Math Computation, Round 23748234
 Mechanical Beasts
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Math Computation, Round 23748234
Mr. Barry,
I appreciate your stated position on computational math, and I sympathize that you don't have absolute control over what the coaches of GATA decide, when push comes to shove. Do you see a better future, i.e. coaches you could influence to change their minds about the appropriateness of computational math questions?
I appreciate your stated position on computational math, and I sympathize that you don't have absolute control over what the coaches of GATA decide, when push comes to shove. Do you see a better future, i.e. coaches you could influence to change their minds about the appropriateness of computational math questions?
Andrew Watkins
Re: Georgia 20092010
Andrew:
I am pretty sure GA won't be reducing or eliminating computational questions anytime soon. Computational math is too large a part of what high school kids take in their courses to make a strong argument for eliminating it or even reducing it. In the GATA question formula, math is already half of what social studies, lit, and science are.
I will say this: I have not heard quiz bowl people criticizing having computational questions in tournaments until recently. I have read the arguments here against computational math questions and I have found them weak. That is my opinion. Content of questions is more important than style. And all high school quiz bowl should start, contentwise, with what is typically taught in high schools in the US. I suppose that idea/position is one that could have its own topic string on this board.
You see, there is no consensus on math questions and there is no consensus on what exactly good quiz bowl is. I respect those that differ from me here on this topic. But, even though I personally do not like math questions (I am too lazy and do not wanna have to do anything to answer a questions!), because math is so large a part of what is taught in US high schools, math questions should, in my opinion, be included in any event that purports to be good quiz bowl as I see it.
I am pretty sure GA won't be reducing or eliminating computational questions anytime soon. Computational math is too large a part of what high school kids take in their courses to make a strong argument for eliminating it or even reducing it. In the GATA question formula, math is already half of what social studies, lit, and science are.
I will say this: I have not heard quiz bowl people criticizing having computational questions in tournaments until recently. I have read the arguments here against computational math questions and I have found them weak. That is my opinion. Content of questions is more important than style. And all high school quiz bowl should start, contentwise, with what is typically taught in high schools in the US. I suppose that idea/position is one that could have its own topic string on this board.
You see, there is no consensus on math questions and there is no consensus on what exactly good quiz bowl is. I respect those that differ from me here on this topic. But, even though I personally do not like math questions (I am too lazy and do not wanna have to do anything to answer a questions!), because math is so large a part of what is taught in US high schools, math questions should, in my opinion, be included in any event that purports to be good quiz bowl as I see it.
J.R. Barry
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Re: Georgia 20092010
Do high schools in Georgia really take class time teaching people how to do arithmetic quickly? In my understanding, every high schooler in the U.S. is supposed to be taking at least Algebra I by the time he's a freshman. Multiplying numbers is more of a thirdgrade topic, even in the worst school systems, and I'm given to understand that Gwinnett County is a very good system.jrbarry wrote:Computational math is too large a part of what high school kids take in their courses to make a strong argument for eliminating it or even reducing it. ... And all high school quiz bowl should start, contentwise, with what is typically taught in high schools in the US. ... because math is so large a part of what is taught in US high schools, math questions should, in my opinion, be included in any event that purports to be good quiz bowl as I see it.
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Re: Georgia 20092010
Moreover, what constitutes "stuff taught in high school" varies considerably depending on how many electives and AP classes are offered by said high school.
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Re: Georgia 20092010
I think the argument that high school quizbowl needs to be solidly grounded in the high school curriculum is both logical and correct; however, I would characterize board consensus as this: "There are lots of skills in the high school curriculum that are not tested by quizbowl. Computational math is easier to convert into quizbowl or a quizbowllike entity than, say, studio art or English composition. However, computation tossups are still likely to be bad quizbowl for the reasons outlined in all the other threads about this topic."
Note in particular: 1. recent arguments that typical content of computation questions in quizbowl does not accurately reflect the scope of the typical high school math curriculum and 2. there seems to be much less consensus on the place of computation in bonuses rather than tossups.
Note in particular: 1. recent arguments that typical content of computation questions in quizbowl does not accurately reflect the scope of the typical high school math curriculum and 2. there seems to be much less consensus on the place of computation in bonuses rather than tossups.
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Re: Georgia 20092010
I offer math theory tossups as a welcome alternative, then; they address WHAT the question asks (your first, and more important, criterion) at least as well as math computation (if you disagree, I'd like to see a topic better covered by a math computation tossup than a math theory tossup), and in most cases better. Moreover, it may be possible to create a truly pyramidal computational tossup, but if so, it is very, very hard, and most writers do not succeed. Since it's far easier to do that with theory questions, I'd respond to the logic of those other coaches by saying that you'll get a greater number of pyramidal questions by asking for math theory, rather than computation.
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Re: Georgia 20092010
soaringeagle22 wrote:I think computation tossups, if they are allowed to exist, sound completely stupid when written pyramidally. If there was a consensus to allow math to be a minor exception to the rule of pyramidality, than maybe they have a place.
Although, we test knowledge in Quizbowl, not skill. I once competed in a horrid tournament that, while pyramidal, still included computation, and also asked a few ballet questions. The latter would be fine, except the participants were asked to name and perform the requested ballet position. Computation is like the "performing" asked in the tournament where we had to dance for the judges (well, our team didn't know squat about ballet to begin with, so others danced) because you have to know more than just knowledge. Quizbowl isn't a test of skill. If it were, than we would all be writing novels and discovering elements instead of just answering tossups about them.
I have to say, I hate this argument being used against mathcomp. The reason asking people to perform ballet positions is stupid isn't because it's an applied skill. It's because no one knows anything about specific ballet positions unless they do ballet. This argument is used in a number of forms, e.g., writing essays, analyzing primary documents, analyzing symbolism as examples of applied skills. Those don't sound ridiculous because they're applied skills, they sound ridiculous because they would take far too long and are far too subjective. They make mathcomp in quizbowl sound more ridiculous than it actually is. I'm not urging the reinstitution of mathcomp, and I recognize the validity of other arguments against it, but I feel the constant use of this reductio ad absurdum insults the intelligence of quizbowlers.
Matt Bollinger
UVA '14, UVA '15
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Re: Georgia 20092010
Matt:
I agree that simple arithmetic computations are not what should be in high school quiz bowl. GATA primarily uses algebra, geometry, trig, and calculus calculations in our varsity State tournament. I think that is preferrable.
I agree that simple arithmetic computations are not what should be in high school quiz bowl. GATA primarily uses algebra, geometry, trig, and calculus calculations in our varsity State tournament. I think that is preferrable.
J.R. Barry
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Re: Georgia 20092010
Looking over this and the other thread, I think this still belongs here:jrbarry wrote:Matt:
I agree that simple arithmetic computations are not what should be in high school quiz bowl. GATA primarily uses algebra, geometry, trig, and calculus calculations in our varsity State tournament. I think that is preferrable.
I will start by saying I am probably better at math than most students you have encountered in school or in quizbowl. I have never failed at anything with numbers on the page, and I read textbooks on everything from analysis to number theory. With that in mind, I will say directly to you that computation has no bearing on what I (or any college professor or any GOOD high school teacher) consider being good at math. There is a weak correlation between successful calculation of a derivative at a point (something tested by the average calculus computation question) and knowledge of how the derivative defines the behavior. To test the latter directly, a tossup on "Derivative" or "Newton's Method" or "Concavity" (in increasing difficulty order) works exceedingly well. If you are responsible for a tournament that relies on such a weak correlation, you are responsible for bad quizbowl.
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Re: Georgia 20092010
Topic 1: Inscribed Shapeseveryday847 wrote:(if you disagree, I'd like to see a topic better covered by a math computation tossup than a math theory tossup)
Ignore units. Find the area of the largest circle that can be inscribed inside a rectangle that is six by ten.
ANSWER: Nine Pi (do not accept Nine)
Topic 2: Solving Equations
Find x if Susie and Janie have the same amount of money. Susie has x dimes and twenty nickels. Janie has x quarters and two nickels.
ANSWER: 6
Topic 3: The Relationship Between Angles and Circles
Find the measure of Angle BAC. Point A is at the center of a circle, and points B and C are on the circle. If lines BD and CD are both tangent to the circle, and Angle BDC has a measure of fifty degrees, what is the measure of Angle BAC?
ANSWER: 130 (degrees)
Topic 4: The relationship between Polynomial Division and Polynomial Substitution
Find the remainder when 2x cubed minus 8x squared minus 9x plus three is divided by the quantity x minus 5.
ANSWER: 8
Topic 5: Simplifying Radicals
Express your answer in simple radical form. Divide the cube root of four by the sixth root of two.
ANSWER: (Square) Root (of) 2 (Prompt 2 to the onehalf power)
Topic 6: Exponential Growth
Find the yintercept of a graph showing exponential growth that goes through the points (1,5) and (2,20).
ANSWER: 5/4 (or 1 ¼ or 1.25) (accept (0,5/4) or equivalents)
Topic 7: Unit Circle
Find all solutions in radians between zero and two pi for the equation sine x plus cosine x equals zero.
ANSWER: 3Pi/4, 7Pi/4 (any order, accept equivalents, must have both answers without
extras)
Topic 8: Nonlinear Graphs
Find the x and ycoordinates for the one point of intersection between the circle given by equation quantity x minus three squared plus quantity y minus four squared equals twentyfive and the circle given by equation quantity x minus three squared plus quantity y plus four squared equals one hundred sixtynine.
ANSWER: (3,9)
Topic 9: Absolute Value Graphs
Find both possible values of A if the graph of the equation y equals k plus A times the absolute value of the quantity x minus h contains the points (1,9), (2,5), and (3,1).
ANSWER: 4 & 4 (either order, accept answers such as plus or minus four)
Topic 10: Trig Identities
Find the value you get when you add the fraction one over the quantity one plus cotangent x to the fraction one over the quantity one plus tangent x.
ANSWER: 1
Let me know if you want more. I can give you multiclue tossups if that would make a difference. Your challenge is to show that theory questions cover the same topics better, as you claim, which is different than claiming that we can fix math by making it less than five percent of the distribution.
I apologize that the semiannual math computation thread is taking place in the middle of the Georgia thread. C'mon peoplethis state doesn't get its own board section.
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Re: Georgia 20092010
Category: Woodrow WilsonShcool wrote:Topic 1: Inscribed Shapes
Topic 2: Solving Equations
Topic 3: The Relationship Between Angles and Circles
Topic 4: The relationship between Polynomial Division and Polynomial Substitution
Topic 5: Simplifying Radicals
Topic 6: Exponential Growth
Topic 7: Unit Circle
Topic 8: Nonlinear Graphs
Topic 9: Absolute Value Graphs
Topic 10: Trig Identities
Jonah Greenthal
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Re: Georgia 20092010
Those aren't announced categories. Woodrow Wilson is a fine topic for a tossup question, as long as he's not the announced topic for a tossup question. (Note to people who haven't had the pleasure of playing on a particular Academic Hallmarks set written a few years ago: Jonah is referring to a particular Academic Hallmarks set written a few years ago.)
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Re: Georgia 20092010
But these always reduce to speed calculation as the determining factor since anybody in quizbowl knows how to set up an algebraic system of equations. That's the point herewhether the question itself involves variables or trigonometric functions or not, the skill you are actually testing to determine who gets the tossup points is how quickly people can divide 480 by 32. Being able to do that at all is the elementary school curriculum, not the high school one; being able to do it in two seconds rather than five is a parlor trick of no relevance to anything.jrbarry wrote:Matt:
I agree that simple arithmetic computations are not what should be in high school quiz bowl. GATA primarily uses algebra, geometry, trig, and calculus calculations in our varsity State tournament. I think that is preferrable.
The presence of such a large volume of questions skewing the distribution (by effectively doubling the science quota through the tumorlike expansion of the math subcategory) and introducing non or bad quizbowl elements into the GATA championships (by rewarding Clever Hans skills rather than real knowledge) is going to keep being the dominating theme when people discuss these tournaments, for obvious reasons.
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Re: Georgia 20092010
Shcool wrote:Topic 1: Inscribed Shapes
Topic 2: Solving Equations
Topic 3: The Relationship Between Angles and Circles
Topic 4: The relationship between Polynomial Division and Polynomial Substitution
Topic 5: Simplifying Radicals
Topic 6: Exponential Growth
Topic 7: Unit Circle
Topic 8: Nonlinear Graphs
Topic 9: Absolute Value Graphs
Topic 10: Trig Identities
In order to meet the challenge, you need to show that those somehow beat corresponding theory tossups, so here are some hypothetical questions to compare. I didn't write the questions because guess what? REAL pyramidal questions take time and consideration to write, whereas unpyramidal tossups on insignifica (such as your computation tossups) are easily massproduced.Shcool wrote:everyday847 wrote:(if you disagree, I'd like to see a topic better covered by a math computation tossup than a math theory tossup)
Replacement Theory Answerlines:
Topic 1:
ANSWER: Inscribed (Accept Word Forms)
ANSWER: Circle
ANSWER: Cyclic Quadrilateral
ANSWER: Ninepoint Circle
Topic 2:
ANSWER: Simultaneous Equations
ANSWER: Cramer's Rule
ANSWER: GaussJordan Elimination
Topic 3:
ANSWER: 360 Degrees (this is a commonlink question on things that notably sum to 360, probably best suited for middle school or JV)
ANSWER: Euclid's Elements
Again, ANSWER: Circle
I might do the rest later, but I just woke up. Anyway, this:
is how I will respond to you. If I must, I could write these tossups to show you that they reward actual knowledge that only students who want to learn something significant about mathematics (as it is studied in every decent high school and every college) can answer early, rather than some insignifica that a 6th grader could easily destroy a Ph.D. on (and I guarantee the kid would, since NO GRADUATE MATH STUDENT USES THIS STUFF, whereas early clues in the rest of the sciences and in history frequently come up at the undergrad and graduate level in their respective majors). I don't know why you just failed to meet the challenge, then told the challenger what his challenge was not about.Shcool wrote:Let me know if you want more. I can give you multiclue tossups if that would make a difference. Your challenge is to show that theory questions cover the same topics better, as you claim, which is different than claiming that we can fix math by making it less than five percent of the distribution.
This, however:
I will agree with.Shcool wrote:I apologize that the semiannual math computation thread is taking place in the middle of the Georgia thread. C'mon peoplethis state doesn't get its own board section.
As it does relate to this thread: Aside from the lack of foresight in basing quizbowl exclusively off curricula (I think the other thread is sufficient to show this, so I will leave that), I will warn you that the material you claim to take directly from such curricula must be what is actually significant in that subject. What I mean is, your math classes shouldn't focus on meaningless computation, so you should not and your history classes don't focus on dates, so your history tossups should not ask for them. Both sets of classes certainly cover those topics, but good teachers often announce to students that these are not the important sections of the material. High School is about gaining an understanding of these subjects, and quizbowl should reflect that understanding, not test every random thing that may or may not come from a teacher's mouth.
Cameron Orth  Freelance Writer/Moderator, PACE member
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Re: Georgia 20092010
I was good at mathcomp in high school. I was so good at mathcomp in high school that I scored 1540 points per game more than I deserved from it. My production immediately fell in college, and it took me a while to recall that I never really had that much knowledge to begin with. I knew how to do a totally insignificant, unacademic parlor trick.
Every area of quizbowl pushes students to be intellectually curious, to read about new ideas and broaden themselves. Except for computational math, which encourages students to recall the trick they learned in seventh grade for multiplying by twelve really fast. The college game tosses up angular momentum and includes clues on ClebschGordon coefficients; it doesn't ask you to calculate the latter (as any Java app can do, and, as you can see, not really using terribly advanced mathematics) for just the same reasons.
I understand the urge to make quizbowl mirror the curriculum; while I think it's not entirely misguided, I think the impression that the academic side of the topics covered in math classes is rapid computation is very misguided and defies the spirit of quizbowl.
Every area of quizbowl pushes students to be intellectually curious, to read about new ideas and broaden themselves. Except for computational math, which encourages students to recall the trick they learned in seventh grade for multiplying by twelve really fast. The college game tosses up angular momentum and includes clues on ClebschGordon coefficients; it doesn't ask you to calculate the latter (as any Java app can do, and, as you can see, not really using terribly advanced mathematics) for just the same reasons.
I understand the urge to make quizbowl mirror the curriculum; while I think it's not entirely misguided, I think the impression that the academic side of the topics covered in math classes is rapid computation is very misguided and defies the spirit of quizbowl.
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Re: Georgia 20092010
40?!? Please tell me that includes bonuses.everyday847 wrote:I was good at mathcomp in high school. I was so good at mathcomp in high school that I scored 1540 points per game more than I deserved from it. My production immediately fell in college, and it took me a while to recall that I never really had that much knowledge to begin with. I knew how to do a totally insignificant, unacademic parlor trick.
Every area of quizbowl pushes students to be intellectually curious, to read about new ideas and broaden themselves. Except for computational math, which encourages students to recall the trick they learned in seventh grade for multiplying by twelve really fast. The college game tosses up angular momentum and includes clues on ClebschGordon coefficients; it doesn't ask you to calculate the latter (as any Java app can do, and, as you can see, not really using terribly advanced mathematics) for just the same reasons.
I understand the urge to make quizbowl mirror the curriculum; while I think it's not entirely misguided, I think the impression that the academic side of the topics covered in math classes is rapid computation is very misguided and defies the spirit of quizbowl.
Matt Bollinger
UVA '14, UVA '15
Communications Officer, ACF
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Re: Georgia 20092010
Some packets in my memory contained three computational math tossups; I sometimes would go 210 on them.ColJade wrote:40?!? Please tell me that includes bonuses.
Andrew Watkins
Re: Georgia 20092010
JRBerry makes a very good point. Math is something taught at school. 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.
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Re: Georgia 20092010
One poster (whom I do not know) says I may be responsible for "bad quiz bowl." Niiiice. Since bad or good quiz bowl is simply a matter of what one prefers, I'll suggest that I have helped promote what I call good quiz bowl.
Matt: I can assure you. The dominating theme concerning GATA tournaments is not now nor has it ever been anything related to math questions.
I communicate quiz bowl coaches all over the country annually. I have either spoken live to or emai conversed with 20 different coaches just in the last 10 days. Not one has ever brought up to me that quiz bowl ought to have fewer or no computational questions. it simply isn't an issue with most coaches I communicate with. I am sure there are quiz bowl coaches who think that there should be less or no computation questions. But it is not a dominating theme among most of us out here in quiz bowl reality land.
I realize that there are many views of high school quiz bowl that differ from mine. That doesn't bother me as much as those differences seem to bother so many posters on this board.
My primary interest is making quiz bowl accessible to as many high school kids who want to pursue it as an activity as is possible.
Matt: I can assure you. The dominating theme concerning GATA tournaments is not now nor has it ever been anything related to math questions.
I communicate quiz bowl coaches all over the country annually. I have either spoken live to or emai conversed with 20 different coaches just in the last 10 days. Not one has ever brought up to me that quiz bowl ought to have fewer or no computational questions. it simply isn't an issue with most coaches I communicate with. I am sure there are quiz bowl coaches who think that there should be less or no computation questions. But it is not a dominating theme among most of us out here in quiz bowl reality land.
I realize that there are many views of high school quiz bowl that differ from mine. That doesn't bother me as much as those differences seem to bother so many posters on this board.
My primary interest is making quiz bowl accessible to as many high school kids who want to pursue it as an activity as is possible.
J.R. Barry
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Re: Georgia 20092010
I assure you that I live in "reality land" as well, and that if you've never heard anyone complain about speedarithmetic contests interrupting their quizbowl game, you desperately need to get your ears checked.
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Re: Georgia 20092010
I live in a state where 1/5 of the questions asked are Computational Math. I see the accomplishment of doing math well, and I respect it. But in the end, we live in fear of kids who can figure out a problem nearly instantly, rather than ones who are actual experts on the subject. We turn to a college student to help us in math rather than our math teachers, simply because he understands how to do math fast (our teachers probably know more math in general, but speed isn't a big deal to them) from his days on the Academic Team. Mathcomp leads to a situation where teams don't have to actually learn in depth math knowledge, they just have to learn fast math. That just seems at odds with Quizbowl's goal of furthering the knowledge of the participants.
Math theory still covers the topics we want to ask in Quizbowl, takes the skill test of doing it fast out of the game, and also rewards actual knowledge of the topic rather than just how to figure it out quickly.
Edit: rewarding the second to last sentence in the first paragraph to emphasize that they learn "in depth" versus "fast" math.
Math theory still covers the topics we want to ask in Quizbowl, takes the skill test of doing it fast out of the game, and also rewards actual knowledge of the topic rather than just how to figure it out quickly.
Edit: rewarding the second to last sentence in the first paragraph to emphasize that they learn "in depth" versus "fast" math.
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Re: Georgia 20092010
I contend that math calculation questions defy this.jrbarry wrote:My primary interest is making quiz bowl accessible to as many high school kids who want to pursue it as an activity as is possible.
Regularly in matches I have moderated and played (six HSNCTs, dozens of regular season NAQT tournaments), I hear "pencil and paper ready" and see three players per team stop paying attention, since they know that they don't have the skill that their mathcalc specialist does. And there's no reason for them to listen and try to learn something and buzz in early the next time; hearing these questions doesn't teach that skill. So they will continue to let the mathcalc specialist compete against the other team's mathcalc specialist.
In contrast, from listening to questions and remembering clues, Dallas Simons will get a science tossup every tournament or so, because he's heard the clue I've buzzed on, or an earlier one, remembered it, and improved. Not so here.
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Re: Georgia 20092010
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.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.
Charlie Dees, North Kansas City HS '08
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Re: Georgia 20092010
Frankly, we don't care if your team loses; we don't favor your team above any other. We care about the standards of quizbowl. To most people on this board, that means the elimination of mathcomp. Whether you think mathcomp is good quizbowl or not, we certainly won't change our standards of quizbowl so that one team in Georgia can win.ToXiCRAiN wrote:JRBerry makes a very good point. Math is something taught at school. 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.
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Re: Georgia 20092010
Cameron, I think you are making the same mistake that Andrew made. Namely, you are assuming that it is easy to write lots of good noncomputational math questions at the difficulty level of an average high school tournament. It is not easy to write a question with the answer Inscribed or Circle that differentiates very good students from pretty good students from decent students from dolts. It needs to not be transparent. I probably could write one on Circle; I have my doubts about Inscribed. While Cyclic Quadrilateral or Ninepoint Circle would make decent bonus part answers, they would not make good tossup answers at an average difficulty high school tournament.
Keep a few things in mind:
* There is a reason that tournaments without computational math almost always have less math than, say, chemistry. It's because the vast majority of quizbowlers don't want to write or play on lots of noncomputational math.
* There is a reason that all of those math teachers who told you that the concepts are what's really important gave you tests with lots of numbers and variable manipulations on them, which is what usually happens for about 7 out of 8 semesters of high school math.
* There is a reason that high school math competitions have a lot of numbers, though there are a few exceptions once you get close to qualifying for the USAMO.
* Even a number of math competitions run by math teachers have relays or some other competition where speed is important.
* There is a lot of disagreement among math teachers as to the extent that calculators (and which calculators) should be used on math tests and in math competitions.
Keep a few things in mind:
* There is a reason that tournaments without computational math almost always have less math than, say, chemistry. It's because the vast majority of quizbowlers don't want to write or play on lots of noncomputational math.
* There is a reason that all of those math teachers who told you that the concepts are what's really important gave you tests with lots of numbers and variable manipulations on them, which is what usually happens for about 7 out of 8 semesters of high school math.
* There is a reason that high school math competitions have a lot of numbers, though there are a few exceptions once you get close to qualifying for the USAMO.
* Even a number of math competitions run by math teachers have relays or some other competition where speed is important.
* There is a lot of disagreement among math teachers as to the extent that calculators (and which calculators) should be used on math tests and in math competitions.
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Re: Georgia 20092010
There's also a reason that math tests last more than ten seconds and allow the use of calculators, namely that being able to do arithmetic quickly is not an academic skill. I would like to see ANYONE who tests the credulity of this board by claiming they support calculation questions because it's "in the curriculum" show me where "doing thirdgradelevel calculation within ten seconds in a race against some other person" is in any high school curriculum, anywhere.Shcool wrote:* There is a reason that all of those math teachers who told you that the concepts are what's really important gave you tests with lots of numbers and variable manipulations on them, which is what usually happens for about 7 out of 8 semesters of high school math.
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Re: Georgia 20092010
I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.
David Reinstein
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Re: Math Computation, Round 23748234
What do people think of allowing calculators for math calc questions. Almost all high school math classes allow them and teach students how to use them. If it's knowing the concepts and not raw number crunching speed that's tested, this solution shouldn't change much.
Evan Adams
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Re: Georgia 20092010
Uh, this is what every calculation question is? Or do you really think that there are people in qb who don't know how to find the area not in the inscribed circle and are hung up on setting up the equations?Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.
If what you're saying is that people want calculation questions even though they are not and never can be good quizbowl, then you've figured out what I've been trying to tell you for years.
Matt Weiner
Founder of hsquizbowl.org
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Re: Math Computation, Round 23748234
That's an interesting proposal. I believe that the PAC/NTAE allowed/s them (this is just a guess based on the fact that they were allowed at Loyola's Ultima, which was supposed to mimic that format). It certainly counters one of the major arguments against computation, though not all of them. Here are my listform thoughts on it:vcuEvan wrote:What do people think of allowing calculators for math calc questions. Almost all high school math classes allow them and teach students how to use them. If it's knowing the concepts and not raw number crunching speed that's tested, this solution shouldn't change much.
 What kind of calculators? Fourfunction? Graphing? Graphing with CAS?
 On that note, supposing that graphing but not graphingplusCAS calculators are allowed, players whose courses use graphingwithCAS calculators will be at an additional disadvantage simply because they are used to a different key layout, etc. (This is similar to many people complaining about having to use a TI83 on the ACT after having used a TI89 for a few years in math class and being very slow as a result, having forgotten or never learned how to use the 83.) I recognize that this issue is somewhat comparable to having slow reflexes on the buzzer, but it still exists.
 Funding issues. Morethanfourfunction calculators are expensive, and not all math classes use them, so sometimes they would have to be bought specifically for quizbowl. (The fact that the AP Calculus curriculum requires them helps somewhat, but not all schools offer AP Calculus and not everyone takes it even if it's offered.)
 Does every player get to have one? One per team? The former possibility exacerbates the funding problem, while the latter exacerbates the problem of one player doing math and the others tuning out computation questions.
 The funding and typeofcalculator problems are jointly exacerbated by the possible issue of calculators being permitted in quizbowl that are not permitted in the players' math courses.
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Re: Georgia 20092010
Uh, no. For one thing, that's not what my question asked. For another thing, do you really think that all students could solve it in the same amount of time that it takes to calculate (6/2)^2?Matt Weiner wrote:Uh, this is what every calculation question is? Or do you really think that there are people in qb who don't know how to find the area not in the inscribed circle and are hung up on setting up the equations?Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.
David Reinstein
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Re: Math Computation, Round 23748234
I understand the reasons why math computation is desired in quiz bowl, though I have made it clear over the years, I do not like math computation as a tossup style. So that said, here are some thoughts I have had on this current discussion.
No, I don't see how math computation questions encourage more students to learn math. If there were a way to calculate the number of times math calculation questions were bageled and lead to awful TELEVISION (yeah, try a math calculation 60second round to know what I mean), it's really like watching paint dry in quiz bowl matches.
If your game format has a handout round, yes, I can see math questions go there. If you don't mind it in one part of a bonus question, I have no issues. But calculation tossups do not reward true mathematics concepts... just algorithms and cool shortcuts.
I also see that calculation questions are important, but they tend to have students lose sight of larger scientific or mathematical concepts. Yes, it's important to know how to convert between units, but as it has been pointed out, there are computer programs out there that can do that. I think it is just as important to view patterns rather than do bruteforce calculations all the time, but I'm not sure quiz bowl is the format for this.
From working with Decathlon, that format gives students opportunities to use calculators during their multichoice exams, but the best students don't need them because they should be taught proper testtaking skills (again, train to win the game). It's not like we're asking those competitors to prove things (unlike in the Math Olympiad). I don't want to go into the arms race regarding calculators, although considering the numerous state graduation exams which have calculator specs, it shouldn't be hard to come up with something.
I do think that if there were more teams that taught those "training skills" with math computation, things would be marginally better. But then we are rewarding the training of skills rather than a true appreciation of mathematics.
No, I don't see how math computation questions encourage more students to learn math. If there were a way to calculate the number of times math calculation questions were bageled and lead to awful TELEVISION (yeah, try a math calculation 60second round to know what I mean), it's really like watching paint dry in quiz bowl matches.
If your game format has a handout round, yes, I can see math questions go there. If you don't mind it in one part of a bonus question, I have no issues. But calculation tossups do not reward true mathematics concepts... just algorithms and cool shortcuts.
I also see that calculation questions are important, but they tend to have students lose sight of larger scientific or mathematical concepts. Yes, it's important to know how to convert between units, but as it has been pointed out, there are computer programs out there that can do that. I think it is just as important to view patterns rather than do bruteforce calculations all the time, but I'm not sure quiz bowl is the format for this.
From working with Decathlon, that format gives students opportunities to use calculators during their multichoice exams, but the best students don't need them because they should be taught proper testtaking skills (again, train to win the game). It's not like we're asking those competitors to prove things (unlike in the Math Olympiad). I don't want to go into the arms race regarding calculators, although considering the numerous state graduation exams which have calculator specs, it shouldn't be hard to come up with something.
I do think that if there were more teams that taught those "training skills" with math computation, things would be marginally better. But then we are rewarding the training of skills rather than a true appreciation of mathematics.
Emil Thomas Chuck, Ph.D.
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Re: Math Computation, Round 23748234
So, the biggest argument it appears for math calculation is: it's in the curriculum. We need to based both the content and the distribution of quizbowl on the curriculum.
I don't think anyone is disputing the content part.
However, a lot of people are up in arms over the distribution part. The literature distribution looks nothing like actual English classes. The science part only covers concepts encountered in science; we don't ask for lab reports or to solve freebody problems. Same with history, we don't ask kids "For 30 points, analyze how Joseph II's reforms affected the peasant class." Plenty of schools don't even teach arts or social science, and almost none of them teach philosophy. The point is that we shoehorn what fits from the curriculum into quizbowl, and augment it with things that we think are important to a wellrounded education but for whatever reason schools don't or can't (budget issues, no AP exam in the subject, students need a fourth year of math instead, etc.).
Therefore, quizbowl is not an accurate representation of a school curriculum. No matter how you try to shoehorn it, it isn't.
Another common argument is that math calculation is an applied skill that can be easily tested using the quizbowl format. I argue that that is actually an argument against math calculation.
By including math calculation, you are necessarily advantaging the kid who can multiply two numbers in his head over the kid that can analyze data or the kid who can write excellent literary criticism, because one of these applied skills is present and the others aren't, in a way that goes beyond how the distribution advantages those students. Let's say Student A reads a lot and writes great critical essays; Student B also reads a lot and isn't as good with the essays. Student A and Student B play each other, and their relative difference in criticism isn't going to affect the game; they'll probably split the questions in the long run. In this case, Student A's advantage is useless. But let's say Student C and Student D are playing; Student C understands a lot of math and can do crazy mental arithmetic, and Student D understands the same amount of math but always completes the math tests in 40 minutes instead of 15. Student C's advantage is magnified  Student C will get the questions at significantly more than the 50% split that we'd expect from two players of roughly equal comprehension. Therefore, Student C's advantage is quite useful. So while Student A's applied skill gets no additional value, Student C's applied skill does. This strikes me as unfair.
Including math calculation necessarily advantages the skill of "doing arithmetic quickly" over all other skills that are not and/or cannot be tested using the quizbowl format. In order to make it a fair playing field for all students, regardless of their skills, quizbowl necessarily needs to be a test of pure knowledge rather than applied knowledge, since a significant amount of applied knowledge (proofs, essays, performances, etc.) cannot be tested using the quizbowl format. Adding even one applied skill imbalances the distribution, because it now overvalues students with that applied skill compared to similar students with different fortes. Quizbowl provides no incentive for a literature player to work on his/her critical approach (something that might actually be useful), but it provides a huge incentive for a math player with the same relative knowledge to work on his/her arithmetic speed (something that rarely, if ever, proves useful). To me, this is a giant imbalance.
I don't think anyone is disputing the content part.
However, a lot of people are up in arms over the distribution part. The literature distribution looks nothing like actual English classes. The science part only covers concepts encountered in science; we don't ask for lab reports or to solve freebody problems. Same with history, we don't ask kids "For 30 points, analyze how Joseph II's reforms affected the peasant class." Plenty of schools don't even teach arts or social science, and almost none of them teach philosophy. The point is that we shoehorn what fits from the curriculum into quizbowl, and augment it with things that we think are important to a wellrounded education but for whatever reason schools don't or can't (budget issues, no AP exam in the subject, students need a fourth year of math instead, etc.).
Therefore, quizbowl is not an accurate representation of a school curriculum. No matter how you try to shoehorn it, it isn't.
Another common argument is that math calculation is an applied skill that can be easily tested using the quizbowl format. I argue that that is actually an argument against math calculation.
By including math calculation, you are necessarily advantaging the kid who can multiply two numbers in his head over the kid that can analyze data or the kid who can write excellent literary criticism, because one of these applied skills is present and the others aren't, in a way that goes beyond how the distribution advantages those students. Let's say Student A reads a lot and writes great critical essays; Student B also reads a lot and isn't as good with the essays. Student A and Student B play each other, and their relative difference in criticism isn't going to affect the game; they'll probably split the questions in the long run. In this case, Student A's advantage is useless. But let's say Student C and Student D are playing; Student C understands a lot of math and can do crazy mental arithmetic, and Student D understands the same amount of math but always completes the math tests in 40 minutes instead of 15. Student C's advantage is magnified  Student C will get the questions at significantly more than the 50% split that we'd expect from two players of roughly equal comprehension. Therefore, Student C's advantage is quite useful. So while Student A's applied skill gets no additional value, Student C's applied skill does. This strikes me as unfair.
Including math calculation necessarily advantages the skill of "doing arithmetic quickly" over all other skills that are not and/or cannot be tested using the quizbowl format. In order to make it a fair playing field for all students, regardless of their skills, quizbowl necessarily needs to be a test of pure knowledge rather than applied knowledge, since a significant amount of applied knowledge (proofs, essays, performances, etc.) cannot be tested using the quizbowl format. Adding even one applied skill imbalances the distribution, because it now overvalues students with that applied skill compared to similar students with different fortes. Quizbowl provides no incentive for a literature player to work on his/her critical approach (something that might actually be useful), but it provides a huge incentive for a math player with the same relative knowledge to work on his/her arithmetic speed (something that rarely, if ever, proves useful). To me, this is a giant imbalance.
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Re: Georgia 20092010
Eh, probably not, but the one kid on each team that can do math calculations the fastest typically does, in my personal experience. Certainly after a year of quizbowl when you realize that there are on the order of thirty different problems you're ever asked to solve...Shcool wrote:Uh, no. For one thing, that's not what my question asked. For another thing, do you really think that all students could solve it in the same amount of time that it takes to calculate (6/2)^2?
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Re: Georgia 20092010
Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.
IS 79 wrote:24. Pencil and paper ready. Nate's fruit stand has 123 apples, 456 oranges, and 789 pears. The total number of fruits is just the sum of those numbers, an exercise in addition that requires carrying the 1 into both the tens place and the hundreds place. Alternatively, one could multiply 456 by three, since there are on average 456 of each type. (*) For 10 points—Nate has how many total fruits?
Harry White
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Re: Math Computation, Round 23748234
Oh yeah, I'm in precalc on a team where everyone else is pretty much doing math at Penn State, and I powered the hell out of that question
Graham Moyer
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Re: Georgia 20092010
That's Numberwang! I could bruteforce that question before the nonelementaryschool clue was read.hwhite wrote:Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.IS 79 wrote:24. Pencil and paper ready. Nate's fruit stand has 123 apples, 456 oranges, and 789 pears. The total number of fruits is just the sum of those numbers, an exercise in addition that requires carrying the 1 into both the tens place and the hundreds place. Alternatively, one could multiply 456 by three, since there are on average 456 of each type. (*) For 10 points—Nate has how many total fruits?
Maybe a tossup on "mean" would have been better?
Greg (Vanderbilt 2012, Wheaton North 2008)
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Re: Math Computation, Round 23748234
Please tell me that this tossup didn't actually happen. Please tell me this is some sort of joke. Please?rjaguar3 wrote:That's Numberwang! I could bruteforce that question before the nonelementaryschool clue was read.hwhite wrote:Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.IS 79 wrote:24. Pencil and paper ready. Nate's fruit stand has 123 apples, 456 oranges, and 789 pears. The total number of fruits is just the sum of those numbers, an exercise in addition that requires carrying the 1 into both the tens place and the hundreds place. Alternatively, one could multiply 456 by three, since there are on average 456 of each type. (*) For 10 points—Nate has how many total fruits?
Maybe a tossup on "mean" would have been better?
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Re: Math Computation, Round 23748234
Apparently, I made this post too long. In an effort to reduce the size, I have split it up into two parts: Antimath, and Promath and Conclusions.
I've decided to revisit the issue of math computation again, from the perspective of a math major who only made his high school varsity team as a sophomore because of his MathComp skill, and from that of a mediocre question writer.
I believe it would useful to examine the basic premises of the various arguments held by each side. Although these premises may have been stated elsewhere, I want to derive them from the arguments of each side for the benefit of this post. Therefore, I will attempt to list all the arguments each side uses*.
For the antimath comp side, I will primarily use the reasoning listed at HSAPQ.
AntiMath Computation:
1. It is not possible to write math calculation tossups in a pyramidal style.** This one is easy! Good quizbowl questions should be pyramidal. Obviously, it is not pyramidality for its own sake – rather, to ensure as much as possible that a more knowledgeable person is rewarded over a less knowledgeable person. As someone (I think I know who, but I don’t want to put words in mouths) once said, you can have deeper knowledge of Historical/Literary/Scientific Topic X, but you can’t have deeper knowledge of 4 * Pi.
2. Math Calculation tossups are fundamentally unlike all other quizbowl. "Quizbowl is about recall of factual and conceptual knowledge. It is not about applied skills."
3. Math Calculation tossups do not educate. If players do not know the answer on a nonmathcomp question, they can learn something useful from it. This "learning" aspect of the game is, to some, the most important part of the game. Most mathcomp questions don't do this (and if they do, the question probably is going well out of its way to do so).
4. Math is covered in other questions. This statement reinforces the above points – mathcomp is okay in bonuses because there aren't pyramidality concerns, and math theory is better because it is more educational.
5. The canon of askable math calculation is too small. This doesn’t really directly involve the basic premises. It is instead a practical concern – there are too few ways to write unique math computation questions that can be answered in a reasonable amount of time.
6. Math is adequately covered in other competitions. This is, IMO, a stupid point. I think at some point someone tired of giving logical reasons and decided that "If you don’t like our way, you have other places you can go" was an acceptable form of argumentation.
Additionally, I'd like to add a few additional points. First, the Sorice Argument:
7. Any computation that can be done by 80% of the field in less than ten seconds is likely to be unoriginal and/or trivial. This underlying assumption here is that a good question must not be trivial. This is among the stated reasons for the illegitimacy of the NAC.
Next, the Wynne Argument
8. On a math computation question, a person can apply the correct concept but still get the question wrong. This goes along with rewarding knowledge – if a person knows how to solve the problem, but in their haste miscalculates, they are penalized.
In summary, a person who is against math computation tossups believes:
A. The point of quizbowl is to further the education of the students by exposing them to new concepts, or to new information about familiar concepts. This should be the highest priority.
B. Quizbowl should strive in all aspects to reward someone with deeper knowledge of the subject. This includes refraining from practices which penalize deeper knowledge.
C. The area that quizbowl tests should be factual and conceptual knowledge, not applied skills.
D. Quizbowl questions should be asked about nontrivial things.
It should be noted that those in favor of math computation bonuses must necessarily lessen the importance of point A, since it was established above that math computation lacks that learning aspect described in point A. The necessity of waiving point C is, however, debatable.
Edit: Fixed Links
I've decided to revisit the issue of math computation again, from the perspective of a math major who only made his high school varsity team as a sophomore because of his MathComp skill, and from that of a mediocre question writer.
I believe it would useful to examine the basic premises of the various arguments held by each side. Although these premises may have been stated elsewhere, I want to derive them from the arguments of each side for the benefit of this post. Therefore, I will attempt to list all the arguments each side uses*.
For the antimath comp side, I will primarily use the reasoning listed at HSAPQ.
AntiMath Computation:
1. It is not possible to write math calculation tossups in a pyramidal style.** This one is easy! Good quizbowl questions should be pyramidal. Obviously, it is not pyramidality for its own sake – rather, to ensure as much as possible that a more knowledgeable person is rewarded over a less knowledgeable person. As someone (I think I know who, but I don’t want to put words in mouths) once said, you can have deeper knowledge of Historical/Literary/Scientific Topic X, but you can’t have deeper knowledge of 4 * Pi.
2. Math Calculation tossups are fundamentally unlike all other quizbowl. "Quizbowl is about recall of factual and conceptual knowledge. It is not about applied skills."
3. Math Calculation tossups do not educate. If players do not know the answer on a nonmathcomp question, they can learn something useful from it. This "learning" aspect of the game is, to some, the most important part of the game. Most mathcomp questions don't do this (and if they do, the question probably is going well out of its way to do so).
4. Math is covered in other questions. This statement reinforces the above points – mathcomp is okay in bonuses because there aren't pyramidality concerns, and math theory is better because it is more educational.
5. The canon of askable math calculation is too small. This doesn’t really directly involve the basic premises. It is instead a practical concern – there are too few ways to write unique math computation questions that can be answered in a reasonable amount of time.
6. Math is adequately covered in other competitions. This is, IMO, a stupid point. I think at some point someone tired of giving logical reasons and decided that "If you don’t like our way, you have other places you can go" was an acceptable form of argumentation.
Additionally, I'd like to add a few additional points. First, the Sorice Argument:
7. Any computation that can be done by 80% of the field in less than ten seconds is likely to be unoriginal and/or trivial. This underlying assumption here is that a good question must not be trivial. This is among the stated reasons for the illegitimacy of the NAC.
Next, the Wynne Argument
8. On a math computation question, a person can apply the correct concept but still get the question wrong. This goes along with rewarding knowledge – if a person knows how to solve the problem, but in their haste miscalculates, they are penalized.
In summary, a person who is against math computation tossups believes:
A. The point of quizbowl is to further the education of the students by exposing them to new concepts, or to new information about familiar concepts. This should be the highest priority.
B. Quizbowl should strive in all aspects to reward someone with deeper knowledge of the subject. This includes refraining from practices which penalize deeper knowledge.
C. The area that quizbowl tests should be factual and conceptual knowledge, not applied skills.
D. Quizbowl questions should be asked about nontrivial things.
It should be noted that those in favor of math computation bonuses must necessarily lessen the importance of point A, since it was established above that math computation lacks that learning aspect described in point A. The necessity of waiving point C is, however, debatable.
Edit: Fixed Links
Last edited by evilmonkey on Thu Jun 18, 2009 10:24 am, edited 2 times in total.
Bryce Durgin
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Re: Math Computation, Round 23748234
Summarizing the promathcomp arguments is slightly more difficult. This is because proponents of math computation have, in general, not spent an adequate amount of time reasoning out and developing their defense. This may be because they so no reason for removing that facet of the game, or because they are working and don't have the time, or because they are young and speak what first comes to mind without thinking it through. This leads those arguing the case to use faulty arguments alongside major points, primarily (I believe) in an attempt to make their argument seem more overwhelming than it is. Since they are easily dealt with, however, the faulty arguments become the primary target, derailing the thread from argumentation of more fundamental points. Therefore, part of my job here will be to separate the wheat from the chaff. I dug through the past few mathcomputation threads to be as inclusive as possible – if I missed something, feel free to mention it.
1. High school quizbowl should reflect, at minimum, the academic part of the high school curriculum . Note the word academic that I placed in this most prominent argument of the promath comp side – I don’t believe anyone (other than a limited number of people in Illinois), truly believe that driver's ed belongs in quizbowl. I believe we just had a thread started about this very point, and I believe that people are agreeing that while the average high school curriculum forms the basis of the canon, it in no way comprises the entire high school canon. Andy made the point earlier that in this case, math theory should acceptably replace math computation. The counter to that is point 1A.
1A. High schools, in general, teach computational math, not theoretical math. I personally wish this were not the case, as mere computational math does little to prepare a student for a math major. But this is the case, since if high school math was theoretical math then you’d have an even higher percentage of students failing.
2. Math computation makes quizbowl accessible to more students. This really doesn't add anything to the argument. This statement reflects the following position, one that I believe most quizbowlers would agree with: "Quizbowl should be as inclusive as it can be, without compromising some certain basic principles that we understand to be part of quizbowl". However, the argument from the other side is that math computation violates those principles, and that theoretical mathematics does not.
2A. Theoretical math doesn't get answered, and therefore does not make quizbowl more accessible. Well… it doesn't, mostly because most people are unaware of the true nature of math. However, I would argue that if we expect a student to be intellectually curious about social science, or fine arts, or literature, we should expect them to be curious enough to test the basics of theoretical math.
3. Computational math can be written pyramidally. Probably the most debated point. If you want to see the main part of this argument, go to this thread
4. It is easier to write a math computation tossup than a math theory tossup. This argument is of lesser concern than the good of the game. However, the next point may elaborate some on this.
5. The askable high school theoretical math canon is as small as the computational math canon. This is a practical concern considerably more pressing than the previous point. I have to say that it is difficult to write a lot of math theory tossups at the high school level in a pyramidal style – because of the way mathematics is structured, questions tend to be either fairly opaque or highly transparent. I mean, I've written good math tossups before, but they are far and few between. Additionally the precise nature of mathematics makes it so repeating phrases word for word is unavoidable – I remember hearing a tossup on "Schwartz" somewhere, and briefly believing someone had plagiarized a tossup I had written before remembering that there was no other possible way to phrase the clues that the questions shared – and if both questions were exactly pyramidal, then those same clues might well in the same order. Therefore, two ideal questions on the same mathematical concept will contain a lot of wordforword overlap.
So, in summary, these are what I believe the main points of the promathcomp side are:
A. Math is an academic part of the high school curriculum, so it should be tested in quizbowl.
B1. Computational math does not violate the basic principles of quizbowl
B2. The negatives associated with computational math are outweighed by the net gain in people that it attracts to quizbowl.
C. Theoretical math tossups are not better than computational math tossups.
Again, if you feel I neglected a point entirely, or if I didn’t characterize a statement properly, it was not intended as a slight.
While making this list, I came to a startling conclusion. One side alleges that it is too difficult to write enough different, nontrivial mathcomp questions that are answerable. The other side alleges that it is too difficult to write enough different, non trivial math theory questions that are answerable. While math has a right to be in quizbowl due to its academic, conceptual nature, on account of the small size of the high school math canon, the amount of math questions should be substantially reduced in high school quizbowl. I would recommend no more than one math question a round, be it a math theory tossup or bonus, or a math computation bonus. Perhaps to allow for more math, we could do something strange, like 1/1 math theory every three rounds, and 0/2 math comp over those same three rounds, with no more than one question of each type in a round. However, due to concern regarding pyramidality and nontriviality of math computations tossups, I cannot in good faith support math computation tossups.
How do I respond to the argument that reduction of math will reduce the number of people in quizbowl? Simple – I don’t have a good argument.
* This doesn't include stupid arguments, like "People who want computational math are inherently looking to benefit their own team" or "People who don’t want computational math hate math". While there are certainly people who fit each category, it is a logical fallacy to assume that all people think that way.
** I want to clarify this statement for my own purposes. While Mr. Riley has shown in the past that this statement is not exactly true to the extent that it is possible to write math calculation tossups that contain clues of varying degrees of difficulty, the number of discrete places where it is possible to buzz on account of new information (rather than simply lag time due to calculation speed) in a math calculation tossup is limited to three or four, which is not sufficient to differentiate between different levels of teams.
1. High school quizbowl should reflect, at minimum, the academic part of the high school curriculum . Note the word academic that I placed in this most prominent argument of the promath comp side – I don’t believe anyone (other than a limited number of people in Illinois), truly believe that driver's ed belongs in quizbowl. I believe we just had a thread started about this very point, and I believe that people are agreeing that while the average high school curriculum forms the basis of the canon, it in no way comprises the entire high school canon. Andy made the point earlier that in this case, math theory should acceptably replace math computation. The counter to that is point 1A.
1A. High schools, in general, teach computational math, not theoretical math. I personally wish this were not the case, as mere computational math does little to prepare a student for a math major. But this is the case, since if high school math was theoretical math then you’d have an even higher percentage of students failing.
2. Math computation makes quizbowl accessible to more students. This really doesn't add anything to the argument. This statement reflects the following position, one that I believe most quizbowlers would agree with: "Quizbowl should be as inclusive as it can be, without compromising some certain basic principles that we understand to be part of quizbowl". However, the argument from the other side is that math computation violates those principles, and that theoretical mathematics does not.
2A. Theoretical math doesn't get answered, and therefore does not make quizbowl more accessible. Well… it doesn't, mostly because most people are unaware of the true nature of math. However, I would argue that if we expect a student to be intellectually curious about social science, or fine arts, or literature, we should expect them to be curious enough to test the basics of theoretical math.
3. Computational math can be written pyramidally. Probably the most debated point. If you want to see the main part of this argument, go to this thread
4. It is easier to write a math computation tossup than a math theory tossup. This argument is of lesser concern than the good of the game. However, the next point may elaborate some on this.
5. The askable high school theoretical math canon is as small as the computational math canon. This is a practical concern considerably more pressing than the previous point. I have to say that it is difficult to write a lot of math theory tossups at the high school level in a pyramidal style – because of the way mathematics is structured, questions tend to be either fairly opaque or highly transparent. I mean, I've written good math tossups before, but they are far and few between. Additionally the precise nature of mathematics makes it so repeating phrases word for word is unavoidable – I remember hearing a tossup on "Schwartz" somewhere, and briefly believing someone had plagiarized a tossup I had written before remembering that there was no other possible way to phrase the clues that the questions shared – and if both questions were exactly pyramidal, then those same clues might well in the same order. Therefore, two ideal questions on the same mathematical concept will contain a lot of wordforword overlap.
So, in summary, these are what I believe the main points of the promathcomp side are:
A. Math is an academic part of the high school curriculum, so it should be tested in quizbowl.
B1. Computational math does not violate the basic principles of quizbowl
B2. The negatives associated with computational math are outweighed by the net gain in people that it attracts to quizbowl.
C. Theoretical math tossups are not better than computational math tossups.
Again, if you feel I neglected a point entirely, or if I didn’t characterize a statement properly, it was not intended as a slight.
While making this list, I came to a startling conclusion. One side alleges that it is too difficult to write enough different, nontrivial mathcomp questions that are answerable. The other side alleges that it is too difficult to write enough different, non trivial math theory questions that are answerable. While math has a right to be in quizbowl due to its academic, conceptual nature, on account of the small size of the high school math canon, the amount of math questions should be substantially reduced in high school quizbowl. I would recommend no more than one math question a round, be it a math theory tossup or bonus, or a math computation bonus. Perhaps to allow for more math, we could do something strange, like 1/1 math theory every three rounds, and 0/2 math comp over those same three rounds, with no more than one question of each type in a round. However, due to concern regarding pyramidality and nontriviality of math computations tossups, I cannot in good faith support math computation tossups.
How do I respond to the argument that reduction of math will reduce the number of people in quizbowl? Simple – I don’t have a good argument.
* This doesn't include stupid arguments, like "People who want computational math are inherently looking to benefit their own team" or "People who don’t want computational math hate math". While there are certainly people who fit each category, it is a logical fallacy to assume that all people think that way.
** I want to clarify this statement for my own purposes. While Mr. Riley has shown in the past that this statement is not exactly true to the extent that it is possible to write math calculation tossups that contain clues of varying degrees of difficulty, the number of discrete places where it is possible to buzz on account of new information (rather than simply lag time due to calculation speed) in a math calculation tossup is limited to three or four, which is not sufficient to differentiate between different levels of teams.
Last edited by evilmonkey on Thu Jun 18, 2009 10:28 am, edited 1 time in total.
Bryce Durgin
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Re: Georgia 20092010
Thanks, Bryce. However, I promise you that whatever flaws exist in my arguments are not there because I am young.
To answer this honorably, I need to show a case of math teachers rewarding students for doing third grade math quickly. ARML is a highly respected math competition, and with good reason. One of the events at ARML is a Relay. The Relay involves three students solving problems separately. The second student needs the answer from the first student to complete the second problem, and the third student needs the answer from the second student to complete the third problem. ARML does not allow any calculators. Speed is very important, since teams get five points for all correct answers submitted within three minutes, three points for all correct answers submitted within six minutes, and no points for anything after that.
Here is the first relay from the 2009 ARML:
None of this proves anything in the long run, of course. ARML should allow calculators and probably should rethink whether or not relays are a good thing, and NAQT shouldn't ask questions that involve simple addition and whose "shortcuts" take as long as brute force. If there were a few people interested, there could be a thread on the difference between good computational questions and bad ones, but that doesn't seem to be the case here.
To answer this honestly, it's a bad question.hwhite wrote:Shcool wrote:I'll do that when you show me somebody on this board claiming that doing thirdgradelevel calculation within ten seconds in a race against some other person is good quizbowl.IS 79 wrote:24. Pencil and paper ready. Nate's fruit stand has 123 apples, 456 oranges, and 789 pears. The total number of fruits is just the sum of those numbers, an exercise in addition that requires carrying the 1 into both the tens place and the hundreds place. Alternatively, one could multiply 456 by three, since there are on average 456 of each type. (*) For 10 points—Nate has how many total fruits?
To answer this honorably, I need to show a case of math teachers rewarding students for doing third grade math quickly. ARML is a highly respected math competition, and with good reason. One of the events at ARML is a Relay. The Relay involves three students solving problems separately. The second student needs the answer from the first student to complete the second problem, and the third student needs the answer from the second student to complete the third problem. ARML does not allow any calculators. Speed is very important, since teams get five points for all correct answers submitted within three minutes, three points for all correct answers submitted within six minutes, and no points for anything after that.
Here is the first relay from the 2009 ARML:
Obviously, these questions are not at the third grade level. However, the last step of the last problem, which probably gets done during a major time crunch without a calculator, is to add 99000+9900+990. By the rules of the competition, which is highly respected by math teachers and math students, a significant number of points are on the line based on quickly and accurately adding those numbers. I would humbly submit that the mathematics involved in adding 99000+9900+990 is at the same level as the mathematics involved in adding 123+456+789.Relay 11 A rectangular box has dimensions 8 x 10 x 12. Compute the fraction of the box's volume that is not
within 1 unit of any of the box's faces.
Relay 12 Let T = TNYWR. Compute the largest real solution x to (log x)^2 times log(square root(x)) = T.
Relay 13 Let T = TNYWR. Kay has T + 1 different colors of fingernail polish. Compute the number of ways that Kay can paint the fingernails on her left hand by using at least three colors and such that no two consecutive fingernails have the same color.
None of this proves anything in the long run, of course. ARML should allow calculators and probably should rethink whether or not relays are a good thing, and NAQT shouldn't ask questions that involve simple addition and whose "shortcuts" take as long as brute force. If there were a few people interested, there could be a thread on the difference between good computational questions and bad ones, but that doesn't seem to be the case here.
David Reinstein
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Re: Math Computation, Round 23748234
And why is it so totally unreasonable that ARML and quizbowl can continue to be two different things, testing different kinds of knowledge in two different ways?
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Re: Math Computation, Round 23748234
There's a lot of nonqb competitions that seem to have absolutely no selfexamination process and become stagnant sideshows as a result. I think spelling bees and Academic Decathlon are pretty useless events that reward all the wrong things, for some immediate examples. I don't know enough about ARML to say whether it's in the same category, but if it really is married to something as dumb as adding numbers quickly, then my suspicions are raised.
It's certainly weird to be told, on the one hand, that other competitions have no relevance to quizbowl and people shouldn't bring up the fact that pretty much all other interscholastic academic events are math/science focused and there's only one place left where wellrounded intellectual curiosity is rewarded...and then told that we have to do things the way ARML does.
It's certainly weird to be told, on the one hand, that other competitions have no relevance to quizbowl and people shouldn't bring up the fact that pretty much all other interscholastic academic events are math/science focused and there's only one place left where wellrounded intellectual curiosity is rewarded...and then told that we have to do things the way ARML does.
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Re: Math Computation, Round 23748234
For what it's worth, this isn't a fair characterization of ARML; as is plain from above, the actual addition you have to do in that last step is trivial as anything. (if you can't add 9 to 0 and get 9, you aren't good at any kind of math, computational or not.) But ARML's legitimacy is completely separate from the more important point that I believe we both phrased differently: why should ARML be a model for quizbowl?Matt Weiner wrote:I don't know enough about ARML to say whether it's in the same category, but if it really is married to something as dumb as adding numbers quickly, then my suspicions are raised.
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Re: Math Computation, Round 23748234
I am not telling you that you have to do things a certain way or that ARML should be the model that quizbowl should follow. I was just providing an example in reaction to the NAQT example showing that a competition run by math educators can make the same mistake that NAQT made in terms of one particularly bad question and can use somewhat similar rules to NAQT, GATA, and IHSA in terms of believing that students who can solve certain problems quicker than other students deserve to be rewarded.
As I said one or two computational math threads ago, I have a lot of respect for collegiate quizbowl, PACE, and HSAPQ, which is one reason I do not threadjack every discussion involving them to insist that they add computational math. They do well without it.
On the other hand, most discussions involving high school NAQT questions, and now this one that started out as a discussion of Georgia 200910, involve lots of people stating that a distribution that approximates 7% computational math in NAQT's case and 12% computational math in Georgia's case is bad quizbowl that needs to be changed immediately to have any legitimacy. It's considered a settled issue because discussions on this board have tilted that way despite the fact that discussions between coaches in several states have tilted the other way.
As Bryce pointed out above, there are arguments on both sides. As some people pointed out in the curriculum thread, the relationship between quizbowl distribution and high school curricula is a complex one. Even though nobody is saying that the quizbowl distribution has to be an exact replica of high school curricula, I don't think anybody is taking the opposite argument either that the quizbowl distribution should be completely independent of high school curricula. Some people in quizbowl, including me, believe that including computational questions makes quizbowl do a better job of approximating curricula and rewards students who have a better understanding of math. I also believe that students learn from computational questions.
As I said one or two computational math threads ago, I have a lot of respect for collegiate quizbowl, PACE, and HSAPQ, which is one reason I do not threadjack every discussion involving them to insist that they add computational math. They do well without it.
On the other hand, most discussions involving high school NAQT questions, and now this one that started out as a discussion of Georgia 200910, involve lots of people stating that a distribution that approximates 7% computational math in NAQT's case and 12% computational math in Georgia's case is bad quizbowl that needs to be changed immediately to have any legitimacy. It's considered a settled issue because discussions on this board have tilted that way despite the fact that discussions between coaches in several states have tilted the other way.
As Bryce pointed out above, there are arguments on both sides. As some people pointed out in the curriculum thread, the relationship between quizbowl distribution and high school curricula is a complex one. Even though nobody is saying that the quizbowl distribution has to be an exact replica of high school curricula, I don't think anybody is taking the opposite argument either that the quizbowl distribution should be completely independent of high school curricula. Some people in quizbowl, including me, believe that including computational questions makes quizbowl do a better job of approximating curricula and rewards students who have a better understanding of math. I also believe that students learn from computational questions.
David Reinstein
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PACE VP of Outreach, Head Writer and Editor for Scobol Solo and Masonics (Illinois), TD for New Trier Scobol Solo and New Trier Varsity, Writer for NAQT (20112017), IHSSBCA Board Member, IHSSBCA Chair (20042014), PACE Member, PACE President (20162018), New Trier Coach (19942011)
Re: Math Computation, Round 23748234
Personally, I believe that it is possible to have math questions be pyramidal in a different way. If I were to give someone a question asking for the sum of the roots of x^4+2x^3186767x^2+5763x+8675309, Joe the Plumber back there might scratch his head and proceed to use rational root theorem or something like that; but Terrence Tao sitting would immediately know to use Vieta's Formulas and find out that it's 2. Also, you could have math problems like the log3=a, log4=b, and log5=c find log2.4 in terms of a, b, and c which tests knowledge of logs and the art of clever factoring. Not all problems have to boil down to speed math.
Also, I think that there's a flawed argument that math should reflect the curriculum of high school math. Just as the books covered shouldn't necessarily be ones that are in your AP Lit class and the music covered shouldn't necessarily be the ones on your iPod, the math covered should not necessarily be the stuff covered in the Barron's Guide to the AP Calculus BC test. Math comp and math theory should be open to anyone who likes math. You could test very cool theorems and identities outside the core of math knowledge in high school that can be done without too much speed third grade math. For instance, things I would like to see in quizbowl: Sophie Germaine's Identity, Shoelace Theorem, Newton's Sums.
Also also, I may have misunderstood, but I think there was an argument somewhere that it wasn't much fun watching kids do math. It might not be fun, but quizbowl isn't much of a spectator sport in the first place. Also, I thought there was a big consensus that quizbowl was for the players not the spectators.
Also, I think that there's a flawed argument that math should reflect the curriculum of high school math. Just as the books covered shouldn't necessarily be ones that are in your AP Lit class and the music covered shouldn't necessarily be the ones on your iPod, the math covered should not necessarily be the stuff covered in the Barron's Guide to the AP Calculus BC test. Math comp and math theory should be open to anyone who likes math. You could test very cool theorems and identities outside the core of math knowledge in high school that can be done without too much speed third grade math. For instance, things I would like to see in quizbowl: Sophie Germaine's Identity, Shoelace Theorem, Newton's Sums.
Also also, I may have misunderstood, but I think there was an argument somewhere that it wasn't much fun watching kids do math. It might not be fun, but quizbowl isn't much of a spectator sport in the first place. Also, I thought there was a big consensus that quizbowl was for the players not the spectators.
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Re: Math Computation, Round 23748234
This still sidesteps the issue everyone else has brought up, which is that quizbowl tests practical, not applied, knowledge; why should comp math be acceptable? You learn analytical skills in English, but we don't test those. And so on. Also, all the anecdotal evidence is there that it has nothing to do with better understanding of math, but comes down to shortcuts and speed. I'm puzzled as to how you can keep asserting that this is not true, when everyone else says, from experience, that it is.Shcool wrote:Some people in quizbowl, including me, believe that including computational questions makes quizbowl do a better job of approximating curricula and rewards students who have a better understanding of math.
This is a statement sorely wanting a valid defense.I also believe that students learn from computational questions.
I think this kind of reflects the problems with comp math in quizbowl as is. I've looked up the things you mentioned, and none of them seem to be at all useful for any real math, just for contrived (and I say that respectfully; creating math problems in such a way is quite an art) contest math. If we could extend quizbowl math beyond the high school curriculum, I'd much rather see it go the way of linear algebra than math team.kldaace wrote:You could test very cool theorems and identities outside the core of math knowledge in high school that can be done without too much speed third grade math. For instance, things I would like to see in quizbowl: Sophie Germaine's Identity, Shoelace Theorem, Newton's Sums.
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Re: Math Computation, Round 23748234
Moreover, quizbowl questions are meant to be converted. If you give a set of vertices for any case where you'd have to use (or be sped up meaningfully by) the Shoelace theorem), thus testing knowledge of it or whatever, then no one will be able to solve it except using that formula. 1% of quizbowl will know it the first year, and that will barely increase among anyone but the elite teams who study the canon a lot. 1% of quizbowl will know it the first year, so either you have a tossup that goes dead or you explain what it is, and now you don't have to know anything except how to multiply three by four and subtract...Sir Thopas wrote:I think this kind of reflects the problems with comp math in quizbowl as is. I've looked up the things you mentioned, and none of them seem to be at all useful for any real math, just for contrived (and I say that respectfully; creating math problems in such a way is quite an art) contest math. If we could extend quizbowl math beyond the high school curriculum, I'd much rather see it go the way of linear algebra than math team.
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Re: Math Computation, Round 23748234
I think the conversion argument is what drives home Matt's point about how computation has turned into mostly 4th grade parlor tricks. If we were to ask about all these socalled interesting and more rigorous computations in 15 seconds, we would see computation, which already in my experience has fairly low conversion, fall off the charts to become totally useless in most games. The reason why if you are going to have calculation you are also going to have to ask on insultingly easy topics is because of the fact that that is the only way to get a good enough conversion rate on those questions to justify keeping them when you look back at what tossups are scored at your average tournament. Most people have a combination of not being naturally fast enough at computation combined with a tendency to make mistakes in such a short timeframe that if all the math, not just 1 of 4 tossups, moved up a few gradelevels it would probably be the undeniable deathknell for that style of question in any circuit.
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Re: Math Computation, Round 23748234
Yes, bad nonquizbowl questions that reward skills of no relevance to intellectual achievement compromise the legitimacy of any quizbowl tournament they are in. Yes, people are going to keep talking about how to improve quizbowl on the quizbowl board. Yes, you should reconsider whether complaining about people doing that is a good idea.Shcool wrote:On the other hand, most discussions involving high school NAQT questions, and now this one that started out as a discussion of Georgia 200910, involve lots of people stating that a distribution that approximates 7% computational math in NAQT's case and 12% computational math in Georgia's case is bad quizbowl that needs to be changed immediately to have any legitimacy.
In addition to the fact that more than 1 in every 10 tossups in the GATA tournament is nonsense, there is also a distributional skew going on between good and bad tournamentsin normal quizbowl, math is a portion of the science distribution, and science is about 20% of what is asked. By cutting math and replacing it with calculation as an additional category, the combined science + calculation distribution is now well over 30%. You end up with a situation like the IHSA tournament where, after you add up the real science questions, the stupid calculation questions, the trash/driver's ed/other nonsense, the questions on things like "vocabulary" and so on, legitimate humanities categories comprise less than 50% of the match all together, and you can basically be the "state champion" by knowing one real category and getting lucky on the stuff that no quizbowl team can prepare for. At good tournaments you can't hope to win by just running science or history or literature or arts; you have to be at least able to compete with the other top teams on nearly all categories.
I have always respected the value of science both in the larger world and in quizbowl, and I've strongly supported making science questions as real as possible (by eliminating "he graduated from college in 1862! answer: Louis Pasteur" type questions in favor of a real science question on, say, rabies or the immune system, among other methods that good science writers use). So I hope no one thinks I have something against science when I say that I am a little irked that nearly all extracurricular academic competitions in high schools are focused on science, math, or calculation. The humanities are important too, and good quizbowl is perhaps the only place where you need to actually know both real science and real humanities topics to succeed. The idea that we should have both a 20% science distribution and a 12 to 20% calculation distribution, in tournaments that have nearly no real history, arts, literature, R/M/P, or social science questions anyway, is basically saying that we should give up on that hardwon balance and just have another clone of Science Bowl (with all the terrible questions and humanitiesfree distribution that implies). I'm not going to stand for that and I don't think any other good quizbowl supporter would either.
Matt Weiner
Founder of hsquizbowl.org
Founder of hsquizbowl.org