Yes, it's another thread about math

Dormant threads from the high school sections are preserved here.
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Ford08
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Re: Yes, it's another thread about math

Post by Ford08 »

Well what I did and do to make my self a help for the team in math is to memorize a lot of numbers of different things such as factorials. I have 9! to 1! memorized. I also have several probality things memorized. I just made myself sit down and memorize a lot of stuff. This does come in handy so if you say you cannot compute numbers fast enough just try and memorize certain things that come up. Thats all the advice I can give.
Calc is for wusseys
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First Chairman
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Re: Yes, it's another thread about math

Post by First Chairman »

BarringtonJP wrote:Middle school Math computation pyramidal toss-up:
Evaluate 11 to the 4th power. This is easy to do if you understand that powers of 11 perfectly mimic Pascal’s Triangle, with 11 to the first power matching the digits of the 2nd line, 11 to the 2nd power matching the digits of the 3rd line, and so on.
Answer: 14,641

Middle school Geometry computational pyramidal toss-up:
What is the area of a right triangle if one leg is 10 inches and the hypotenuse is 26 inches? It may be useful to recall the Pythagorean Theorem to find the length of the other leg. Of course, it’s even faster if you recognize how to use the 5,12,13 triple that applies to this triangle.
Answer: 120 sq. in.
No problem with the middle-school answer space, but I'm just a stickler on the style. I'm more of a "set up the problem" person rather than just asking the question first and the method later.

Pencil and paper ready (Important to clue in the student that this is a computational question!), numerical answer required! When asked to evaluate 11 to the 4th power (the real question), one can recognize Pascal's triangle can give you insight. Specifically...

Pencil and paper ready, numerical answer required! To find the area of a right triangle with a leg of 10 and hypotenuse of 26, one can apply the Pythagorean Theorem, or recognize that the lengths are multiples of the Pythagorean triple 5-12-13. For ten points...


I am also a fan of a bit more tangible word problem in proper proportions in a tournament set.
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Captain Sinico
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Re: Yes, it's another thread about math

Post by Captain Sinico »

Regarding computational math in general, I think you guys are really muddying the waters by vaunting the "number theory" and other things used in computation. I claim that the theory useful for quizbowl computation boils down to a very few (~10) tricks and formulae that generally do not reflect any deep or interesting properties of the problems (which are themselves usually very cursory) and do not reflect the richness of the field of mathematics, even at the high school level; in fact, I think you sully the name of mathematics by pretending that the average computation question is anything like interesting.
Furthermore, this is all essentially so because attempts to ask anything deeper or harder will usually result in dead questions. After all, who among us can generally do a deep, interesting calculation via a non-obvious method in under a minute? I know I cannot; non-trivial calculations require rumination and deliberation, things that are essentially and necessarily absent from quizbowl computational math.
Solving a math computation question usually has two components: determining a method, then calculating. Due to the highly limited nature of the methods available (as discussed above), people skilled in the latter tend to dominate, at least among those interested enough to know the several things required to do the former, in my experience. However, only the former is quizbowl in the sense that I understand the word. Thus, to my view, computational question outcomes are dominated by the non-quizbowl skill of computation speed in general, and this is essentially so.
Furthermore, deliberating for too long about the method to use (perhaps because one is cognizant of a wider variety of methods) or attempting to use a more elegant method often leads to defeat since opponents (or players in the writer's expectation) can use a more common or brutal method that they can apply more quickly. Thus, such questions create a trade-off between method-finding and computation and are often inexorably putative to knowledge.
Thus, my thinking is strongly against computational math questions, especially tossups. To summarize: I think the problems are generally trivial and few in type, that the methods useful in solving them are few and shallow, that this is necessarily so, and that this leads inexorably to outcomes dominated by computation speed and to questions that penalize knowledge.

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