Computational bonuses

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Computational bonuses

Post by Important Bird Area » Sat Jul 11, 2009 7:59 pm

Because the previous 23,748,234 threads about math comp have focused on tossups, I wanted to start a thread to discuss computational bonuses.

In the Who is really anti-math? thread, Dwight wrote:
This distinction between doing a problem and doing a problem fast is why I will almost always argue that calculation is an adequate topic for bonuses (which test, "Do you know how to do the problem?") but is never appropriate for tossups (which test, "Can you do the problem faster than other people? If not, we'll tell you how to do the problem and then see if you can plug and chug faster than other people.").
By contrast, Matt wrote in the irc a couple of months ago that NAQT should just "rip the bandaid off" and abolish all computation questions, whether tossups or bonuses.

NAQT plans to reduce computation tossups for the 2009-2010 competition year; we will almost certainly be producing computation bonuses to replace them. Reasoning as follows: x number of teams like computation and want to keep it around in some form. Meanwhile, the big three arguments against computation tossups don't apply to bonuses at all. (1. Computation tossups are difficult-to-impossible to write pyramidally. 2. Computation tossups don't test an appropriate selection of the high school math curriculum. 3. Computation tossups disrupt the flow of the game, in part because they have terrible conversion rates.) A general argument that would exclude computational bonuses would likely rely on additional arguments (such as "quizbowl should test knowledge of the liberal arts rather than applied skills") that are (at least) harder to quantify, and perhaps more controversial within the community.

So: here's your computational bonus thread. What are the arguments pro and con? What should these look like when they're written?
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Re: Computational bonuses

Post by Auroni » Sat Jul 11, 2009 10:17 pm

Well, I hold a similar position to that of computational tossups, in that these bonuses are worthless when testing gimmicks (such as painting rooms and all of that). My preference would be to integration computational parts into bonuses about scientific or mathematical laws, such as asking for the current in a simple circuit, and then asking about Ohm's law, and then about ammeters/voltmeters/Kirchoff's laws. Or, maybe one that would utilize an integration by parts and proceed to test knowledge of other integration techniques.
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Re: Computational bonuses

Post by Ondes Martenot » Sat Jul 11, 2009 10:22 pm

I think having some math comp could be decent, in that the one of biggest flaws of computational tossups is that they test speed mainly and not knowledge, while a math comp bonus could easily fix this. For example, a part of a bonus such as:

A. Find the dot product of the vectors <1, 1, 0> and <0, 1, 1>

basically asks do you know what a dot product is, not can you do it quickly. Since the arithmetic is simple, it doesn't matter if it takes you 2 seconds or 3 seconds to figure it out, as long you understand what a dot product is. So I guess the important thing is to make bonuses that test your understanding and keep the artithmethic as simple as possible so as to remove any element of speed into the bonus.
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Re: Computational bonuses

Post by kayli » Sat Jul 11, 2009 10:40 pm

I think that, as long as the numbers are simple, you can test how well the competitors know how to compute things. Computation is important to an extent, and this way gets rid of the doesn't-actually-know-how-to-compute-this-but-knows-what-this-is factor without having to worry about doing tedious work. I think they should constitute one and very occassionally two of the math bonus. For example, a simple bonus could have the first part ask for the the arithmetic mean, the second part ask for geometric mean, and the third part ask to compute the harmonic mean of 2 and 3 (ten seconds should be enough to add two fractions and multiply it's reciprocal by two with time to check for dumb mistakes).

I think that theory is not the cure-all for math in quizbowl. I think that there should be a small amount of computation. Computation, so long as it's not tedious or tricky or too time consuming, is a good indicator of how well a student actually knows math. If a person doesn't know how to calculate the Hamming distance of a code, does he/she deserve points for knowing what it is? Well, I'm not too sure of that myself.
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Re: Computational bonuses

Post by Sen. Estes Kefauver (D-TN) » Sat Jul 11, 2009 10:44 pm

If a person doesn't know how to calculate the Hamming distance of a code, does he/she deserve points for knowing what it is? Well, I'm not too sure of that myself.
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Re: Computational bonuses

Post by Cheynem » Sat Jul 11, 2009 10:56 pm

No, I see Kay's point here. It's actually about the same as Aaron's: a simple computational bonus in which the computation per se is minimal but the knowledge of how to compute is actually tested does reward knowledge, in this case the mathematical steps of calculating something like a dot product or whatever a Hamming distance is. If it rewards knowledge as opposed to just speed or trickiness, that's something and arguably about as valid as having a conceptual idea of what a dot product is (now, since I don't know what a Hamming distance is, if the actual calculation is more about lots o' steps and calculation as opposed to knowledge, then that sucks and the question should just ask you to identify a Hamming distance).
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Re: Computational bonuses

Post by The King's Flight to the Scots » Sun Jul 12, 2009 12:22 am

I don't think it's a good idea to give computational math any kind of distribution. Anything academic is still better than "If there are 4 red marbles and 3 green marbles..." Something like the Ohm's Law bonus mentioned earlier would be acceptable, however.
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Re: Computational bonuses

Post by cornfused » Sun Jul 12, 2009 2:07 pm

Cheynem wrote:whatever a Hamming distance is.
Basically, it's the number of changes you need to make in order to turn one thing (number, word, string) into another thing. The Hamming distance between 12345 and 923a5 is two.
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Sun Jul 12, 2009 2:46 pm

Except the issue with calculation bonuses is that you have to test three concepts instead of one if you don't want to make it all or nothing. However, that would quickly cause one to run out of possible answers very quickly.
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Re: Computational bonuses

Post by Sen. Estes Kefauver (D-TN) » Sun Jul 12, 2009 2:51 pm

No, I see Kay's point here. It's actually about the same as Aaron's: a simple computational bonus in which the computation per se is minimal but the knowledge of how to compute is actually tested does reward knowledge, in this case the mathematical steps of calculating something like a dot product or whatever a Hamming distance is.
I disagree with Kay's point, and am actually kind of troubled that we're even considering it - it's very clear that the argument is that if somebody knows enough to recognize a description of something, but doesn't actually have the firsthand knowledge to apply that description, than they don't deserve points for it in quizbowl. Really, that's all it boils down to. You can rephrase the argument like this to demonstrate how flawed I think it is - If you have never read Lolita, then you never deserve to get points for a question on it even if you are familiar enough with the basics of the plot to recognize it. Or, the only way you deserve points for a tossup on John Adams is to spontaneously give a description of something he did. Anyone who plays quizbowl should know this is simply an untenable position. There is literally no difference between that and what Kay has been arguing for math that I can see. There's nothing that makes math so inherently special, because there is an analogue to computation for every subject, and I see it as nothing more than some form of snobbery against those people who know something from it's name coming up before but don't know specifics about it (guess what, that means in a well written question they wouldn't get as much of a chance to score points as a math expert, Kay).
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Re: Computational bonuses

Post by kayli » Sun Jul 12, 2009 3:59 pm

Harper v. Canada (Attorney General) wrote: I disagree with Kay's point, and am actually kind of troubled that we're even considering it - it's very clear that the argument is that if somebody knows enough to recognize a description of something, but doesn't actually have the firsthand knowledge to apply that description, than they don't deserve points for it in quizbowl. Really, that's all it boils down to. You can rephrase the argument like this to demonstrate how flawed I think it is - If you have never read Lolita, then you never deserve to get points for a question on it even if you are familiar enough with the basics of the plot to recognize it. Or, the only way you deserve points for a tossup on John Adams is to spontaneously give a description of something he did. Anyone who plays quizbowl should know this is simply an untenable position. There is literally no difference between that and what Kay has been arguing for math that I can see. There's nothing that makes math so inherently special, because there is an analogue to computation for every subject, and I see it as nothing more than some form of snobbery against those people who know something from it's name coming up before but don't know specifics about it (guess what, that means in a well written question they wouldn't get as much of a chance to score points as a math expert, Kay).
I think that math is inherently different in that computation is a very large part in what you do. When math is being tested it's never about what theorem or postulate says what but rather it tests knowing something and applying it. That's why in major math competitions, the focus is based upon proving and problem solving. This isn't to say that the same should be applied to quizbowl because they're two different animals. But math is in large part based on computation and application. There are analogues in other fields, but they are arguably less important in their fields than computation is in math.

Also, I'm not saying that the math expert would not have as good a chance of getting points. I think we're talking about bonuses, and here I'm advocating allotting one part of the bonus to computation. If one part of the bonus were a simple computation, then this distinguishes a team with deeper math knowledge (ex. knowing Vieta's and applying it) vs a team which knows the idea behind the formulas. This makes it so that a good math person will get 20-30 on a bonus, and a person who has knowledge of math will get 10-20. I'm not advocating complete snobbery against those who don't know computation as well, but I am advocating computation as a ways of rewarding those who do know the application of a mathematical idea.

I'm not a very good writer at all, but this is kinda what I would like to see:

FTPE answer these questions about polynomials:
1) This theorem gives a way of putting constraints on the solutions of a polynomial from factors of the leading coefficient and the constant.
Answer: Rational root theorem
2) Using these formulas named after a French mathematician, one can use the product and sums of the roots of the polynomial to express the coefficients of the polynomial and vice versa.
Answer: Vieta's formulas (accept Vieta's laws, Vieta's theorem, Viète's formulas, Viète's laws, and Viète's theorem)
3) Using Vieta's formulas, find the products of the roots of the following polynomial: x^5-x^4+x^3+4x^2-2x-3.
Answer: 3

Again, please don't hammer me too hard about my question quality. But that's a general idea of what I would kinda want.
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Re: Computational bonuses

Post by Cheynem » Sun Jul 12, 2009 4:19 pm

Putting aside quality of the writing (which being unfamiliar with math, I cannot comment on), I would not be opposed to such bonus structures. The idea, as least I'm trying to gather it, is that as a solid hard point of a bonus, you reward knowledge of application of a formula or whatever (which should not be about "crunch these numbers speedily!" but rather "do you know what this is actually asking for?"). I don't see it as snobbery to perhaps have a part of a bonus test this knowledge any more than having a bonus about, say, The Great Gatsby ask about _the green light_ or _West Egg_ or something that's a little deeper than the author, title, or protagonist. In this sense, the bonus part is not requiring you to have read the book but to have at least read a summary of important points about it--to have a little deeper knowledge. As long as a math bonus part is requiring this deeper knowledge of math computation to test knowledge and not speed or number crunching, I do not have a problem with it.

To use a really simplistic analogy, asking someone to find the derivative of like x^5 does not reward speed or number crunching but rather knowledge. If you know how to apply the power rule, you will get points. If you don't, you won't. As pointed out, it would be kind of untenable for an entire bonus to ask about stuff like this, but I think it could work as parts.
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Re: Computational bonuses

Post by Sen. Estes Kefauver (D-TN) » Sun Jul 12, 2009 4:25 pm

I think that math is inherently different in that computation is a very large part in what you do. When math is being tested it's never about what theorem or postulate says what but rather it tests knowing something and applying it.
Last I checked, being able to perform the equivalents - ie write essays analyzing different features of a novel, or being able to argue a conclusion in a history paper based on analyzing different events, or being able to calculate scientific equations, etc. are all extremely important things you need to be able to do to pass a certain level of class from high school onward.
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Re: Computational bonuses

Post by kayli » Sun Jul 12, 2009 4:52 pm

Harper v. Canada (Attorney General) wrote:
I think that math is inherently different in that computation is a very large part in what you do. When math is being tested it's never about what theorem or postulate says what but rather it tests knowing something and applying it.
Last I checked, being able to perform the equivalents - ie write essays analyzing different features of a novel, or being able to argue a conclusion in a history paper based on analyzing different events, or being able to calculate scientific equations, etc. are all extremely important things you need to be able to do to pass a certain level of class from high school onward.
Why don't you find or write me a quizbowl-feasible question that has one correct answer that requires you to do that?

Sure, they are important. But they can't be put into quizbowl. A computational math bonus part, so long as it doesn't require dumb or tedious work, can be put in such a way that tests deep knowledge of a subject. I see nothing wrong in using computational math as a test for knowledge. Last time I checked, every time you learn something new in history or read a book, you don't proceed to write an essay about it. As for math, if you learn a theorem and don't practice it, there's something amiss in the schooling.
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Sun Jul 12, 2009 5:28 pm

Arsonists Get All the Girls wrote:I think that math is inherently different in that computation is a very large part in what you do.
About as much as you do in, say, physics, but I don't see you running around asking for exclusively computational physics.
When math is being tested it's never about what theorem or postulate says what but rather it tests knowing something and applying it.
1) Math theory does test knowing it.
2) It seems to me that what you mean by "applying" is essentially "plug-and-chug", which anyone playing Quizbowl can do.
That's why in major math competitions, the focus is based upon proving and problem solving. This isn't to say that the same should be applied to quizbowl because they're two different animals.
You just defeated your own argument there.
But math is in large part based on computation
Knowing how to calculate something quickly is something that is not expected except when trying to impress people at a party. Everyone uses calculators nowadays.
and application.
You want applied math? Pick up a physics textbook.
There are analogues in other fields, but they are arguably less important in their fields than computation is in math.
And math is special because?
Also, I'm not saying that the math expert would not have as good a chance of getting points. I think we're talking about bonuses, and here I'm advocating allotting one part of the bonus to computation.
I know perfectly well how to compute the maxima of a function, but in the quick-paced nature of Quizbowl, it becomes very easy for someone thinking quickly to make a mistake. I cannot count how many times I've dropped a 2 somewhere.
If one part of the bonus were a simple computation, then this distinguishes a team with deeper math knowledge (ex. knowing Vieta's and applying it) vs a team which knows the idea behind the formulas. This makes it so that a good math person will get 20-30 on a bonus, and a person who has knowledge of math will get 10-20. I'm not advocating complete snobbery against those who don't know computation as well, but I am advocating computation as a ways of rewarding those who do know the application of a mathematical idea.

I'm not a very good writer at all, but this is kinda what I would like to see:

FTPE answer these questions about polynomials:
1) This theorem gives a way of putting constraints on the solutions of a polynomial from factors of the leading coefficient and the constant.
Answer: Rational root theorem
2) Using these formulas named after a French mathematician, one can use the product and sums of the roots of the polynomial to express the coefficients of the polynomial and vice versa.
Answer: Vieta's formulas (accept Vieta's laws, Vieta's theorem, Viète's formulas, Viète's laws, and Viète's theorem)
3) Using Vieta's formulas, find the products of the roots of the following polynomial: x^5-x^4+x^3+4x^2-2x-3.
Answer: 3

Again, please don't hammer me too hard about my question quality. But that's a general idea of what I would kinda want.
Several problems with this:

1) A player would learn absolutely nothing from that third bonus part.
2) A person who knows about a formula would most likely be able to compute it as well. Typically, bonuses are structured such that around 80-90% get the first part, about half get the second part, and 10-20% get the third part. If you were to try to follow that, you would need to come up with an equation that is so complex that people wouldn't be able to solve it in 5 seconds or is easily guessable.
3) Why not just ask for the name and give the formula as a clue?

There are reasons why almost all the top players who have had full exposure to all types of Quizbowl dislike math calculation.
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Re: Computational bonuses

Post by kayli » Sun Jul 12, 2009 6:21 pm

About as much as you do in, say, physics, but I don't see you running around asking for exclusively computational physics.
But... we're not discussing physics are we? If you have have a physics question on a topic that isn't a falling ball that takes very little time to calculate without tedious work, then I don't see why you shouldn't have it.
1) Math theory does test knowing it.
2) It seems to me that what you mean by "applying" is essentially "plug-and-chug", which anyone playing Quizbowl can do.
Knowing what a mathematical concept is and actually using it is completely different. Knowing what integration by parts and actually doing it are completely different things. How many people know what trigonometric functions and integrals are? How many people can find the integral by trig substitution? It might be plug and chug for people who know what it is; but for those who don't, it's a concept that needs to be learned.
That's why in major math competitions, the focus is based upon proving and problem solving. This isn't to say that the same should be applied to quizbowl because they're two different animals.
You just defeated your own argument there.
I probably didn't make it clear. I meant to say that overwhelmingly, whenever math is being tested competitively, questions require calculations. The same problems shouldn't be used for quizbowl, but the idea that computation is a necessary part in math should still be in both competitions.
Knowing how to calculate something quickly is something that is not expected except when trying to impress people at a party. Everyone uses calculators nowadays.
I'm not advocating doing dumb work like fast multiplication and division. I want simple problems that test a subject ensuring that people who know how to use a theorem or formula will be distinguished from those who don't.

On a somewhat unrelated note, people need to stop using the calculator argument. There's a reason why people spent so much time learning addition, subtraction, multiplication, and division tables. You're not always going to have calculator with you, and society will never evolve out of the need for the knowledge of how to do those operations.
You want applied math? Pick up a physics textbook.
I'm not talking about applied math. I'm talking about applying a theorem. It's completely and utterly different.
And math is special because?
1) You can actually write a question for math computation`
2) Math computation and math theory are learned hand in hand. If you read a book, you don't automatically go to write an essay on the use of spirals as an image system; but in math, once you learn something, you proceed almost immediately to use it in calculation.
I know perfectly well how to compute the maxima of a function, but in the quick-paced nature of Quizbowl, it becomes very easy for someone thinking quickly to make a mistake. I cannot count how many times I've dropped a 2 somewhere.
I'm not advocating computations that should take more than five seconds to finish. The problem should not include large numbers or excessive computation. It's not the math problems fault if you drop a 2. It's your own. It's also not the question's problem if someone forgets to add the middle name Quincy to his answer. It's his own.


I'm not a good question writer, and that problem is pretty flawed I guess. I'm just trying to say that I would like the bonuses to be in the form 1) easy theory 2) harder theory that is still knowable by 50% of people 3) use the harder theory to solve this problem quickly. For example, I'm pretty sure most people who have taken calculus know how to calculate the volume of a shape by using washers but not a lot would really remember the exact formula.

EDIT: Accidentally put italics instead of quotes.
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Sun Jul 12, 2009 7:06 pm

Arsonists Get All the Girls wrote:
About as much as you do in, say, physics, but I don't see you running around asking for exclusively computational physics.
But... we're not discussing physics are we? If you have have a physics question on a topic that isn't a falling ball that takes very little time to calculate without tedious work, then I don't see why you shouldn't have it.
Hey, let me declare that we're not discussing math anymore. Problem solved.
1) Math theory does test knowing it.
2) It seems to me that what you mean by "applying" is essentially "plug-and-chug", which anyone playing Quizbowl can do.
Knowing what a mathematical concept is and actually using it is completely different. Knowing what integration by parts and actually doing it are completely different things. How many people know what trigonometric functions and integrals are? How many people can find the integral by trig substitution? It might be plug and chug for people who know what it is; but for those who don't, it's a concept that needs to be learned.
[/quote]
So what you're saying is that for the people who know about the theory, it's simple plug and chug, while for those who don't know about it, they won't get it? Then why not ask about the theory in the first place?
I probably didn't make it clear. I meant to say that overwhelmingly, whenever math is being tested competitively, questions require calculations. The same problems shouldn't be used for quizbowl, but the idea that computation is a necessary part in math should still be in both competitions.
Except that this is not a math competition. Those competitions are designed to test applications, while Quizbowl is designed to test about knowledge. This is why only :chip: uses questions that begin with "why".
Knowing how to calculate something quickly is something that is not expected except when trying to impress people at a party. Everyone uses calculators nowadays.
I'm not advocating doing dumb work like fast multiplication and division. I want simple problems that test a subject ensuring that people who know how to use a theorem or formula will be distinguished from those who don't.
Which is why we have math theory questions. All calculation does is devolve it into "dumb work".
On a somewhat unrelated note, people need to stop using the calculator argument. There's a reason why people spent so much time learning addition, subtraction, multiplication, and division tables. You're not always going to have calculator with you, and society will never evolve out of the need for the knowledge of how to do those operations.
Everyone knows what 7*8 is. No one ever learned the times tables form 13*13 to 100*100. Either you will make arithmetic trivial, tedious, or relying on a simple parlor trick. And knowledge of how to do math is math theory.
You want applied math? Pick up a physics textbook.
I'm not talking about applied math. I'm talking about applying a theorem. It's completely and utterly different.
Look at what I've said earlier, then.
And math is special because?
1) You can actually write a question for math computation
Just because I can write a question doesn't mean I should.
2) Math computation and math theory are learned hand in hand. If you read a book, you don't automatically go to write an essay on the use of spirals as an image system; but in math, once you learn something, you proceed almost immediately to use it in calculation.
Not necessarily. If one learns about something in history class, one usually has to analyze it at some point, be it in an essay or a test or whatnot. Same thing with math: One does not have to perform computations with it immediately after learning about it, but instead one does a couple of applications as homework or as a test problem.

Also, while I'm on the subject, you aren't really doing a good job testing how well you can apply the concept. I can probably count on one hand the number of problems that I was able to solve confidently within one minute. And I consider myself good at math.
I know perfectly well how to compute the maxima of a function, but in the quick-paced nature of Quizbowl, it becomes very easy for someone thinking quickly to make a mistake. I cannot count how many times I've dropped a 2 somewhere.
I'm not advocating computations that should take more than five seconds to finish. The problem should not include large numbers or excessive computation.
And then would be answerable by basically everyone who knows about the theory.
It's not the math problems fault if you drop a 2. It's your own. It's also not the question's problem if someone forgets to add the middle name Quincy to his answer. It's his own.
So despite the fact that I know how to do the problem, I should get penalised by it because I'm trying to get it done within five seconds? I'd hate to have you as a math teacher -- you seem to have no idea of partial credit.

Also, your analogy sucks. I have never seen anyone forget to put in a Quincy or anything of the sort.

I'm not a good question writer, and that problem is pretty flawed I guess. I'm just trying to say that I would like the bonuses to be in the form 1) easy theory 2) harder theory that is still knowable by 50% of people 3) use the harder theory to solve this problem quickly. For example, I'm pretty sure most people who have taken calculus know how to calculate the volume of a shape by using washers but not a lot would really remember the exact formula.

EDIT: Accidentally put italics instead of quotes.
And how would you be able to test that without being completely vague, giving away the answer, or making it such that the only people who get the second part are the ones who would get the third part?
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Re: Computational bonuses

Post by kayli » Sun Jul 12, 2009 7:45 pm

So what you're saying is that for the people who know about the theory, it's simple plug and chug, while for those who don't know about it, they won't get it? Then why not ask about the theory in the first place?
My old clarinet teacher new the theory behind finding the volume of a solid, but he did not know how to do it mathematically. Should a person who knows theory but not how to use it be rewarded the same amount of points as a person who knows both? No.
Except that this is not a math competition. Those competitions are designed to test applications, while Quizbowl is designed to test about knowledge. This is why only :chip: uses questions that begin with "why".
Calculation tests knowledge. A person who knows how to calculate an integral is not the same as a person who knows only what an integral is. One should be rewarded more points by demonstrating that knowledge.
Which is why we have math theory questions. All calculation does is devolve it into "dumb work".
Again, calculation tests knowledge. As long as you use simple number that reduce well, I don't see how that could be tedious. The harmonic mean of 2, 4, 6, 8 is tedious and requires dumb. The harmonic mean of 1/2 and 1/3 is not. It requires that a person knows what a harmonic mean is and, since the numbers are in fractional form, it's very easy to compute.
Not necessarily. If one learns about something in history class, one usually has to analyze it at some point, be it in an essay or a test or whatnot. Same thing with math: One does not have to perform computations with it immediately after learning about it, but instead one does a couple of applications as homework or as a test problem.
Analyzing and assimilating historically important facts and details isn't 99% of history. Applying theorems and formulas to problems is 99% of math.
Also, while I'm on the subject, you aren't really doing a good job testing how well you can apply the concept. I can probably count on one hand the number of problems that I was able to solve confidently within one minute. And I consider myself good at math.
You should strongly reevaluate your strength in math.
And then would be answerable by basically everyone who knows about the theory.
See previous arguments.
So despite the fact that I know how to do the problem, I should get penalised by it because I'm trying to get it done within five seconds? I'd hate to have you as a math teacher -- you seem to have no idea of partial credit.
Talk to me about partial credit when I see it in quizbowl.
Also, your analogy sucks. I have never seen anyone forget to put in a Quincy or anything of the sort.
Everyone makes mistakes. Everyone has those days... where they might accidentally say one thing instead of another similar thing.
And how would you be able to test that without being completely vague, giving away the answer, or making it such that the only people who get the second part are the ones who would get the third part?
A lot of people know what something is but don't know/forgot how to use it.
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Sun Jul 12, 2009 8:27 pm

Arsonists Get All the Girls wrote:
Also, while I'm on the subject, you aren't really doing a good job testing how well you can apply the concept. I can probably count on one hand the number of problems that I was able to solve confidently within one minute. And I consider myself good at math.
You should strongly reevaluate your strength in math.
All right, here's one-fourth of one of my math assignments. If you think you're that good, you try solving one of these within one minute.

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Re: Computational bonuses

Post by at your pleasure » Sun Jul 12, 2009 8:48 pm

You should strongly reevaluate your strength in math.
Note the qualifer "under one minute" I am sure that given, say , a pretty reasonable average time per question of 3-5 minutes, there are a much larger number of a problems Harry could solve confidently. Also note the rider "confidently", since even if one could theoretically do a question in less than a minute, it's still to your advantage in most situations to take your time since hasty problem solving produces more mistakes. The key differences between quizbowl(espcially timed quizbowl) and math tests are that 1) within reasonable limits, how fast you can do a problem does not affect your reward on a math test, unlike timed quizbowl, 2) there is enough time to use theorems to approach problems that don't have "use this theorem to do x" in them, and 2) thanks to partial credit(which partially attempts to remedy the fact that students make mistakes under testing circumstances that they would not make under non-testing circumstances) and calculators, a student is less likely to be excessively penalized for trivial errors under testing conditions than under quizbowl conditions.
Applying theorems and formulas to problems is 99% of math.
Er, you forgot the bit of math where you come up with theorems and formulas. God did not send down the quadratic formula with the Ten Commandments; a bunch of smart people tooled around with different methods of solving quadratic eqations for a few hundred years until one of them came up with this especially useful method, which someone had the good sense to put into algebraic form at some point.
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Re: Computational bonuses

Post by Nine-Tenths Ideas » Sun Jul 12, 2009 8:58 pm

Kamen Rider Punch Hopper wrote:So despite the fact that I know how to do the problem, I should get penalised by it because I'm trying to get it done within five seconds? I'd hate to have you as a math teacher -- you seem to have no idea of partial credit.

Also, your analogy sucks. I have never seen anyone forget to put in a Quincy or anything of the sort.
I have seen someone forget to put a Quincy in or something of the sort, and you have too. There's no point in flat out lying to make a point- not so good players do this all the time, even when they're prompted on Shelley and can't actually remember which one. It doesn't speak much to their quality as players, but hey. They were trying to remember his name in 5 seconds. They should get 5 points, partial credit, for half, right?

Look- comp math isn't that great and it certainly shouldn't be in tossups, but a well-executed bonus like Kay described- though perhaps not demonstrated- would be kind of okay when used sparingly.
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Re: Computational bonuses

Post by Deviant Insider » Sun Jul 12, 2009 9:03 pm

Kay's Vieta example is just fine. I've taught that formula several times and don't know its name because it does not appear in textbooks I've seen, but I could have gotten the last part quickly based on my knowledge of the formula and my ability to divide three by one. That is a case in which being able to use the formula demonstrates more important knowledge than knowing its name, and using the formula can be done easily if you understand it.
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Sun Jul 12, 2009 9:10 pm

Christianity and alcohol wrote:I have seen someone forget to put a Quincy in or something of the sort, and you have too. There's no point in flat out lying to make a point- not so good players do this all the time, even when they're prompted on Shelley and can't actually remember which one. It doesn't speak much to their quality as players, but hey. They were trying to remember his name in 5 seconds. They should get 5 points, partial credit, for half, right?
Actually, I have not seen anyone omit part of an answer that has caused the answer to change (e.g. John Adams for John Quincy Adams). Now, I have seen someone forget what the first name is (Which Strauss is it again?), but that is an issue of not knowing who it is, not a mistake in the same way that dropping a 2 is in a math calc question.
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Re: Computational bonuses

Post by Ben Dillon » Mon Jul 13, 2009 3:45 pm

Not really sure how the "partial credit" concept somehow got wrangled into this discussion. There is no real analogue to partial credit in quiz bowl, unless you count the idea of prompting when given a partial answer. But I can't conceive of any situations in which prompting on computational math is desirable, let alone kosher.

"Hmmm... the answer is pi, the player gave 22/7... okay, I'll prompt."

In fact, I'd argue as a math teacher that there are virtually no situations that are truly "partial" credit. In grading almost any problem, if it's worth multiple points, you devise some rubric for awarding the points as singletons, e.g. 5 out of 5 for reaching the end (x), 4 out of 5 for reaching level x-1 close to the end, down to perhaps 1 out of 5 for attempting the problem. In other words, a discrete rubric is attached that is likely based on a boolean basis of "did the student complete each of a series of smaller tasks within the larger problem", NOT a more holistic "did the student get the larger problem, and to what extent".

Not sure how well I've phrased the above :/
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Re: Computational bonuses

Post by Haaaaaaaarry Whiiiiiiiiiite » Mon Jul 13, 2009 3:56 pm

Basically the subject of "partial credit" came in because in virtually all cases on a math test, if a person accidentally drops a minus sign, then the teacher will give the student a 4/5 or something similar on the problem. However, in Quizbowl, one cannot do this, and therefore one can get burned despite having full knowledge of the concept at hand.
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Re: Computational bonuses

Post by Important Bird Area » Mon Jul 13, 2009 4:00 pm

Ben Dillon wrote:But I can't conceive of any situations in which prompting on computational math is desirable, let alone kosher.
How do people feel about prompting on unsimplified fractions? (Current NAQT policy is that they are flat-out wrong.)
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Re: Computational bonuses

Post by jonah » Mon Jul 13, 2009 4:00 pm

Ben Dillon wrote:Not really sure how the "partial credit" concept somehow got wrangled into this discussion. There is no real analogue to partial credit in quiz bowl, unless you count the idea of prompting when given a partial answer. But I can't conceive of any situations in which prompting on computational math is desirable, let alone kosher.

"Hmmm... the answer is pi, the player gave 22/7... okay, I'll prompt."
Some formats (I forget what the exact IHSA rules on this are, but it might be one of those formats) require prompting if units are omitted, or an equivalent form different from the one the question specified is given (e.g., saying "two to the one half" instead of "root two" or "two point five" instead of "three halves"). Neither of these are desirable in my opinion: the first one basically just penalizes people for not listening to a part of the question that's only artificially being made central, while the second one has been discussed before, to the general consensus that any mathematically equivalent answer ought to be acceptable. Even if I say six halves when I mean 3. They're still kosher according to the rules of the formats in question, though.
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Re: Computational bonuses

Post by jonah » Mon Jul 13, 2009 4:02 pm

Champa Kalhari wrote:
Ben Dillon wrote:But I can't conceive of any situations in which prompting on computational math is desirable, let alone kosher.
How do people feel about prompting on unsimplified fractions? (Current NAQT policy is that they are flat-out wrong.)
I think unless the answer is being given with the intent of delaying the game (a consideration which, if I recall correctly, is already part of several NAQT rules), any mathematically equivalent answer ought to be acceptable. If the answer is 2.5, the packet should have 2.5, 2 and a half, and 5/2 all listed as answers; other ones should be acceptable upon protest (or if the moderator is knowledgeable enough to know that the given answer is equivalent). Similar reasoning should apply to situations involving radicals.
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Re: Computational bonuses

Post by Jeremy Gibbs-Marangoni Effect » Mon Jul 13, 2009 4:06 pm

I second Jonah's assertion that all mathematical equivalents should be acceptable.
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Re: Computational bonuses

Post by grapesmoker » Mon Jul 13, 2009 5:59 pm

I've managed to get through more than 4 years of college-level math and even get a math degree without ever once having done anything like the computation implied by Viete's theorem. While I wouldn't ever sell myself as a particularly good mathematician, I have a fair amount of math knowledge that I've accumulated by way of classes and I don't see a bonus like that rewarding any of that knowledge at all. Moreover, it seems that Kay is arguing that math is mostly about applying theorems to problems, which is a particularly reductionist view of math, but even if that were true, it would only justify such computational bonuses if the problems in question were actually computational. If you're asked to prove a theorem (which is 99% of everything you are ever asked to do in an upper-level math class) you will rarely be doing any extensive computation in the sense of arithmetic manipulation. Rather, you'll be trying to figure out which other bits of your knowledge can be used to construct the proof that you need. For that, you need to be familiar with the theorems in question, which is exactly the kind of things that quizbowl asks about.
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Re: Computational bonuses

Post by Deviant Insider » Mon Jul 13, 2009 6:36 pm

Your view of math is also reductionist. Keep in mind that nobody is arguing for the elimination of theoretical math questions.

High school math is not taught solely for the benefit of students who will become mathematicians, and there is no reason for the math that shows up in high school quizbowl to be different. The high school curriculum is supposed to be helpful for future engineers, scientists, economists, etc. It places a high priority on variables and functions, for better or worse, often in ways that pure mathematicians would find uninteresting. I do not think that the only way to judge a quizbowl math question is to ask whether the question covers a subject that would be interesting to a pure mathematician. If it would be interesting to an engineer, then it might be a good math question.

I have taken an overall courseload equivalent to a math major, and I would be very hesitant to discount something because it did not come up in my courses. I barely scratched the surface of the overall subject, and there are a large number of fields within mathematics I know nothing about.
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Re: Computational bonuses

Post by grapesmoker » Mon Jul 13, 2009 7:09 pm

Shcool wrote:Your view of math is also reductionist. Keep in mind that nobody is arguing for the elimination of theoretical math questions.
I haven't really said what my view of math is. I've pointed out what math classes look like at the college level, which is not simply my view but a factual statement about all the classes I took.
High school math is not taught solely for the benefit of students who will become mathematicians, and there is no reason for the math that shows up in high school quizbowl to be different. The high school curriculum is supposed to be helpful for future engineers, scientists, economists, etc.
So? I'm not going to be a mathematician, and I was never a particularly good theorist. I can do, and have done my fair share of math computation (most of which I've done in physics classes). Nothing I've ever done has placed a premium on being able to quickly do simple computations. That's because most of the computations are just not simple, and the ones that are simple are not important.
It places a high priority on variables and functions, for better or worse, often in ways that pure mathematicians would find uninteresting. I do not think that the only way to judge a quizbowl math question is to ask whether the question covers a subject that would be interesting to a pure mathematician. If it would be interesting to an engineer, then it might be a good math question.
This is a strange view of "pure" mathematics which excludes many areas of math that are heavily applicational but no less "pure." Surely the theory of differential equations is one of the most useful things for a physicist or engineer to know, but I think it would be weird to call that not pure math.

Anyway, that's a stale debate. What I was reacting to was the notion that somehow to "do" math meant to use certain knowledge to compute things within a 5 second window. I just don't agree that this is what doing math is all about, and furthermore I don't think it makes for good quizbowl. You're still stuck with an extremely narrow range of askable computations and you're still rewarding people for basically crunching numbers fast. As pointed out above, if you are going to require performative competence to give people points in math, why not in every category? Diagram this sentence, explain Frank Jackson's arguments for qualia, recite the 48 vows of the Amitabha Buddha!

Let me shamelessly steal from Gilbert Ryle and suggest that in quizbowl there is a distinction between "knowing how" and "knowing that." The category of things that fall under "knowing how" make for bad quizbowl, while (all things being equal) things that fall under the category of "knowing that" make for good quizbowl. If you start demanding that people demonstrate their ability to apply mathematical theorems to problems, you will be trying to shoehorn a math competition into a quizbowl format, and I believe this is a bad idea.
I have taken an overall courseload equivalent to a math major, and I would be very hesitant to discount something because it did not come up in my courses. I barely scratched the surface of the overall subject, and there are a large number of fields within mathematics I know nothing about.
The fact that one has not heard of something is not by itself evidence of anything. But if you spend a lot of time working in some field and then find yourself unable to answer a question about it, there is good reason to suspect that the answer to that question is obscure. At Sun-n-Fun this weekend there was a bonus part on something called the Einstein-de Haas effect (the 2nd most famous thing named for de Haas). Having taken 2 years of solid state physics and not encountered this phenomenon in any depth, I'm deeply suspicious about it being an askable bonus part. I can of course be wrong on the subject of any particular answer choice, but I don't think my suspicion is unwarranted.
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Re: Computational bonuses

Post by First Chairman » Mon Jul 13, 2009 11:23 pm

jonah wrote:
Champa Kalhari wrote:How do people feel about prompting on unsimplified fractions? (Current NAQT policy is that they are flat-out wrong.)
I think unless the answer is being given with the intent of delaying the game (a consideration which, if I recall correctly, is already part of several NAQT rules), any mathematically equivalent answer ought to be acceptable. If the answer is 2.5, the packet should have 2.5, 2 and a half, and 5/2 all listed as answers; other ones should be acceptable upon protest (or if the moderator is knowledgeable enough to know that the given answer is equivalent). Similar reasoning should apply to situations involving radicals.
Speaking personally, I disagree: while I agree with the example that 2.5, 5/2, and 2 1/2 are equally acceptable answers, I think that fractions should always be appropriately simplified. I would not accept 2 and 44/88ths just as I would not accept esoteric answers or "synonymous" answers. "A Tale of Two Cities" is not equivalent to "A Story of Two Cities." Okay, that analogy may be flawed, but another one that could be similar (I argue) is giving me the Russian translation for "A Tale of Two Cities" as an answer.

Should I prompt on unsimplified fractions? If your rules state that all answers must be simplified, then I would hold that you must rule the answer incorrect or else you render the rule moot. Granted, I often would "warn" whenever an answer is not simplified, but if you don't accept square root of 8 for 2 root 2, then you shouldn't accept unsimplified fractions. If your rules state that unsimplified answers will warrant a prompt from the moderator, I can see that as a potential "stalling" tactic, but I also see it as a way to institutionalize a two-answer situation for such questions. Usually, we should prompt whenever the information in the player's answer is noted as not sufficient to uniquely identify an answer and that on prompts, the answer should be EXACTLY as stated. (In other words, you cannot slip up and add/transpose letters in your answers: "Johnson > JohnsTon", instead of "root 8" > "2 root 2".)
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Re: Computational bonuses

Post by Jeremy Gibbs-Marangoni Effect » Mon Jul 13, 2009 11:56 pm

Unless the point of a computational question is to simplify an expression (hopefully not), I see no reason to include rules that disqualify any mathematically equivalent forms. To use Dr. Chuck's example, the square root of 8 and two times the square root of 2 represent exactly the same number. Isn't the value of the quantity given the important thing?
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Re: Computational bonuses

Post by at your pleasure » Mon Jul 13, 2009 11:57 pm

However, because "Square root of 8" and "2 root 2" are the exact same thing, there is no basis for saying that the former is insufficient information when the latter, which is identical and contains the same amount of information, is acceptable. The key difference between your Russian translation example and simplifed fractions is that there is no good reason whatever for giving the Russian translation of " A Tale of Two Cities" unless you want to delay the game or just be a dick. On the other hand, there may be good reasons to give a unsimplifed fraction or radical(say, you're too worried about being beaten to the tossup to bother).
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Re: Computational bonuses

Post by grapesmoker » Tue Jul 14, 2009 12:08 am

Russian dance music wrote:However, because "Square root of 8" and "2 root 2" are the exact same thing, there is no basis for saying that the former is insufficient information when the latter, which is identical and contains the same amount of information, is acceptable. The key difference between your Russian translation example and simplifed fractions is that there is no good reason whatever for giving the Russian translation of " A Tale of Two Cities" unless you want to delay the game or just be a dick. On the other hand, there may be good reasons to give a unsimplifed fraction or radical(say, you're too worried about being beaten to the tossup to bother).
Yeah, this isn't even debatable. It would be completely contrary to the notion of rewarding knowledge to not accept a literally equivalent answer, simplified or not. People don't give answers like 100/50 unless it makes sense in the context of the problem, and if it does and is right, then it must be accepted.
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Re: Computational bonuses

Post by Mechanical Beasts » Tue Jul 14, 2009 1:42 pm

Agree with the above posters; moreover, there are situations like 1/sqrt(2) where math teachers prefer sqrt(2)/2 for reasons unimportant (I guess because they've defined that forms without radicals in the denominator are simpler) whereas 1/sqrt(2) looks just as simple.

This is exactly the same as the earlier discussion of "har har har, I asked for 'odds', suffer my wrath."
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Re: Computational bonuses

Post by kayli » Tue Jul 14, 2009 3:42 pm

Right. I think most of us can agree that 99.9% of people who compete in quizbowl can reduce and rationalize fractions and roots and that it's an unnecessary nuisance to force people to take extra time to simplify which would both take time (with the possibility of not answering the question) and increase the margin of error. I think that the moderators should be able to count answers as stalls whenever instead of saying "one over two" they say "one trillion, one hundred eleven billion, one hundred eleven million, one hundred eleven thousand, one hundred eleven over two trillion, two hundred twenty two billion, two hundred twenty two million, two hundred twenty two thousand, two hundred twenty two."
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Re: Computational bonuses

Post by Mechanical Beasts » Tue Jul 14, 2009 4:13 pm

I think the fact that you'd have to count a technically correct (however insipid and annoying) answer as a "stall" is an argument against clocks, really. Is it a "stall" to say James Abbott McNeill Whistler instead of just Whistler? No, ordinarily; what if saying the full name kills the next tossup? It's just stupid to have to game with the clock.
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Re: Computational bonuses

Post by kayli » Tue Jul 14, 2009 4:53 pm

Crazy Andy Watkins wrote:I think the fact that you'd have to count a technically correct (however insipid and annoying) answer as a "stall" is an argument against clocks, really. Is it a "stall" to say James Abbott McNeill Whistler instead of just Whistler? No, ordinarily; what if saying the full name kills the next tossup? It's just stupid to have to game with the clock.
Well, I was kinda thinking in terms of HSNCT where timing matters, and a 10 second response might have an impact on the game. *Shrug*
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Re: Computational bonuses

Post by Cheynem » Tue Jul 14, 2009 5:17 pm

That's Andy's point--stalling is a silly thing to have to consider in quizbowl and while it is relevant because NAQT uses a clock, I don't think it should be.
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Re: Computational bonuses

Post by kayli » Tue Jul 14, 2009 6:20 pm

Cheynem wrote:That's Andy's point--stalling is a silly thing to have to consider in quizbowl and while it is relevant because NAQT uses a clock, I don't think it should be.
Oh, I see. If there's no clock, then yeah the most annoying of answers should be accepted... with a snear.
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Re: Computational bonuses

Post by at your pleasure » Thu Jul 16, 2009 11:33 pm

Also, a long answer is not always an attempt to be annoying. Sometimes, the full name happens to stick better in one's head than the shorter version.
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Re: Computational bonuses

Post by Jesus vs. Dragons » Fri Jul 17, 2009 2:53 am

Russian dance music wrote:Also, a long answer is not always an attempt to be annoying. Sometimes, the full name happens to stick better in one's head than the shorter version.
I can't say Jewett, it must be Sarah Orne Jewett. Sorry for digression. I don't like math comp.
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Re: Computational bonuses

Post by cvdwightw » Tue Jul 21, 2009 1:57 pm

Forgive me for butting into an old thread, but I haven't had much time to post stuff on the board this past week.

1. I do not believe that mathcalc should be extant (at all) at higher levels of competition. This includes all college-level competition and I'm undecided about the high school national level.
2. Regardless of whether it is or is not bad quizbowl (it almost certainly is, but I'm not going to go there), the concept of "tying the quizbowl distribution to the curriculum" holds strong sway in many states. This means that there is often a disproportionate amount of math relative to what can actually be asked about.
3. The canon of accessible "theoretical" answers at the high school is (roughly estimating) two to three times as large as the canon of accessible "computation" formats. Replacing 4 computation tossups a round with 4 theory tossups just isn't going to happen unless there's a huge explosion in the canon of high school math. Keep in mind that many reasonable theoretical math answers, like "slope-intercept form," are virtually impossible to write a halfway decent tossup on.

Just to counter some arguments in this thread:
A. Harry White argues that including any computation bonus part screws up the easy-medium-hard structure of a bonus. This is incorrect. Asking players to perform a trivial calculation, then asking for the name of the theorem or whatever that gives that result, does allow a medium-easy or hard-medium structure in the same way that asking for a book first, then asking for its author, allows a medium-easy or hard-medium structure in a literature bonus.
B. Jerry argues that college math courses have little to no computation. I'm going to guess that I've taken as many or more applied ("impure") math courses as Jerry, and I agree with him - assigning values to parameters and performing the resulting computation is (if anything) a last step, and I've had that viewpoint reinforced in several science and engineering classes. However, we're comparing tadpoles and frogs here. I'm going to guess that I've taken as many or more high school math courses as Jerry, and that is not at all what high school math courses look like. High school math courses have computation up the wazoo, even and especially if it's trivial and boring. Maybe I'm just a JR Barry proxy, but I don't find the "that's how it's done in college" argument compelling for arguing why stuff shouldn't be in regular and lower level high school quizbowl.
Dwight Wynne
socalquizbowl.org
UC Irvine 2008-2013; UCLA 2004-2007; Capistrano Valley High School 2000-2003

"It's a competition, but it's not a sport. On a scale, if football is a 10, then rowing would be a two. One would be Quiz Bowl." --Matt Birk on rowing, SI On Campus, 10/21/03

"If you were my teammate, I would have tossed your ass out the door so fast you'd be emitting Cerenkov radiation, but I'm not classy like Dwight." --Jerry

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Mechanical Beasts
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Re: Computational bonuses

Post by Mechanical Beasts » Tue Jul 21, 2009 2:14 pm

cvdwightw wrote: B. Jerry argues that college math courses have little to no computation. I'm going to guess that I've taken as many or more applied ("impure") math courses as Jerry, and I agree with him - assigning values to parameters and performing the resulting computation is (if anything) a last step, and I've had that viewpoint reinforced in several science and engineering classes. However, we're comparing tadpoles and frogs here. I'm going to guess that I've taken as many or more high school math courses as Jerry, and that is not at all what high school math courses look like. High school math courses have computation up the wazoo, even and especially if it's trivial and boring. Maybe I'm just a JR Barry proxy, but I don't find the "that's how it's done in college" argument compelling for arguing why stuff shouldn't be in regular and lower level high school quizbowl.
Well, here's the issue. Implicit in Jerry's argument is "... and college courses more closely mirror what's important and academic than high school courses." If you accept that premise, then it's reasonable that quizbowl ought to respond to a "that's how it's done in college" argument.

I think Jerry was merely trying to refute the notion that there is "classroom math" that involves mathcalc and "real math" that does not, since there are [college] classrooms that don't involve mathcalc. (That notion, were it to stand, would make the "tie it to the curriculum" argument more powerful, I think.) Instead we have a state of affairs where high school math does, regrettably, include mathcalc and does, regrettably, have a bunch of problems.
Andrew Watkins

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