Pyramidality, Math calculation, and the Goldfish Tournament

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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by dschafer » Fri Nov 21, 2008 8:55 pm

Captain Scipio wrote:I don't think your post, Dan, quite gets everything right. I know we write 1/1 math for pretty much every ACF packet ("Other Science" being under our control) and it's not especially uncommon to see that level in the edited product. Also, the MOP topics given seem to cover only Euclidian plane geometry and rudimentary number theory. The askable math topics are much, much broader than that, even at the high school-level (including things like the entirety of calculus and statistics, for example.) So, while some of those topics are beyond what's askable, even in lower-level college tournament, there are whole swathes of other math theory that are askable (and are asked!)

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Is 1/1 math okay for a submitted ACF packet? My reading of http://acf-quizbowl.com/documents/packe ... stribution has been that submitted packets should contain 1 math question total, but if 1/1 math is okay, that would be excellent.

I absolutely agree that there is a lot of interesting areas that are asked in the math theory canon; I would just love to see it grow even broader!
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Captain Sinico » Fri Nov 21, 2008 10:28 pm

Huh; I guess that does seem to imply no more than 1/1 math. I'm a big proponent of 1/1 math, so maybe we'll bring that up at the next ACF cabal convocation. Sorry for not knowing rules I signed off on!

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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by jbarnes112358 » Sun Nov 23, 2008 10:33 pm

rjaguar3 wrote: I have enjoyed college-level quizbowl math. Unfortunately, in Illinois, it would be unacceptable because it would go dead in every single room.
I believe that if people start putting more non-computational math questions in tournaments, players will start learning math topics, even some that don't necessarily come up in high school math classes. People learn all sorts of things for quizbowl not learned in their classes, everything from art, music, lit, RMP, philosophy,and science and whatever else. They learn it because they find the topics inherently interesting, or they simply learn it because it comes up in tournaments. I see no reason why math theory cannot find its rightful place in the quizbowl canon. As these topics are introduced, many will go dead at first. If I am not mistaken, the only zero we had on a bonus at QuAC yesterday was a math theory bonus, and not an especially obscure one either. All three parts are learned in trig or calculus. When people start to realize that math theory comes up on a regular basis, they will start picking up the information the same way they have for all the other topics in the canon.

Some of the biggest advocates for non-computation math questions are math people like myself who know that there is much more to mathematics than number crunching, which is all too often seen as being almost synonymous with mathematics. We know that mathematics is a rich and diverse field of study. Once the subject gets a foothold in high school quizbowl, the canon will expand for mathematics like it has for everything else.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Deviant Insider » Tue Nov 25, 2008 8:06 am

I was going to do this as a separate thread, but since this thread is already headed in the noncomp math direction, here are answers to quizbowl questions I have written:

Tossups:
Additive Identity, Ambiguous (Case), Archimedes, Asymptote, Augmented, Bayes (Theorem), Bell/Gaussian/Normal Curve/Distribution, Brahmagupta, Buffon’s Needle, Cantor, Catenary/Hyperbolc Cosine/Cosh, Cauchy-Schwartz (Inequality), Chain Rule, Chi Square(d), Circumcenter, Commutative, Completing the Square, Conditional, Continuous, Convex, Correlation Coefficient, Cosecant, Cube, Cycloid, Cylindrical Shell, Determinant, Differential (Equations), Diophantine (Equations) (accept Diophantus), Discrete, Distributive, Domain, e, Erdos, Extreme Value (Theorem), Flatland, Fourier, Gauss, Godel, Goldbach (Conjecture), Gradient, Green, Group, Harmonic (Series), Hero(n), Hexagon, Hexahedron, Hilbert, Hypatia, Hyperbolic Sine, Independent, Inverse, Kite(s) (or Deltoid(s)), Klein Bottle, Lagrange, Latus Rectum (or Latus Chord), Leibniz, L'Hospital, Linear Programming, Logistic, MacLaurin, Mandelbrot, Mean Value Theorem, Mutual(ly) Exclusive, Napier, Nash, One-to-one (accept Injective), Outlier, Partial (Derivative), Partial Fraction, (Integration by) Parts, Penrose (Tiles or Tiling or Tessellation), Perfect Numbers, Pi, Piecewise, Plane, Poisson, Power (of a Point Theorem), Prime (Numbers), Pythagorean (Theorem), Reference (Angle), Related Rate(s), Riemann, Rolle, Runge-Kutta, Sample Space, Secant, Separable (Differential Equations), Simpson, Sphere, Spiral, Stewart(’s Theorem) (or Apollonius(’s Theorem)), Supplementary, Synthetic (Division or Substitution), Tetrahedron, Trapezoid (Rule), Twin Prime(s), Venn, Wiles, Zeno

Bonuses:
Apollonius/Euler/Boole/Godel, Euclid’s Elements, Parabola/Parabola/Ellipse/Hyperbola, Babbage/Turing/von Neumann/Hopper, Trisecting an angle/doubling a cube/squaring a circle/Fermat's Last Theorem, Odd/Odd/Both/Even/Odd, Algebra/Googol/Rational/Precalculus, Principia/Fluxion/Optics, Euler/Cantor/Bernoulli/Poincaré, Hyperbolic (or Saddle Geometry)/Lobachevsky/Bolyai/Riemann, Fractal/von Koch/Kuhn/Butterfly, In which century were each of the following mathematical concepts first developed?, Topology/Inflection/Difference/Dodecahedron, Arc/Co/Oid (Accept Id)/Hyper, Pi/Magic Square/Pascal's Triangle/Pythagorean Theorem

This list is far from perfect or complete, but I think it shows that there are a lot of askable math topics that are appropriate for high school students. I would think that high school tournaments should have at least 1/1 math, even if a lot of people are opposed to computation. Such questions probably will have a lower conversion rate than other questions, especially as they are being introduced, but a significant number of questions can be written now that will have conversion rates significantly above zero.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by AlphaQuizBowler » Sun Nov 30, 2008 4:01 pm

Precalculus
Would you mind posting the question? I'm really curious what it would be.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Deviant Insider » Sun Nov 30, 2008 4:16 pm

From 2003...

Given their origins, identify these mathematical terms.
A. This word comes from the Arabic for the reunion of broken parts and was first used in 825.
B. This word was coined in the 1930s by a nine-year-old named Milton Sirotta
C. This category of numbers was used by Euclid, but he, unlike us, would have included the square root of two as this type of number.
D. This word, which is often used as the title of certain mathematics courses, was first used as a noun in 1969.
ANSWERS:
A. Algebra
B. Googol
C. Rational
D. Precalculus

Actually, a lot of the bonuses I listed above are kind of weak.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by dbarman » Sun Nov 30, 2008 4:42 pm

Shcool wrote:From 2003...

Given their origins, identify these mathematical terms.
A. This word comes from the Arabic for the reunion of broken parts and was first used in 825.
B. This word was coined in the 1930s by a nine-year-old named Milton Sirotta
C. This category of numbers was used by Euclid, but he, unlike us, would have included the square root of two as this type of number.
D. This word, which is often used as the title of certain mathematics courses, was first used as a noun in 1969.
ANSWERS:
A. Algebra
B. Googol
C. Rational
D. Precalculus

Actually, a lot of the bonuses I listed above are kind of weak.
How is D a question that involves good knowledge? Knowing when Precalculus first became a noun is not very useful.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by at your pleasure » Sun Nov 30, 2008 5:05 pm

A is kind of transparent and not terribly important.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Gautam » Sun Nov 30, 2008 5:06 pm

Shcool wrote:answers
Does it not occur to you that a vast number of these answers continue to be hard for the high school level? Tossups on Cauchy-Schwartz, Maclaurin, Cantor, Runge-Kutta, Lagrange, Stewart's theorem, and bonuses on things like Hyperbolic/Lobachevsky/Bolyai/Reimann are all hard and unnecessary. I don't see how the 'because I've written a question on this before, this becomes an "askable math topic"' makes for good quiz bowl writing.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Mechanical Beasts » Sun Nov 30, 2008 5:12 pm

Anti-Climacus wrote:A is kind of transparent and not terribly important.
Etymology in all cases is unimportant.
gkandlikar wrote:
Shcool wrote:answers
Does it not occur to you that a vast number of these answers continue to be hard for the high school level? Tossups on Cauchy-Schwartz, Maclaurin, Cantor, Runge-Kutta, Lagrange, Stewart's theorem, and bonuses on things like Hyperbolic/Lobachevsky/Bolyai/Reimann are all hard and unnecessary. I don't see how the 'because I've written a question on this before, this becomes an "askable math topic"' makes for good quiz bowl writing.
I wanted someone with actual credibility re: difficulty to say it first, but yeah, while I'd include at least one more than Gautam (Maclaurin series are things you learn about in high school), Runge-Kutta was the hard part of an EFT bonus last year. That's its lone appearance as something other than a clue on collegiate.quizbowlpackets.com. That's hard.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Sir Thopas » Sun Nov 30, 2008 5:31 pm

I would also go so far as to say that many of these are utterly untossupable. I would like to see a good tossup on "one-to-one", for example.

This is not to say that there aren't many math theory questions to be written for high school. It just seems that many of these are suspect and doubtfully pyramidal anyway.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Mechanical Beasts » Sun Nov 30, 2008 5:33 pm

Sir Thopas wrote:I would also go so far as to say that many of these are utterly untossupable. I would like to see a good tossup on "one-to-one", for example.

This is not to say that there aren't many math theory questions to be written for high school. It just seems that many of these are suspect and doubtfully pyramidal anyway.
Injectivity could totally be tossed up; it'd just be incomprehensible for the first four lines at the high school level.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Deviant Insider » Sun Nov 30, 2008 5:47 pm

Many of the questions were written for competitions between the New Trier team and New Trier faculty, which is why they are difficult. Also, many of them were written years ago, before there was as much discussion on question quality, which is why many of the bonus answers in particular are pretty weak, as I already said. However, if you look through the list of tossup answers, you will see that the vast majority of them are appropriate for high school students currently enrolled in AP Calculus, especially if those students care about mathematics.

Gautam listed probably the five toughest tossups from a list of about one hundred. (I'm taking out MacLaurin, since his name comes up in every Calculus BC course.) That doesn't change the fact that there are a lot of viable high school math questions.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Mechanical Beasts » Sun Nov 30, 2008 5:57 pm

Shcool wrote: Gautam listed probably the five toughest tossups from a list of about one hundred. (I'm taking out MacLaurin, since his name comes up in every Calculus BC course.) That doesn't change the fact that there are a lot of viable high school math questions.
No one disputes that; in fact, we argue that there are so many viable conceptual math tossup subjects that we don't need to use computational math!
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Auks Ran Ova » Sun Nov 30, 2008 7:29 pm

Did you honestly list "Flatland" as a math tossup?

In addition to having a number of questions that are too hard, that list features at least a few questions that I can't imagine a good tossup existing on. How does one write a non-awful tossup with the answer "related rates"?
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Terrible Shorts Depot » Sun Nov 30, 2008 9:25 pm

I feel like one can't write a tossup any sort of operation, e.g. completing the square, without it being either dumb beyond belief or insanely hard. Admittedly, I don't know much about math, but I'm just not sure if there are any clues out there.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by Deviant Insider » Sun Nov 30, 2008 11:56 pm

Other questions on the list were written for a one-on-one competition in which matches are staggered so that certain questions are used for students with winning records while others are used for students with losing records. Two examples taken from rounds for students with losing records:
Which method is used to convert a general conic equation without an xy term into an equation appropriate for a specific conic section? This method can also be used to convert a quadratic function into vertex form or to solve a quadratic equation. Give the three-word phrase which involves halving and squaring the linear term.
This is the common name given to calculus problems that often involve right triangles. One common example involves seeing how quickly the distance between two cars increases as one heads North and the other heads East. Name these problems in which values of some derivatives are used to find the value of another derivative.
These questions are also dated. Crap, I'm not doing so well today.

To improve these questions, you would want to start out by saying the technique often involves subtracting b squared over four a and can be used to demonstrate the quadratic formula, or these problems are used to calculate the errors of radar guns and typically demonstrate the applications of implicit differentiation.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by bridgepleyerrm11 » Fri Feb 20, 2009 4:01 pm

but if you put knowladge of math terms in then it's not really math anymore...
I really like the 'thinking' related math questions that the naqt(s) use

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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by AKKOLADE » Sat Feb 21, 2009 12:18 am

bridgepleyerrm11 wrote:but if you put knowladge of math terms in then it's not really math anymore...
I assume you mean 'it's not really math computation any more.' You would be correct - replacing math computation questions with non-math computation questions would make them different from math computation.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by at your pleasure » Sat Feb 21, 2009 2:46 pm

but if you put knowladge of math terms in then it's not really math anymore...
I really like the 'thinking' related math questions that the naqt(s) use
Correct me if I am wrong, but there is a fair amount of important math stuff that does not involve calculation.
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Re: Pyramidality, Math calculation, and the Goldfish Tournament

Post by rjaguar3 » Sat Feb 21, 2009 3:00 pm

bridgepleyerrm11 wrote:but if you put knowladge of math terms in then it's not really math anymore...
I really like the 'thinking' related math questions that the naqt(s) use
As a Mathcounts champion, USAMO honorable mention and math major, let me tell you that is definitely not the case. For example, the USAMO consists of 6 proofs to be done in 9 hours, and is not focused on computation (like Mathcounts).
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