossups are necessarily not pyramidal or something, which is silly; the above fix in fact makes the tossup pyramidal if you're right that the first clue is the most famous. (Whereas we were saying that computational math tossups are necessarily not pyramidal because you're only solving one problem in all but a few almost-never-encountered cases.)
master15625 wrote:I guess the only reason why I support computational math is that I feel that is the way we usually get some of our points. I know really realize the grand scheme of what quizbowl is all about, to learn from the questions. I also now do not support computational questions either, especially if like 1 of them shows up every one half; but I do believe that some there should exist a computational math tossup but really sparingly. Nonetheless, I'd rather answer good math questions at math contests than answer math questions at quizbowl in any case.
It's good to hear this; it's pretty understandable to be biased towards what you're good at, and it's good that you're looking at the big picture now re: what's fair rather than what supports your own team.
Cheynem wrote:
I know that it is of utmost importance that it teaches someone something rather than pyramidality
Wait...you make it sound like that's mutually exclusive!
Well, for what it's worth, only one thing can be priority number one, and "making the fairest questions possible" and "making the most interesting, learning-oriented questions possible" aren't always entirely parallel objectives (when difficulty is concerned, for example). But I agree that it is very rare that you have to sacrifice pyramidality for teaching, or teaching for pyramidality.
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Re: Math Computation, Round 23748234

Post by master15625 » Thu Jun 18, 2009 7:46 pm

Cheynem wrote:
I know that it is of utmost importance that it teaches someone something rather than pyramidality
Wait...you make it sound like that's mutually exclusive!
I initially viewed that pyramidality was more important than teaching something which is wrong. I do not see that as mutually exclusive.
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Re: Math Computation, Round 23748234

Post by Cheynem » Thu Jun 18, 2009 7:52 pm

Wait, I don't think that's wrong! I definitely agree that not every tossup can perfectly hit both marks and I would probably argue that, especially in novice level or high school (perhaps not nationals) level difficulty sets, some "learning" may have to be sacrificed for pyramidality. I define this as it's okay in these sets for a reasonable chunk (not a lot) of the intended people playing the set to recognize and buzz in on the opening clues. This would be the philosophy "We are not writing this novice set or this high school set for the very best teams, so there is the chance that a good player or a player with deep knowledge in a field will not learn anything or very little on some of these tossups." This is different than, I would assume, the philosophy that goes into writing something like ACF Nationals or Chicago Open or ICT, where it should be rare that a player can one-line a topic without very very deep knowledge and that even tossups in a player's subject area should be able to teach a little. I would argue that in a high school or novice level set, teaching may not be the most fundamental priority--writing good, pyramidal questions should, and in a majority of cases, that will also teach. But a fair question (solid clues) is better than a question that "teaches" but is unbuzzable by the majority of the intended field for a few lines in.
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Re: Math Computation, Round 23748234

Post by Deviant Insider » Thu Jun 18, 2009 11:13 pm

Here is an old thread showing examples of pyramidal computational questions.

As far as the HSNCT examples are concerned, it was the 11's problem that my team was talking about. My team consisted of two students who got 5's on the Calc BC Test last year, one who probably got a 5 this year, and 1 who probably will get a 5 next year. None of them are into Math Team. I can't remember whether we eventually got it or not, but none of them jumped on it. Afterwards, we talked about some things that they should have known, like the fact that they could have added 1-11 and multiplied by 11 and there are some formulas useful for solving the problem. Nothing like it had been in their recent classwork, since we teach that before Precalculus. I don't doubt that there were several teams that had at least one player who found the question as simple as Andrew, and for those players multiplication speed determined whether or not they got power and, if they had a knowledgeable opponent, whether they got any points at all. It's possible that some people negged because they blew 66x11, though that doesn't turn out so messy and can be changed to 6x121 if wanted. However, some learning took place on that question.
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Re: Georgia 2009-2010

Post by jonpin » Thu Jun 18, 2009 11:18 pm

Jeremy Gibbs Free Energy wrote:
He also does have the best math player in the state, Eric Chen. Please do not remove math from the questions. Brookwood is a powerful team, and they need to win JV and V state, we cannot afford to lose math computation else it may hurt Brookwood's chances of winning both state tournaments next year.
If this is a motivation for advocating to keep math calculation, then something is very wrong. Trophy whoring is not a justification for keeping something, only whether it fits the bill of good quizbowl or not is a justification.
Just because no one else seems to have said it, the way I'm reading Mr. Obvious Troll here is that he's not actually from Brookwood as a few have suggested, but arguing sarcastically.

In terms of the actual thread, I've always liked mathcomp and I won't lie: I liked it as a high-schooler and young college student because I was good at it*. However, over time, especially as I've done a lot of moderating this year, I've discovered that the vast majority of these questions are garbage. I don't know for sure that it's impossible to write a good calc tossup, but I do know that the ones that are written now are not good.
I like something similar to how NSC incorporated comp this year, mixed in with some ideas in this thread:
  • A few common-link number tossups in each set, maybe 1 every few rounds. I think the question-space here is not as small as people are making it out to be. Clues here should be academic and not awful; "This was the length in years of a 17th century European conflict" or "This is Joseph's age throughout Kafka's The Trial" but not "This is the atomic number of zinc" or "This is the number of French hens in 12 Days of Christmas#." Depending on clue nature, this would be either straight GK, general science, or just math.
  • Calculation could be used in parts of bonuses. Here, pyramidality is not as much a concern. We wouldn't want trivial stuff here, and probably things like "FTPE, give the derivative of these functions" is on the bad side of the scale (leading towards extreme conversion, 0 if you don't know derivatives and likely 30 maybe only 20 if you do), but maybe having a part in a physics bonus where the team has to find the effective resistance in a parallel circuit.
*-When I didn't hilariously botch them. For instance, the elevens question quoted earlier, I looked at and said after a few seconds "858". Because I did 1+...+11 = 12*13/2 = 78 instead of 12*11/2 = 66.
#-Please tell me the "12 Days" clues like that have passed out of the game, and not even bad writers use them anymore.
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 11:30 pm

Shcool wrote:However, some learning took place on that question.
I gotta say, I preferred having our math teacher advisor teach us about Lebesgue integrals at HFT than I would if he had taught us a parlor trick for adding consecutive numbers quickly. One is actually useful in the real world; the other, kinda neat for a few minutes.
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Re: Math Computation, Round 23748234

Post by at your pleasure » Thu Jun 18, 2009 11:33 pm

"This was the length in years of a 17th century European conflict"
I would note that the clue is ambiguous(and therfore not terribly useful) unless you give a specific clue about said war("This was the length in years of a 17th century European conflict that saw the second denfenstration of Prague").
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Re: Math Computation, Round 23748234

Post by jonah » Thu Jun 18, 2009 11:44 pm

Sir Thopas wrote:
Shcool wrote:However, some learning took place on that question.
I gotta say, I preferred having our math teacher advisor teach us about Lebesgue integrals at HFT than I would if he had taught us a parlor trick for adding consecutive numbers quickly. One is actually useful in the real world; the other, kinda neat for a few minutes.
Wait, which are you saying is useful and which is neat for a few minutes?
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Re: Math Computation, Round 23748234

Post by Sir Thopas » Thu Jun 18, 2009 11:53 pm

jonah wrote:
Sir Thopas wrote:
Shcool wrote:However, some learning took place on that question.
I gotta say, I preferred having our math teacher advisor teach us about Lebesgue integrals at HFT than I would if he had taught us a parlor trick for adding consecutive numbers quickly. One is actually useful in the real world; the other, kinda neat for a few minutes.
Wait, which are you saying is useful and which is neat for a few minutes?
With respect to Gauss, he did plenty more important things than figure out how to add numbers quickly.
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Re: Math Computation, Round 23748234

Post by kayli » Thu Jun 18, 2009 11:55 pm

To Guy, I'd argue that a lot of those tricks are important in mathematics. The adding of a sequence is a central tenant of good math. In fact, many people argue that you should learn such tricks well before calculus if you really want to understand/master math. A lot of these tricks have much wider applications for the general population anyways.

I believe that such things should be tested more so than things like Cauchy's Residue Theorem. After all, it's more accessible and has wider immediate applications. I'm not the only one who thinks that one should master such arts before learning calculus. The entire (or at least majority) of the Art of Problem Solving community seems to agree.

Viva discrete math!
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