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

[Mechanical Beasts]

Right. Math computation should die. My only point was to argue the original point, which is that if you must have it--if there's a busload of schoolchildren about to be dropped to their deaths thanks to Doc Ock if you don't include it--then having it at the end is particularly bad.

We included no math computation in last fall's HFT II, and though we're currently "discussing" the subject, I can only imagine that we'll continue to restrict our quiz bowl tournament to having quiz bowl content.

[jenkster08]

I've only played a few NAQT games, but I was really ambivalent to how they asked the math questions.

In my opinion, pyramidal math questions just should not exist. However, a balanced distribution that tests the full array of academic subjects should have a proportional amount of math questions. After all, math is usually 1/7-1/5 of a high school student's courseload in school. Why should math have a different place in academic bowl, quiz bowl, scholar's bowl, etc.?
But I can see why a lot of people have disdain for pyramidal math questions of NAQT. I thought the questions were unnecesarrily wordy and complicated and tried really hard to put on a mask of difficulty on math questions that are easy at heart. For example, I've heard likes of this (it probably isn't an actual question, but demonstrates my problems with pyramindal math questions):
"Alan paints 480 houses in 10 years. You can find this answer by using the formula work = rate x time and then using a conversion factor of 12. FTP, what is the average number of houses Alan paints in one month during this period?"
Problem 1: Since NAQT offers the benefit of powering, this question is trickery. You have to wait until just before the FTP just to know what the question is asking for. Students who want to power will most definitely neg.
Problem 2: Why so wordy? This is a rather simple problem that has been stretched on forever and forever by unnecessary pyramidal clues. If NAQT wants to avoid immediate buzzer races, they should make it more complex, like "74 hen lay 74 dozen eggs in 2 months. How many hen are needed to lay 37 dozen eggs in 4 months?" (And just ask that straight without any excessive wordage and there won't be a buzzer race.)

I've also read a lot about the different set of skills that math questions test on this forum. To me, at the heart of it, calculation speed is a reflection of your familiarity and mastery of mathematics. In that sense, it does too test depth of knowledge in math, just as a pyramidal question on White Lotus Rebellion tests your depth of knowledge in history.
For example:
What is the center of the circle whose equation is:
x^2 + 6x + y^2 - 10y = 10
Those who have a depth and familiarity with math will buzz in at -10y. Yes, this can have a potential for buzzer race, but it does teach depth and familiarity with the subject at hand.

Also, consider something like this: "20 people take History, 15 people take Lit, and 24 people take science, and however many take both history and lit but not science. that type. How many students are there total?"
Most people will go drawing the venn diagram, but experienced math people would use Principle of Inclusion and Exclusion. Math questions doesn't have to test speed of addition, multiplication, or what ever operation you like, it can be a test of how well you know mathematical concepts and how quickly you can use them in the problem to create an answer.

With that said, I think Panasonic has it right when it comes to calculation questions. They are not long-winded and cut to the chase, but they're not useless buzzer beaters (especially not so in the later rounds!).

[Maxwell Sniffingwell]

You seem to be working with a few false assumptions, jenkster. I also enjoy comp math, but I'm not convinced that it belongs in quizbowl. Here's why:

"Alan paints 480 houses in 10 years. You can find this answer by using the formula work = rate x time and then using a conversion factor of 12. FTP, what is the average number of houses Alan paints in one month during this period?"

This is not the kind of question NAQT would ask - simply because by the time it says "this answer," you don't know what "this answer" is.
Here's a sample question:

4. Pencil and paper ready. A non-invertible, two-by-two matrix has 1, 3 as its first row and x, 2 as its second
row. The value of x can be determined by realizing that the determinant must equal zero for the matrix to
be non-invertible. (*) For 10 points—find the value of x that makes the determinant zero.
answer: 2/3

Notice by the time the first sentence (not including "Pencil and paper ready.") is read, the question is solvable - you know that you'll be solving for x. In your problem, it's unclear what the question is - perhaps this is better:

"Alan, who paints at a constant rate of houses per month, paints 480 houses in 10 years. You can find this answer by using the formula work = rate x time and then using a conversion factor of 12. FTP, what is the average number of houses Alan paints in one month during this period?"

Easy fix, more NAQTish.

Problem 1: Since NAQT offers the benefit of powering, this question is trickery. You have to wait until just before the FTP just to know what the question is asking for. Students who want to power will most definitely neg.

For real NAQT questions: No, it isn't; no, you don't; no, we won't.

Problem 2: Why so wordy? This is a rather simple problem that has been stretched on forever and forever by unnecessary pyramidal clues. If NAQT wants to avoid immediate buzzer races, they should make it more complex, like "74 hen lay 74 dozen eggs in 2 months. How many hen are needed to lay 37 dozen eggs in 4 months?" (And just ask that straight without any excessive wordage and there won't be a buzzer race.)

I get the impression that the wordiness is giving skilled players a chance to power the question... or giving regular players enough time as possible before the 10-second clock starts.

I've also read a lot about the different set of skills that math questions test on this forum. To me, at the heart of it, calculation speed is a reflection of your familiarity and mastery of mathematics.

No. I am a very good comp-math player, and am familiar with math up to a high level. But when it comes to multiplying numbers, calculating determinants, or solving systems of equations, a hypothetical autistic-savant fifth-grader would be able to beat me to the buzzer. Yes, you need to know the "tricks" and be comfortable with math. But the raw speed at which you can crunch numbers matter a LOT more than you think.

What is the center of the circle whose equation is:
x^2 + 6x + y^2 - 10y = 10
Those who have a depth and familiarity with math will buzz in at -10y. Yes, this can have a potential for buzzer race, but it does teach depth and familiarity with the subject at hand.

Where does this reward depth? Again, a seventh-grader (not even a savant this time) would buzz at the same time as me... or my college math professor... or Leonhard Euler himself. Depth means that we design questions so that the order goes Euler, professor on that subject, me, seventh grader, clueless fourth grader, rock. This question would get everybody but the fourth-grader and the rock buzzing at the same time.

Pencil and paper ready. 20 people take History, 15 people take Lit, and 24 people take Science. The only multi-course schedule allowed is Lit/History, and there are 51 students total. To solve for the number of students who take that Lit/History course load, one could draw a Venn diagram, or use the Principle of Inclusion and Exclusion. (*) FTP, how many students take both Lit and History?

This isn't bad, as far as math questions go.
And neither are the questions at Panasonic, though I don't like how they allow calculators and occasionally turn into number-crunching races.


The problem with math as a whole is that it's nearly impossible to get that Euler-professor-me-7th grader-4th grader-rock buzzing order; I'm a faster calculator than my professor, for example.

But on, say, a Greek history question, Herodotus would outbuzz a classics professor, who would outbuzz me, ... a 7th-grader ... a 4th-grader ... and last the rock.


Does this make sense, jenkster?

[Irreligion in Bangladesh]

I agree with everything Greg says, and I'd like to add that this --

The problem with math as a whole is that it's nearly impossible to get that Euler-professor-me-7th grader-4th grader-rock buzzing order; I'm a faster calculator than my professor, for example.

illustrates one of the better reasons against computation in quizbowl. The "quick computation" skill outranks the "deep conceptual knowledge" skill in computational tossups - mostly due to the small amount of computational time allotted...you can't ask deeper topics because they would require too much time to compute. This is the only subject/category in quizbowl where "deep conceptual knowledge" is not the most important skill in determining who buzzes in early. (Remember that buzzer speed is always secondary to depth of knowledge in pyramidal questions.) This makes computational math considerably different compared to the other 80-95% of the game.

Math is a part of the schooling curriculum, but it doesn't translate well to being tested in the pyramidal quiz bowl format. It's better from a quiz bowl standpoint to drop a curriculum-based category distribution if it requires unwieldy questions such as computational math.

[Matt Weiner]

Greg, I don't know if you saw the actual HSNCT questions this year, but several people including myself did note that a few of them were impossible to power or impossible to figure out the desired answer until the end, because what you were supposed to do with the numbers simply wasn't indicated early enough in the question.

I actually agree with one premise that jenkster08 posted--"pyramidal" math questions are a waste of time. They aren't pyramidal, they're just confusing and long. If for some reason we must have math tossups, just ask the question and get it over with instead of playing with this "this work's title is an anagram of 'Add Louses'" type of "hint"-style clues.

Of course, it would be much better to just drop math tossups, leave a few in bonuses to satisfy people who really like multiplication, and move towards a better NAQT HSNCT as a result.

[AKKOLADE]

I actually agree with one premise that jenkster08 posted--"pyramidal" math questions are a waste of time. They aren't pyramidal, they're just confusing and long. If for some reason we must have math tossups, just ask the question and get it over with instead of playing with this "this work's title is an anagram of 'Add Louses'" type of "hint"-style clues.

Oh my God yes. This. I was a pretty good math player back in high school - probably best in WV my senior year and close to it my junior, for whatever little that's worth - but NAQT math questions have always just been a train wreck. They are almost always unclear about what they're asking about, and almost turn into a mini-game of "learn how NAQT does math and profit" rather than just quiz bowl.

[jenkster08]

I'll try my best to work on the quoting thing later, hehe.

Cornfused, someone less familiar in math will not have the ability to make split-second decisions on how to solve a problem or making clear all the steps. For example, I was practicing for Panasonic today on AOPS's online game (it's like quiz bowl math, but no one reads it to you, you read the question yourself.).

The difference in the game was that I was playing middle schoolers, granted they are national-calibre middle schoolers, but I had more experience, and that helped me make the RIGHT split-second decisions. In this problem:
"What is the area of a triangle with sides 5, 5, and 6?" I've done more math than the middle schoolers, seen more types of problems, so I knew that I could draw a height from the vertex and calculate the height, but the middle schoolers chose to use Heron's formula instead. That's a type of problem where experience and a comfortable grasp of math helps.

I understand that the circle question may not be a really good example because many people do know the trick to that, but another concern of mine is why should a 7th grader really good at math (say any of the 7th grade Mathcounts champions) not beat you at a math question? Here, in this case, they might have even more experience (who knows what they do all day!) and play on AOPS thing all the time. They probably do have a raw speed that helps, but they have a clear advantage in any sort of speed over someone who is not as confident in their grasp on math. I've felt this too, when I'm not too confident and missing some questions, I doubt myself a little too much, and that slows me down. It may seem like a millisecond to outsiders, but that instant of doubt makes the difference in the world of math buzzing/competition.

There is a hierarchy (that's what we strive for right, that the best team win most of the time?) in math. It may appear tighter on a time-scale than a normal quiz bowl question, but it's there. However, it may not reward it according to the age scale you provide there, but age/seniority does not always go side by side with hierarchy.

I believe there are many good, non-pyramidal math questions that are out there and can still be written without any redundancy. These are the ones that tournaments should utilize.

[Sir Thopas]

I understand that the circle question may not be a really good example because many people do know the trick to that, but another concern of mine is why should a 7th grader really good at math (say any of the 7th grade Mathcounts champions) not beat you at a math question? Here, in this case, they might have even more experience (who knows what they do all day!) and play on AOPS thing all the time.

The seventh grader shouldn't beat me at QB just because he chooses to spend his time learning calculation speed and contrived tricks that don't help outside the world of math competition, while I choose to learn actual mathematical concepts like calculus or linear algebra or whatever, sacrificing computational speed as irrelevant in doing so.

[theMoMA]

Hey, here's the thing. Computation bowl is not quizbowl. The type of skill being asked for, and the format of the asking, are completely different from pyramidal quizbowl. It's very odd that in some formats the quizbowl game is put on hold for a completely different competition in mid-match. If anyone can refute or reconcile this argument, I'd love to hear it.

[jenkster08]

I understand that the circle question may not be a really good example because many people do know the trick to that, but another concern of mine is why should a 7th grader really good at math (say any of the 7th grade Mathcounts champions) not beat you at a math question? Here, in this case, they might have even more experience (who knows what they do all day!) and play on AOPS thing all the time.

The seventh grader shouldn't beat me at QB just because he chooses to spend his time learning calculation speed and contrived tricks that don't help outside the world of math competition, while I choose to learn actual mathematical concepts like calculus or linear algebra or whatever, sacrificing computational speed as irrelevant in doing so.

Calculus is a good topic, too, but linear algebra is outside the scope of high school curriculum. The hierarchy still applies to calculus and advanced math questions. Whoever is more familiar and knowledgeable in Calculus should beat the lesser familiar/knowledgeable.

I still don't see what's to hold a seventh grader from beating you to a quiz bowl question. Is that not possible? You could that a regular 7th grader should not beat you at such math questions. But I doubt a regular 7th grader could respond so quickly, because he/she is not as experienced and knowledgeable as you are in math. But if he is, I don't see why he can't beat you.

[vcuEvan]

You talk about your experience with learning various methods at solving problems. My problem is that in quizbowl, all of these problems are simply repeated over and over with different numbers. I mean there's the one with the marbles, the cards, the two trains at different speeds, the dartboard, the picture frame. My teammate Mehdi Razvi did quite well with computation at the HSNCT my senior year after spending two hours going through a packet and learning the various tricks for these problems.

I also agree about computation being a completely different game. Those who have a deep understanding of mathematics should in theory be just as open to math theory tossups instead. Right?

[jenkster08]

Hey, here's the thing. Computation bowl is not quizbowl. The type of skill being asked for, and the format of the asking, are completely different from pyramidal quizbowl. It's very odd that in some formats the quizbowl game is put on hold for a completely different competition in mid-match. If anyone can refute or reconcile this argument, I'd love to hear it.

When you say that, I kinda picture a basketball shootout between the two halfs. Math is not solely computation bowl, and if there are questions like "what is 28*32," then that's a bad question. There is computation involved in math, yes, but it still requires knowledge and tests how well you grasp that certain topic. It is not "completely different." Math to quiz bowl is more like clay court tennis is to hard court tennis than ping pong is to badminton. Clay court tennis requires different skills and accentuate different strengths (difference between Nadal on clay and on hardcourt?) You need to be fast on the defensive, be able to move and slide well on a clay court, skills that are not emphasized or even used (sliding? not everyone's Kim Clijsters) on a hard court. Still, tennis doesn't divide the sport into two categories. They still count rankings that treat clay tournaments in the same way as hard court tournaments. Quiz bowl shouldn't treat math any differently.

Adamantium - NAQT provides a poor example of math questions. People who have done Mathcounts or any high school math contests (even ones not demanding speed) can see that there are a wealth of good viable questions for quiz bowl. There are some math concepts that you can't just grasp overnight reading over a formula table.

But someone said they won't need the calculating skills in the future. Okay, in most cases, do I need to know the name of the old man in Old Man and the Sea in the future? I don't see quiz bowl as a way of preparing you for life...

[evilmonkey]

I also agree about computation being a completely different game. Those who have a deep understanding of mathematics should in theory be just as open to math theory tossups instead. Right?

Not at the high school level, simply because there is not nearly enough theory to write about.

...Euler-Prof-Me-7th Grader-Rock

[My version of what he said] Thats not necessarily true

I don't think he's talking about the superstar 7th graders, necessarily. He's just talking about the normal ones. And in that sense, I agree with him. I guess I can see that its just too damn hard to write enough math that would fit that criteria. I think maybe one math theory tossup every few rounds as a sub-cat of science, and 1 MATHCOMP bonus a round should be enough math.

[Mechanical Beasts]

I'm going to clip the tennis analogy from your post:

[If] there are questions like "what is 28*32," then that's a bad question. There is computation involved in math, yes, but it still requires knowledge and tests how well you grasp that certain topic. It is not "completely different." Math to quiz bowl...Quiz bowl shouldn't treat math any differently.

I'd like to see an explanation about why math computation isn't completely different from quiz bowl, testing entirely different skills, since all you said had to do with tennis.

I submit that if math tossups were decreasingly abstruse descriptions of a problem that can be solved in one of ten ways (taken from a You Gotta Know article, perhaps), and players have to race to answer with which one of those ways applies, then they would be MORE like quiz bowl. Would they also suck more as a mode of academic competition? Also yes!

We also don't ask teams to write essays every seven tossups. Nor do we ask teams to speed-mime the plot of the answers to any lit tossups. Computational math competitions are cool, and I daresay I'd do okay at one, but it's not quizbowl and does not belong there.

Adamantium - NAQT provides a poor example of math questions. People who have done Mathcounts or any high school math contests (even ones not demanding speed) can see that there are a wealth of good viable questions for quiz bowl. There are some math concepts that you can't just grasp overnight reading over a formula table.

But someone said they won't need the calculating skills in the future. Okay, in most cases, do I need to know the name of the old man in Old Man and the Sea in the future? I don't see quiz bowl as a way of preparing you for life...[/quote]

[Sir Thopas]

But someone said they won't need the calculating skills in the future. Okay, in most cases, do I need to know the name of the old man in Old Man and the Sea in the future? I don't see quiz bowl as a way of preparing you for life...

It's the difference between memorizing formulas and being exposed to books, poems, paintings, etc., that you may not have heard of, and turn out to really enjoy. So yes, in the future, you have the experience of having read The Old Man and the Sea, if you so choose. I think most people would agree that this, rather than list memorization, is top-flight quizbowl.

[aestheteboy]

But someone said they won't need the calculating skills in the future. Okay, in most cases, do I need to know the name of the old man in Old Man and the Sea in the future? I don't see quiz bowl as a way of preparing you for life...

It's the difference between memorizing formulas and being exposed to books, poems, paintings, etc., that you may not have heard of, and turn out to really enjoy. So yes, in the future, you have the experience of having read The Old Man and the Sea, if you so choose. I think most people would agree that this, rather than list memorization, is top-flight quizbowl.

Honestly, computation is pretty useful, and I'd rather be able to solve simultaneous equations like 10 seconds faster than everyone else than know about Stern-Gerlach Experiment. Heck, I'd rather be able to calculate fast than know about di Chirico, and he's super interesting. My point is, utility is poor indicator for the appropriateness of a question. There is non-subjective, non-judgmental reason why computational math isn't quizbowl, which Andrew Hart already pointed out.

[Mechanical Beasts]

Honestly, computation is pretty useful, and I'd rather be able to solve simultaneous equations like 10 seconds faster than everyone else than know about Stern-Gerlach Experiment. Heck, I'd rather be able to calculate fast than know about di Chirico, and he's super interesting. My point is, utility is poor indicator for the appropriateness of a question. There is non-subjective, non-judgmental reason why computational math isn't quizbowl, which Andrew Hart already pointed out.

I'd rather know about the Stern-Gerlach experiment. I'm never going to need to solve simultaneous equations that Mathematica can't solve (or approximate solutions to) far, far faster. But knowing about science that's been done before helps me think about science that I might want to do. I'm working this summer for a moderately famous polymer chemist. The first thing I got when entering the lab was reading material. Having learned more about AGET ATRP, I can understand where the group is going with their research and come up with experiments of my own.

But utility is, true, in general a poor indicator.

[Maxwell Sniffingwell]

speed-mime

ohgodpleasemommycanwe

[Sen. Estes Kefauver (D-TN)]

OK, I think I have already made my voice heard on the matter of math calculation questions of all shapes and sizes being awful indicatiors of knowledge of math, so I don't really want to rehash all of that right now, but I want to address something else that seems endemic to Martin Ye's posts. Quizbowl is NOT a mirror of the curriculum at high schools, and it has no business being such a thing. It has business being quizbowl, it's own self-contained game. When you start asserting that quizbowl needs to be a mirror of curriculum, you then start dealing with nonsense like drivers ed, PE, and agriculture being required parts of the distribution and topics like Social Science, myth, and especially philosophy being virtually nonexistant. This is not as it should be, and before people begin using the "it needs to match the curriculum" argument to defend the precense of math, they need to actually consider the full ramifications of their stance and quite hopefully stop playing that card.

[jenkster08]

I still don't see the fundamental difference between math and other types of questions. It has its differences with history and humanities, but I don't see the contrast between math and those subject as though if we were comparing apples and oranges. Familiarity and knowledge of math is a prerequisite for computational speed. Math is academic. History is academic. They both require intelligence to grasp and understand and master. (I actually started this post before Charlie's post - then what is quiz bowl? Is it a test of academic knowledge? Maybe I have a different definition of it than all of you because frankly, I might not even do quiz bowl.)

Knowing the formulas is not so different from knowing the terms of a treaty or the plot of a novel. But math is more of an applicable subject. Well, the others are too (learn from history and great books?) in the real world, but they can more easily separate themselves from the applicative aspect. Quiz bowl, like some of you say, should separate math from application and simply focus on theory. After all, it has done so successfully with science (although if the constants were any easier to work with... there'd be a complaint probably about computational science). But working with numbers is the applicative nature of math and science.

From my perspective, the opponents of math on this board are opponents of speed. That's why there's such a great enthusiasm for pyramidality, so that there are as few occasions of buzzer beating as possible. That's noble, in that you want to find out who does indeed KNOW MORE. But to me, speed does not disqualify a certain person's knowledge base. Whatever he is fast at, he's probably done so with lots of practice and much confidence in his knowledge of the subject.

I'm going back to studying for now. Thanks to all for a wonderful discussion. It's probably one of the most engaging ones I've been a part of. This board has a wonderful introduction to the professionalism of the adult world. Thanks for that.

[theMoMA]

In math, knowledge doesn't equal points...end of story?

[Matt Weiner]

Knowing the formulas is not so different from knowing the terms of a treaty or the plot of a novel.

If you want to write a pyramidal tossup on "the quadratic equation," be my guest. That's exactly what we mean by "conceptual math."

If you want to test the ability to multiply numbers, go do Mathcounts or something.

[Tegan]

From my perspective, the opponents of math on this board are opponents of speed.

While I do support math computation inclusion, I don't think I agree here.

I think that people who, in general, oppose math computation inclusion are people who don't see math as a subject rooted in "knowledge" vs. " a skill". I think there is an overall feel that quizbowl should be strictly "recall of knowledge", and absolutely nothing else.

I can see this. There was a time that I thought quizbowl could/should be more than simple recall. I have edged away from that more recently. I have come over the believe that this has to be the way things are.

However, I think there is still a misconception, IMO, that computation heavily emphasizes skill over recall. If you are asked a math problem, you have to know the basic algorithm to do it. I think that, with a minority of exceptional cases, for the most part, the real timing in computation comes down to recalling the particular algorithm, and having the confidence that it is correct, and then acting on it.

I know that a lot of people are very much against quick recall questions, so in that case, yes, there are people against that kind of speed (so am I).

[Matt Weiner]

To me, the #1 problem with math questions is that there's only about 20 or 30 types of mad-lib problems (and that's being generous, it might be closer to 15 types if you count very similar problems as one) that you can fit into the length limits of a quizbowl question, and such a small canon is way too limiting. Imagine if we asked 2 or 3 history questions per game, but there were only 20 plausible history answers. The category would be a total farce. That's what math is right now.

[jbarnes112358]

Calculus is a good topic, too, but linear algebra is outside the scope of high school curriculum.

I'm not sure this is the standard people who are writing for these national tournaments are using. I do not know what percentage of questions at NSC or HSNCT are outside the high school curriculum, but I suspect it is quite high. (The same no doubt is true for NAC, as I'm not sure what part of the high school curriculum teaches you how to identify the names of candy bars when the vowels are omitted.)

More of these kids know some linear algebra than you might think. We offer it as a course option at our school, for example.

There are so many mathematical things you could ask about regarding theory, concepts, terminology, or notation. Good math questions could possibly contain equations, could ask about math rules, properties of special functions, famous theorems and the like. At something like HSNCT or NSC, there is no reason to restrict questions to just the core high school subjects. Students learn about mathematical things outside of the high school curriculum, just as they learn things about art, music, philosophy, or particle physics. The problem I have with most of these computation questions is that they basically come down to who can cipher fastest, not who knows the most about mathematics.

Regarding your circle example, it basically comes down to who is most adept at completing squares, at least as far as necessary to obtain the desired numbers. Even then, to buzz when you said you would buzz would be a bit dangerous. How do you know the right hand side of the equation is going to be a constant? It is the kind of thing where of the 8 people in the game, nearly everyone knows how to do the problem. I just don't see the point in testing who can do it fastest. If the objective of a pyramidal quizbowl tournament is to see which teams are the most knowledgeable about a wide variety of academic topics (including mathematics), i think it is a stretch, at best, that computational questions, most of which reward speed of computation over mathematical knowledge, advance that objective.

John Barnes
Mathematics teacher and quizbowl coach
Maggie Walker Governor's School

[Gautam]

Hey,

Stop comparing quiz bowl to tennis, aops, or amc/aime/usamo/whathaveyou. You can surely do both, but it is impossible to write a single "good" question that can be used in a math competition which can also be used in a quiz bowl competition. I have been a regular visitor of aops for a long time and have done quite a bit of amc/aime work, but, like Evan Adams already said, got (NAQT) computational math tossups using quick tricks I learned from looking at previous packet. There is absolutely no way of eliminating speed as a variable, and it is equally difficult to reward "knowledge".

Having tried to write some computation tossups, I feel bad writing questions that in no way adhere to the standards I otherwise follow.

Gautam

[Maxwell Sniffingwell]

The only way we found that this was doable was basically a 30-20-10: Make your tossup a list of problems (of decreasing obscurity of method rather than difficulty, so someone who knows HOW to do #1 beats someone who knows HOW to do #2... in other words, don't follow up "The fourth root of 1024576" with "42-10") with the same common, simple answer, such as pi, 3, or 1.

[Gautam]

The only way we found that this was doable was basically a 30-20-10: Make your tossup a list of problems (of decreasing obscurity of method rather than difficulty, so someone who knows HOW to do #1 beats someone who knows HOW to do #2... in other words, don't follow up "The fourth root of 1024576" with "42-10") with the same common, simple answer, such as pi, 3, or 1.

sure. I think we all agree that is the best way to write comp math. it's just that those also play a lot more differently than usual quiz bowl questions because one need not keep the first problem in perspective while solving the third problem. On the other hand, if you were playing a history tossup, which clearly mentioned that the person was russian in the first line, and mentioned it was a female empress in the fourth line, you cannot just buzz in on the fourth clue and say Queen Elizabeth.

Gautam

[Maxwell Sniffingwell]

...which is why we should have MORE 30-20-10 math bonuses and LESS math tossups. If we're going to hold the amount of math steady, that is.

[theMoMA]

The only way we found that this was doable was basically a 30-20-10: Make your tossup a list of problems (of decreasing obscurity of method rather than difficulty, so someone who knows HOW to do #1 beats someone who knows HOW to do #2... in other words, don't follow up "The fourth root of 1024576" with "42-10") with the same common, simple answer, such as pi, 3, or 1.

sure. I think we all agree that is the best way to write comp math. it's just that those also play a lot more differently than usual quiz bowl questions because one need not keep the first problem in perspective while solving the third problem. On the other hand, if you were playing a history tossup, which clearly mentioned that the person was russian in the first line, and mentioned it was a female empress in the fourth line, you cannot just buzz in on the fourth clue and say Queen Elizabeth.

Gautam

Well, it's a common link. You don't have to keep the first clue in mind either during a common link history tossup on Catherines, or whatever.

[Matt Weiner]

I find that at the HSNCT level, you pretty much always have people racing to complete the arithmetic on the first statement of the problem, and there is no time to start over when you get the new "method." The "pyramidal" restatements are just so much filler to maybe give people a chance at power when the original question is easy enough.

[Mechanical Beasts]

Especially true because at HSNCT this time--more than any other--questions literally ran approximately like

It is really important for Jim to figure out how many miles per gallon he'd get, by dividing the number of miles he drives on his trip, 240, by the number of gallons of gas he burns, 12. Using this, or any other method, (*) FTP calculate the number of miles per gallon Jim gets if he can drive 240 miles on 12 gallons.

In other words: "Problem. Filler words. Restatement of problem."

This is particularly unfortunate because computational math used to be slightly better, in that at least it tried to be pyramidal, instead of just giving teams more than the traditional ten seconds.

[naturalistic phallacy]

To me, the #1 problem with math questions is that there's only about 20 or 30 types of mad-lib problems (and that's being generous, it might be closer to 15 types if you count very similar problems as one) that you can fit into the length limits of a quizbowl question, and such a small canon is way too limiting. Imagine if we asked 2 or 3 history questions per game, but there were only 20 plausible history answers. The category would be a total farce. That's what math is right now.

Not only are repeated math set-ups a waste of space that could be used for more legitimate questions about math theory or what have you, they're just plain boring.

[Mechanical Beasts]

Not only are repeated math set-ups a waste of space that could be used for more legitimate questions about math theory or what have you, they're just plain boring.

I, for one, find it terribly exciting when I'm reading to recognize "oh, this is the one where you divide the first number by two and multiply it by the rest of the Pythagorean triple; I wonder how long it takes to multiply eight by" FIFTEEEEEN. Oh, wait, that was the finals.

[Maxwell Sniffingwell]

Not only are repeated math set-ups a waste of space that could be used for more legitimate questions about math theory or what have you, they're just plain boring.

I disagree. I mean, yes, math comp is bad quizbowl. But honestly, I still enjoy it, because I like doing math. Admittedly, I haven't played as much NAQT as other people (2 IS tourneys and an HSNCT in high school; one IS-A, one SCT, and ICT Div II in college,) so maybe I'll tire of that stuff soon. But I played two years of Scholastic Bowl in Illinois, and I never got tired of the math.

[disclaimer] Please note, this is not a defense of the acceptability of comp math in good quizbowl. It is simply a personal statement defending the enjoyability of said comp math. [/disclaimer]

[naturalistic phallacy]

Not only are repeated math set-ups a waste of space that could be used for more legitimate questions about math theory or what have you, they're just plain boring.

I disagree. I mean, yes, math comp is bad quizbowl. But honestly, I still enjoy it, because I like doing math. Admittedly, I haven't played as much NAQT as other people (2 IS tourneys and an HSNCT in high school; one IS-A, one SCT, and ICT Div II in college,) so maybe I'll tire of that stuff soon. But I played two years of Scholastic Bowl in Illinois, and I never got tired of the math.

[disclaimer] Please note, this is not a defense of the acceptability of comp math in good quizbowl. It is simply a personal statement defending the enjoyability of said comp math. [/disclaimer]

Yeah, I guess coming from a state that has their state league play on modified A-sets, it got old very quickly. This is not to say that all of quizbowl needs to be flashy and exciting; it just seems like there is a lot less quizbowl learning taking place during computational math because of all of the repeats.

[grapesmoker]

But working with numbers is the applicative nature of math and science.

This statement is false; I got a double-major in physics and math while keeping my computations to a minimum. Numbers are only plugged back in after the theory is worked out anyway, and for anything beyond "do this trivial operation," everyone uses a calculator.

[jbarnes112358]

To those of you that insist that computation questions test mathematical knowledge of concepts, I will concede the point. However, most of the computation questions come down to who can multiply or do some other basic calculation fastest. True, you need some mathematical knowledge to know what to do to solve the problem. But, there are better ways to test mathematical knowledge where the emphasis is on knowledge directly, not through computation speed tests. Here is a possible example, which might be worked into a toss-up somehow, but might be better as a bonus.

Event A and event B are mutually exclusive. The probability of event A is 1/4 and the probability of event B is 1/2. What is the probability of the event "A or B"?

You could adapt such questions to have no numbers or numerical computations at all. But, the emphasis here is on knowledge of the addition rule of probability of mutually exclusive events. Adding 1/2 and 1/4 is trivial and immediate. It is the knowledge of the addition rule that is being tested here, not speed computation by computation tricks and what not. In fact, it would be important to use easy numbers to ensure that you are testing knowledge of probability, not facility at speedy arithmetic. For example, you could use 3/14 and 5/12 as your two probabilities, but then you shift the focus of the question from testing probability knowledge to testing the ability to do fifth grade arithmetic fast.

If you wanted to make the above one part of a bonus, then the other two parts could be:

Event A and event B are independent. The probability of event A is 1/4 and the probability of event B is 1/2. What is the probability of the event "A and B"?

Here multiplication is trivial and immediate, and can be done by anyone who knows the answer within 3 seconds. Again the emphasis is on mathematical knowledge, not computation speed.

Third part:

Event A has a probability of 1/4. What is the probability of the "complement of A"?

These questions require mathematical knowledge of concepts and terminology. You need to know what computations are needed to answer the questions, but you don't need to be able to do speed computations.

In fact, you could remove the numbers completely by using x and y in place of 1/4 and 1/2.

[Buzz Buzzard]

Not only are repeated math set-ups a waste of space that could be used for more legitimate questions about math theory or what have you, they're just plain boring.

I disagree. I mean, yes, math comp is bad quizbowl. But honestly, I still enjoy it, because I like doing math. Admittedly, I haven't played as much NAQT as other people (2 IS tourneys and an HSNCT in high school; one IS-A, one SCT, and ICT Div II in college,) so maybe I'll tire of that stuff soon. But I played two years of Scholastic Bowl in Illinois, and I never got tired of the math.

[disclaimer] Please note, this is not a defense of the acceptability of comp math in good quizbowl. It is simply a personal statement defending the enjoyability of said comp math. [/disclaimer]

It's number-cruncher reinforcer stuff, i.e. Mathcounts type questions (except with a ten-second time limit and in the context of a quiz bowl match).



I say this as a Mathcounts competitor way back in the day (May of 1987) participating for Team Michigan.

I'm -sure- I wasn't quite the 2nd smartest math geek in the 8th grade class of 1987, but I did finish 2nd place in the individuals that year, and lo, got a free trip to DC out of it.

And, as an 8th grader, W00T!!!!1!!!.

Good times. Like when the Michigan contingent, on the day prior to competition (I think Thursday, after we got settled in) decided to use our five-day free Metro passes to go exploring on the DC Metro without any of the advisors around.

No, they weren't real pleased when they found out we'd gone touring, but it was a fun little trip to wherever we went.

Apologies for the tangent.

[David Riley]

I'll wager that 70% of regular contributors to this board don't remember who Buzz Buzzard was . . .

[Mechanical Beasts]

I'll wager that 70% of regular contributors to this board don't remember who Buzz Buzzard was . . .

Spoilers below!

Woody Woodpecker's arch-nemesis, duh.

[negatron]

Instead of these silly word problems that deal with algebra computation and geometry computation, let us throw in calculus computation and linear algebra computation.

What is needed for math computation to become a serious category of quizbowl is to expand its canon. Go beyond the high school curriculum (similar to what has happened to the other subjects of quizbowl). Make the questions harder. Alot harder but still pyramidal so that by the end of the question, anyone could get it (at least anyone who has the slightest idea how to do high school math)

One idea would be to ask math "trivia." For example:
A continuous function from an arbitrary space to a space with this property has a graph that is closed in the product space of the fromspace and tospace. Compact sets are closed by it. It guaranties the uniqueness of the limits of nets, filters, and sequences. For ten points name this kind of space in which two distinct points can be separated by neighborhoods.
Answer: Hausdorff.

The problem is people won't get it at the end unless they are very good at science trivia. So I think the following question is a better example:
This smooth operator is used in the weak formulation of a boundary-value problem. It is the main part of the norm in an L-p space and comes in gauge, Lebesgue, and Daniell formulations. It can also be defined as the limit of a sum on the points in a net as the net is refined of a function. FTP name this operator that turns x^2 into 1/3*x^3.
Answer: integral

[Sen. Estes Kefauver (D-TN)]

We've already covered this, but yes that is exactly what good math tossups need to be written on things like. The problem is there is not enough stuff that is askable at the high school level to warrant more than like 1 tossup a game (Haussdorf being in that too hard category)

[DumbJaques]

This is just a friendly reminder that everyone who uses the forums needs to abide by our rules, including the signature rule. Please indicate your identity (ie Bob from Boise State University Online) or angry, unemployed computation question writers will promptly dispatch you. As soon as nobody wants computation anymore.

In case someone is missing this, the set of people to whom this message is addressed is the intersection (MAAAAAATH) of the set of all humanity and the set of posters posting in this thread who are named "negatron."

[pray for elves]

I take great offense to things like Hausdorff spaces and integrals being labeled as "trivia". Call it "math theory" if you want a name.

Also, as no high school I've ever seen offers courses in point-set topology, Hausdorff is not a good answer selection for a high school tournament, even if I've written tossups on him or his namesakes myself for college tournaments.

[Mechanical Beasts]

I take great offense to things like Hausdorff spaces and integrals being labeled as "trivia". Call it "math theory" if you want a name.

Also, as no high school I've ever seen offers courses in point-set topology, Hausdorff is not a good answer selection for a high school tournament, even if I've written tossups on him or his namesakes myself for college tournaments.

Yeah, I know that Harvard's first year math classes allude to such topologies--the one I took at one point required us to say "and we know this because the space is Hausdorff," and I'm sure that Math 55 had to do a lot more with it, since they cover some topology--but generally that means that it's too hard for high school, considering that 90% of my math class would be unable to answer that question, simply because it was so non-critical at the time. But the point was well taken. I believe others of the same mind have posted elsewhere both in this thread and others.

[yisun]

We included no math computation in last fall's HFT II, and though we're currently "discussing" the subject, I can only imagine that we'll continue to restrict our quiz bowl tournament to having quiz bowl content.

I'm writing a lot of the math for HFT III, which will probably not have computation due to the difficulty of writing a large number of such questions given the existing canon. However, (as a math major) I think math is an important academic field and that it deserves at least some representation in quiz bowl. The problem that I've come across while writing high school math is that there is very little that can be asked within the canon. There are things in Algebra, Geometry, Basic Calculus, and (really stretching things here) Linear Algebra / Diff Eqs, but it is very difficult to write anything substantive about these subjects in the form of a quiz bowl question -- in particular, the answer space is extremely small, since the set of all askable math concepts that high school students know is not very large. So I think there are two possible solutions to this problem:

1) Change to much harder math computation (at the level asked in high school math competitions like the AMC or even the AIME). As it is, I think the middle school MathCOUNTS champion would beat a relatively good math player 9 times out of 10. [I recently saw a 9th grade alum of MathCOUNTS get the first 22 questions in a state sprint round in 5 minutes. These are a fair bit more complicated than the current computational math. The comparable version is the countdown round, where the answers are ridiculously fast.] One caveat here -- harder questions would require more time allotted, which I can see being unpopular. This would remain technically non-pyramidal, but it would reward deeper knowledge of math; once solving the problem becomes more important than calculating the answer and not everyone can solve all the problems (or even close), people with a deeper grasp of math will do better. [A potential counterargument here is that this rewards math "skills" and not math "knowledge." I agree; there are two areas of math -- building theories that people can know about and solving problems with these theories. In high school, though there are so few theories to know that this is impractical, and I think testing application of the theories is a pretty good substitute.]

2) Expand the canon greatly to include more advanced things. In this fix, anything with any remote connection to the high school curriculum would be fair game (i.e. "hard" plane geometry (Ceva, Menelaus, Desargue Theorems), theorems about polynomials, number theory, combinatorics, etc) as well as some basic non-elementary ideas (simple analysis, topology, linear algebra, abstract algebra). Obviously the specific difficulty level here could be adjusted, but the change would have to be quite significant to allow for interesting and *pyramidal* questions.

I'd be interested to hear what people think is better or whether people have alternatives.

It's the difference between memorizing formulas and being exposed to books, poems, paintings, etc., that you may not have heard of, and turn out to really enjoy. So yes, in the future, you have the experience of having read The Old Man and the Sea, if you so choose. I think most people would agree that this, rather than list memorization, is top-flight quizbowl.

I challenge this. Ideally math computation should expose you to different types of math ideas that you haven't seen before, and you should learn about these by actually learning to do the problems and others like them. Personally I did well on math computation because this happened for me with MathCOUNTS in middle school, and I don't really see a reason it could not happen here.

[Ike]

I remember a tossup in the HSNCT this year that mentioned something about cyclic polynomials, and the probability that a polynomial is cyclic. I believe that questions like those need to be seen in more frequency if math comp is going to be included in the spectra of quizbowl, because 1.) its impossible to power it unless you know what cyclic entails - it does provide the definiton of cyclic just as power ends. and 2.) It provides a "step pyramid" in terms of pyramidality.

There is (I believe) a never ending, long standing argument about whether computation should be in quizbowl, but pragmatically all quizbowl comp questions can tweak in a factor like that to add "step pyramidality." At the very least I would like to see this change implemented. Another good example is that one tossup on f-stops and cameras.

The physics computational problems seem to aid those, as well as that one tossup on molarity to molality, but I'm really hoping those do count toward the computation distribution and not Science.

Another solution I would like to see implemented in NAQT is one Tu on comp and one bonus on comp. The bonus comp i thought of involves giving a team a problem, like lets say, finding the probablity that when rolling two 9 sided dice, the sum of the two numbers is a prime. Then, they have 10 seconds to answer it for 30, 15 seconds for 20, 20 seconds for 10. If they answer incorectly, the next phase of the bonus is initiated.

Again those are two pragmatic solutions I believe would assist the Computation problem.

[Sen. Estes Kefauver (D-TN)]

An acquaintance of mine from this board told me if you are right and you compromise to make a change, you still end up wrong. This is all I have to say here.

[Matt Weiner]

There's still no good argument as to why we need to go through all these contortions to include (still entirely hypothetical) "good" math calculation at all. Sorry if this is going around in circles, but..there just isn't. It doesn't need to be there, it's not quizbowl, and collegiate quizbowl and the tournaments in high school that don't use calculation are doing just fine without it. If your school is not good at quizbowl, then get better, don't recruit your math team and demand that their game be played for 1/5 of the round.