Computational math in high school quizbowl

Dormant threads from the high school sections are preserved here.

What role does computation have in HS quizbowl?

No role whatsoever.
15
21%
Less than the status quo.
29
41%
More than the status quo.
10
14%
The status quo.
17
24%
 
Total votes: 71

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Computational math in high school quizbowl

Post by theMoMA » Fri Jul 20, 2007 10:27 pm

The thread on ideal high school distribution got me thinking about computational math and its place in high school quizbowl. I think it has no place.

-Pretty much all data has shown that the conversion rates for computational math are far below the conversion rates of other categories.

-Computational math does not lend itself well to good tossups. They are generally apyramidal and go dead too often.

-Computational math does not lend itself well to good bonuses. Such bonuses are converted at much lower rate, and can swing matches unfairly. They also tend to test on the same concept multiple times instead of testing differentiated levels of knowledge.

I certainly understand why question companies include a math distribution. Some places demand it, and many can't see quizbowl without it. I'm not crusading to eliminate computation (though I think the would would be a better place with it gone), I just want to question why a topic that is so likely to go unconverted that just doesn't fit the tossup/bonus format is such a staple of high school quizbowl.

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Post by BuzzerZen » Fri Jul 20, 2007 10:36 pm

Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
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Post by Auks Ran Ova » Fri Jul 20, 2007 10:39 pm

Not soon enough.
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Post by Matt Weiner » Fri Jul 20, 2007 10:41 pm

BuzzerZen wrote:Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
something about my cold dead hands

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Post by theMoMA » Fri Jul 20, 2007 10:49 pm

BuzzerZen wrote:Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
1/1 Veterinary medicine? 1/1 accounting? 1/1 electrical engineering?

Computer science is for the most part a practical discipline; it is not required for the typical education and it is not generally recognized as knowledge that a well-rounded person should know. I think it's pretty generous that there is any computer science at all, and I'll leave it at that.

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Post by First Chairman » Fri Jul 20, 2007 11:08 pm

Actuarial science 1/1

The best "show killer" on television is a category round of math calculation questions. We do not teach students how to calculate with a few spotlights on them, a television camera to record their performance, and a game show host with a green jacket asking them the problem with no clue how to interpret an equation properly. There are ways to do calculation questions, and I prefer the collaborative way (bonus questions or worksheets) rather than individual tossups which have greater chance of dying a horrific and silent death.
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Post by Captain Sinico » Fri Jul 20, 2007 11:48 pm

I guess I'm not a big fan of rote computation-based math myself in general, given how deemphasized it is in "the real world." That said, it continues to occupy an important part of most every high school education, so, in spite of the fact that it tends not to make for good quizbowl, I can understand how people would want it. Therefore, I think the best position is to include it to some extent and to do the best one can to make good quizbowl out of it (which can be done to a greater or lesser extent.)

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Post by Captain Sinico » Fri Jul 20, 2007 11:49 pm

BuzzerZen wrote:Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
When everyone in high school takes a real computer science course? I really can't think of any good fraction of 20/20 good, answerable computer science questions at that level.

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Post by Irreligion in Bangladesh » Sat Jul 21, 2007 3:25 am

Given my experience in Illinois, I can pretty safely say that if you train someone to compute for quizbowl purposes, they'll do it. At the moment, the national status quo for computation isn't enough to convince teams that they need their fourth player or whoever to be a computational ace - that likely explains the subpar conversion rate.

Computational math is not only non-pyramidal, but it is a different test than every other question in a packet. Every other subject is quick recall off of a fact. Computation is quick recall of a process, then carrying out that process. In an analogy that stretches a bit, the equivalent for literature would be writing an essay. In a more apt observation, computational math is simply not in tune with the rest of quizbowl. Computational questions change the flow of the game in the same manner that lightning rounds between halves of a tossup-bonus format change the flow of the game.

The "high school curriculum" argument can be used here, but that doesn't help quizbowl. What would help quizbowl is to treat math like a science instead of an outlying category. Give it 1/1 or slightly less in the science distribution, and make it about the same style of topics that are found in other science questions.

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Post by porcupine » Sat Jul 21, 2007 1:13 pm

I am a fan of computational math questions. I think that they do reflect a skill necessary in the real world and are therefore justified, but at a rate of approximately 1 per set, not 2 or 3 as has been seen before. However, I will admit that I am biased in their favor as I tend to do really well on them at NAQT.

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Post by AKKOLADE » Sat Jul 21, 2007 1:30 pm

I believe computational math should not be used in quiz bowl, since it tests a different set of skills (the ability to quickly perform operations) compared with other questions (the ability to recall knowledge, not how to apply that knowledge).

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Post by jhn31 » Sat Jul 21, 2007 3:02 pm

I think all subjects should be covered, including computational math.

As for pyramidality, at our self-written tournament at MSU, we didn't even try to make them pyramidal and told teams "All questions are pyramidial, except for the math questions which will be preceded by 'Pencil and Paper Ready.'"

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Post by Deviant Insider » Sat Jul 21, 2007 4:42 pm

Computational math and computational science should be in quizbowl. They are major subjects in all high schools, and (unlike foreign languages) fair and interesting questions can be written with them.

The fact that conversion rates are lower is not a valid reason to eliminate them unless you are also in favor of getting rid of social sciences, which also get converted less than other subjects, and in favor of more pop culture, which gets great conversion rates. There is room in a 20/20 (or 9-minute half) match for questions with low conversion rates. Additionally, if teams know that there will be a significant amount of math questions throughout the year, then they recruit and retain students who are good at math and practice math, and then they convert math questions.

Though their pyramidality is different than noncomputational questions, that does not mean that they are not pyramidal. Teams that are better in math generally answer the questions before teams that are worse in math, just like teams that are better in literature generally answer those questions before teams that are worse in literature. Nonpyramidal questions test thumb speed, which is not what computational questions test.

Good computational bonuses can be written. It is easier to write them in Illinois format, where the entire bonus is read, teams have thirty seconds to work, and the controlling team then gives all their answers.

If teams are used to computational questions, they do not interrupt the flow of a match. We in Illinois are used to them, and our rhythm gets thrown off when such questions are not used.

If math is a show killer, somebody will have to explain why MathCounts has been on ESPN but not Quizbowl. As has been discussed on other threads, good quizbowl itself is a show killer, but we love it anyways.

Math is different than other subjects, but that is not necessarily a bad thing. Science is different than other subjects as well--it requires more conceptual understanding and less knowledge about stuff people did in the past--but that is not a reason to get rid of it or lessen it.

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Post by theMoMA » Sat Jul 21, 2007 5:24 pm

Math is obviously taught in high school, but in general computation is the means to understanding the framework, not the thrust of an education in mathematics. Questions should be on the framework, not the gruntwork. Questions on the parallel line postulate, vertical angle theorem, fundemental theorem of algebra, Stokes' theorem, etc. accomplish what computational math questions do not: fairly represent a large portion of the high school curriculum in a way that fits the quizbowl format, tests more accurately for understanding of concepts as opposed to rewarding the antiquated skill of paper calculation, allows people who are not good at math to learn it and understand it instead of practicing said antiquated skill, and most importantly, facilitates conversion rates roughly on par with other categories.

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Post by grapesmoker » Sat Jul 21, 2007 5:55 pm

theMoMA wrote:
BuzzerZen wrote:Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
1/1 Veterinary medicine? 1/1 accounting? 1/1 electrical engineering?

Computer science is for the most part a practical discipline; it is not required for the typical education and it is not generally recognized as knowledge that a well-rounded person should know. I think it's pretty generous that there is any computer science at all, and I'll leave it at that.
People take computer science in high school; I took 2 years of it, and in my high school it was one of the most impacted courses. People who talk about computer science being mostly a "practical" discipline like accounting are woefully misinformed. Serious computer science is more plausibly a subset of applied math, which is why real CS people complain about tossups about which symbol represents comments in bash scripts or whatever.
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Post by theMoMA » Sat Jul 21, 2007 6:50 pm

Appropriate computer science answers at the high school level are going to tend to be on the practical discipline side of things, not the mathematics that make CS a legit subset of the college science distribution.

Students take all sorts of classes in high school on things that are practical but inappropriate for quizbowl. I'm not going to sit here defending blender tossups because home ec exists, or push for a 1/1 bandsaw distribution. CS is at best a high school elective, and most likely even then the curriculum lends itself to the "what character does what" instead of meaningful science.

I am not calling for no CS at the high school level. I'm just saying that the current amount is probably even a little generous given the nature of CS education in high schools.

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Post by grapesmoker » Sat Jul 21, 2007 7:48 pm

theMoMA wrote:Appropriate computer science answers at the high school level are going to tend to be on the practical discipline side of things, not the mathematics that make CS a legit subset of the college science distribution.
Appropriate high-school level CS question topics include things like basic data structures, the key features of object-oriented programming, simple algorithmic analysis, and maybe even a little bit about Turing machines and other significant automata, as well as elementary graph theory. All of these are covered in the high school curriculum to some extent and yet are based on a lot of interesting mathematics that can be used as a leadin clue.
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Post by Ben Dillon » Sat Jul 21, 2007 9:14 pm

I guess I'll put my vote in for the "high school curriculum" argument. To me, mathematics should be included as separate from science because it is separate in the curriculum of almost every high school in the nation. I won't go so far as to say that the questions necessarily need to be computational, but I don't think that the computation needs to be excised from the questions either. (I have been struggling with the apyramidal nature of computational questions, though... gotta be a way to do this without describing how to solve the problem while people are trying to solve the problem.) History of math questions seem entirely appropriate as math questions to me, btw, e.g. Galois was killed in a duel.

As for things like computer science, it falls under that broad heading of "electives". I think it valid that a distribution include electives, but they don't always have to be the same ones. To me, electives include things like computer science, home ec, and theology. So a 1/1 or 2/2 electives distribution seems perfectly fine to me as long as it's not pinned down to specific electives like computer science for every distribution.

High schools are moving to have courses like "Film Appreciation", so questions involving "Mr. Smith Goes to Washington" should be following this trend, moving from the Trash pile to the Elective pile.
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Post by Strongside » Sat Jul 21, 2007 9:33 pm

I believe that computational math should be present in high school quiz bowl, but its emphasis should be decreased. An example of this is instead of having 2 or 3 computation tossups in a packet, to have 0 or 1 tossups. Instead of computational math, aksing questions about math terms or concepts or some other subject would be better.

Some of the computation tossups are silly or impractical. It can be frustrating in a match between two good teams to have a computation question or two that leads to "dead air" and interrupts the flow of the game.

In high school I had a neutral opinion to paper and pencil questions, I didn't hate them, but I didn't love them either. Now that I am in college I do not miss paper and pencil questions.
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Post by cvdwightw » Sun Jul 22, 2007 2:07 pm

I have two very general opinions on this subject:

1. Computational math has a place in the high school canon.
2. Some formats have way too much of it.

I base my opinions on the following:
1. Most quizbowl playing high school students will take 4 years of mathematics, to be divided between Algebra (I and II), Geometry, Trigonometry, Math Analysis, Calculus, and Statistics. I find this both an important and reasonably varied part of the high school curriculum (as opposed to, say, Fine Arts, which is usually performance-based for 3 out of 4 years if 4 years are taken). A large part of this is computational (e.g. it doesn't matter if the student knows what Cramer's Rule is if the student can't use it), using mostly real-world numbers (as opposed to upper-division college math, which uses mostly variables that can stand for anything). Also, a decent amount of science at the high school level is computational. I would not hesitate to group this with computational math, as it pretty much amounts to word problems with a scientific context. The ability to do computational math is a vital one at the high school level, and since the high school course structure is more rigid than the college course structure, I find it slightly easier and more relevant to use the "what's learned in the classroom should be at least somewhat reflected in quizbowl" argument.

2. For the reasons most people have already stated, it is difficult to write good, pyramidal computational math questions. However, I don't necessarily think mathematics questions need to be as pyramidal as other questions. Compare "For 10 points, name the country with capital Kabul" with "For 10 points, find the line perpendicular to y = 3x - 2 passing through the point (4, -2)". One of these will produce an instant buzzer race; the other will often require several seconds of people working on the question before a buzzer sounds. If it were the case that these math questions would produce buzzer races, MathCounts would be pretty boring to watch and frustrating to compete in. However, the ability to calculate whatever needs to be calculated as before other people is similar to the ability to recognize a clue in, say, a literature tossup before other people. Thus, I like jhn31's idea of telling teams every question but the math ones will be pyramidal, because the math questions by their very nature are slightly pyramidal. This having been said, it certainly does not translate very well into a quiz bowl format, and too many of this kind will break up the flow of the game. Four computational tossups are just way too much.

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Post by Sen. Estes Kefauver (D-TN) » Sun Jul 22, 2007 2:50 pm

2 things.

I can confirm that computer science IS NOT always a part of every high school curriculum. I go/went/whatever to a school that to the best of my knowledge offers no computer science class without doing dual credit at the local VoTech. The most we get is keyboarding class (and this is a large semi-urban school, too)

Other thing - while in a way it is always arguable that math creates its own pyramidality, that is a flawed argument. It creates its own tests of speed is a much more accurate way to put it. We have a kid on NKC who is amazingly fast at math. He has a very number-oriented brain that is kind of scary to be around. However, when he powers math tossups that are at the Algebra 2 level or below, I generally also know exactly what is going on with the question - however, I just have a brain that is pretty much uncapable of calculating any actual numbers (I once said that there were 400 years between 1600 and 1900). When it comes to knowledge of how the math works, I know as much as this kid, he just has an ungodly talent for cranking out the actual numbers in his head. I wouldn't argue that him being able to answer the calculations faster than me always means he knows more about the math. Infact, often I am the one who gets the math theory questions. So I don't think that argument works.
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Post by dschafer » Sun Jul 22, 2007 3:20 pm

Necessary preface to every post I make in a math related topic: I like math.

I think a key point here is what kind of math we are talking about. There is non-pyramidal math, certainly: "What is 123*456?" is a short, non-pyramidal question, just as "Who wrote Hamlet?" is a short, non-pyramidal question. On the other hand, it is certainly possible to write good pyramidal math tossups.

Next, a computational math tossup should never make someone think "Man, I wish I had a calculator right now." Numbers should be small enough that a calculator would actually slow you down.
theMoMA wrote:-Pretty much all data has shown that the conversion rates for computational math are far below the conversion rates of other categories.

-Computational math does not lend itself well to good tossups. They are generally apyramidal and go dead too often.

-Computational math does not lend itself well to good bonuses. Such bonuses are converted at much lower rate, and can swing matches unfairly. They also tend to test on the same concept multiple times instead of testing differentiated levels of knowledge.
Just as in any other subject area, pyramidal math computation tossups need to be written so that the people with deeper knowledge get the answer sooner, and people with less substantial knowledge should get the quesiton later. Additionally, math tossups should not go unanswered any more than any other type of tossup should. For reference, here's a math tossup I wrote for this year's JIAT:
JIAT Round 1, question 13 wrote:TOSSUP 13
Pencil and paper ready. A garden is in the shape of an isoceles triangle with side lengths 10, 13, and 13. To determine the area of this garden, one could use Heron’s formula, or one could realize that the altitude of the triangle to the side of length 10 can be found using a Pythagorean Triple. FTP, find the area of a triangle with side lengths 10,13, and 13.
60

BONUS 13
FTPE, find the area of the following triangles:
10: A triangle with sides 6, 8, and 10.
24
10: A triangle with sides 9, 40, and 41.
180
10: A triangle with sides 4, 4, and 4.
4sqrt(3)
Ideally, on the tossup here, everybody should have a decent drawing of the triangle by the end of the first sentence (if you don't, why not?). Someone really familar with finding triangle areas will drop the altitude to the base immediately; someone less famiilar would only do so after the question mentions it. At that point, the altitude is the ? in a 5-?-13 right triangle (again, this is mentioned); which should give 12 immediately. Now, you have the base and height of a triangle, and you are done. This tossup is gettable by the time "area" is said.

What would happen with this tossup in a tournament? I don't have stats on me, but most people won't draw the triangle. Once the triangle is not drawn, they will stop listening to the tossup, which means that despite the fact that the method is given in the middile, nobody will even attempt to solve it, and it will go dead. So, why does this occur rather than the ideal situation? I really have no answer here.

Now, on to the bonus. The first one is gettable by anyone who can recognize that 6-8-10 is a right triangle; the second one the same, but with a much more obscure triple. The third one requires either knowledge of the formula for area of an equilateral triangle or some quick cleverness in dropping the altitude. The average on this bonus would be around 13, I suspect; few teams (I hope) would 0 it, and teams with better math knowledge should 20 or 30 it.

This question, I personally believe, addresses all three of the issues in the original post; it is convertable by most teams (if they paid attention to it), it is pyramidal, and it has a bonus that scales in difficulty.

EDIT TO ADDRESS COMPUTER SCIENCE:
theMoMA wrote:
BuzzerZen wrote:Yeah I know we all like having a math thread once a year, but the real issue is when is 1/1 computer science going to gain popular acceptance?
1/1 Veterinary medicine? 1/1 accounting? 1/1 electrical engineering?

Computer science is for the most part a practical discipline; it is not required for the typical education and it is not generally recognized as knowledge that a well-rounded person should know. I think it's pretty generous that there is any computer science at all, and I'll leave it at that.
Necessary preface to every post I make in a CS related topic: I like CS.

I will, however, argue that the presence of an AP Computer Science test makes it a much more likely candidate for a high school question than the three disciplines you mentioned.

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Post by leapfrog314 » Sun Jul 22, 2007 3:26 pm

What about noncomputational math!?

There often seems to be way too little emphasis on math theory and history; when there is any, it's often screwy and just frustrates real math players. An only slightly paraphrased example:
What do you call a plane which is divided into two open intervals by a line down the middle?
ANSWER: An open half-plane.
Even at PACE (I'm not ragging on PACE, just this one question) there was a question which began
Their Hausdorff
and could have pretty much stopped there.

When can we have more real questions about math as a subject? I understand that math isn't taught the same way science is taught, for example, but then again, I never took a class in which I learned about a single anthropologist.

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Post by Quantum Mushroom Billiard Hat » Sun Jul 22, 2007 3:53 pm

I agree completely with the fact that good computational math tossups can be written. I just want to bring up the point that there are only a few combinations of numbers that are workable in most formats. A question that involves, say, a 5,12,13 right triangle is fine, but there is not nearly as much that can be done to make the question interesting as with a lit or history question. The best computational questions I have heard recently are those that make use of physics formulas, and then explain these formulas later in the question. These end up being fairly pyramidal, since someone who knows the formula will get the question first, but also keep computation a necessary part of the question.

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Post by theMoMA » Sun Jul 22, 2007 4:08 pm

I think the problem with
Pencil and paper ready. A garden is in the shape of an isoceles triangle with side lengths 10, 13, and 13. To determine the area of this garden, one could use Heron’s formula, or one could realize that the altitude of the triangle to the side of length 10 can be found using a Pythagorean Triple. FTP, find the area of a triangle with side lengths 10,13, and 13.
Is that the paraphrase is basically:
Pencil and paper ready. Oblique statement of the question. Method. Recapitulation of the question.
There is basically one "clue" in this question. Why not have a question on Heron's formula, which is a really important thing in geometry and has all sorts of clues that can be applied to it?

To apply this to other categories, imagine if this were a current events question.
Four notorious bombers are housed in the Colorado supermax. One bombed the Olympics in 1996 and some abortion clinics, one was the accomplice to McVeigh in the Oklahoma City bombing, one was arrested for having a bomb in his shoe, and one sent bombs in the mail and was known as the Unabomber. FTP, name these four bombers.
That wouldn't be an acceptable question, yet it follow exactly the format of nearly all "pyramidal" calculation questions.

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Post by Captain Sinico » Sun Jul 22, 2007 4:30 pm

I'd argue that that question has more than one clue, but that the clues aren't very good in that they don't reveal anything substantive about how to get the answer, only the names of methods; in short, they don't really tell the players anything unless they already know it. If, rather than saying "Hero's formula is fantastic!" you note what Hero's formula is and how to use it, then you're getting closer to an actually pyramidal math question. In such a question, if people already know the method, they have an advantage and, if not, then you're telling them something useful to get the answer.
For example, our high school tournament uses computational math tossups and I've written some (they were sometimes too hard, but anyway...) I've tended to try for something more like:
State the problem outright. Give some clues about a couple methods to solve it. Straight-up tell how to solve it by a couple methods. Straight-up tell how to solve it by the best method I can think of. Re-state the problem.

In a question of this type, regardless of your computational skill, if you already know how to solve the problem, you have an advantage and, if you already know the best method I know (or maybe even a better one,) you have a marked advantage. There's still the matter of computing the thing, but it's not all that's at play, or even the most important thing. In fact, it doesn't seem to me all that different from the matter of knowing a clue and quickly remembering the answer. In this way, we can ask comp. math, but shift the balance back towards knowledge and understanding and away from sheer number-crunching ability, which is as it should be both in math education and in quizbowl.
Now, this entails a lot of things. First, I have to be asking a question that isn't so hackneyed that everyone already knows the best way to solve it and also one that isn't so easy that there's no significant difference in the time to compute the answer regardless of how you solve it. Secondly, I have to be asking a problem involved enough that there are a couple ways to solve it and those ways should lend themselves to some kind of sequential revelation. These are serious practical issues of question-writing, but really aren't so different from those encountered with other questions. In this way, I think some pyramidal math tossups can be written (though I prefer not to answer them, myself.)
Another way is to ask a series of related problems with the same answer and arrange them in order of inverse difficulty. This has more practical problems, though, since students can't work a lot of problems at once, so I don't tend to like that kind.

Anyway,
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Post by ScoBo » Sun Jul 22, 2007 5:23 pm

Background note: I am a computer engineering major, and did get a significant number of math questions playing in high school.

Missouri's format includes 20% math, which in a 20-question packet might be fairly reasonable but in Missouri's 50-question format it makes games drag on even longer than they already do.

I think 10-15% is a good range for math questions. I also agree that math history and theory need to be included, but at the same time think the reason that it isn't quite as prevalent is that the range of gettable answers seems rather limited (though the wide range of potential calculation questions seems to contradict this). I learn processes on how to do a computation but don't necessarily remember the theory behind it, which means I might recognize something asked in a theory question but many times will have no idea what the question is actually asking for.

The same goes for computer science - while I know a lot in this area, I find it difficult to write computer questions. It's difficult enough to think of an answer people would be familiar with, then to determine if it's feasible to write a question for it - a lot of times it seems that people would be familiar with a term but when I try to write a question about it I'm unable to do so. I didn't truly learn any theory until my first college course as most of my experience before was teaching myself different programming languages. Even though Liberty HS has over 2000 students, the demand for computer courses is so low that all they really offered when I was there was web programming and courses that teach Microsoft Office.
dschafer wrote:Next, a computational math tossup should never make someone think "Man, I wish I had a calculator right now." Numbers should be small enough that a calculator would actually slow you down.
A very important point. Another thing to remember is math questions are always harder during the game than they seem when you're writing them. This is a major problem for us at Rolla - since most of us are engineering majors, the typical math question seems way too easy so we tend to write questions that are too complex (whether it be describing a complex diagram and asking a question about it, or requiring way too many successive calculations to come up with a final answer).

One notable example involved providing dimensions for the beams and rungs of a ladder. Asking for the total volume at this point probably would have been sufficient for a 15-second computation. But then came "if the ladder is set on fire", giving a volume-per-second burn rate and ultimately asking how long it would take the ladder to be completely consumed by the flames. Of course, this question was so extreme that it never made it to a game packet but there are several examples of questions that are way too hard that make it through and eventually go unanswered in our tournaments.

As for the typical format of a math question, while the Colorado bombers example does effectively highlight how the question is actually structured, I can't really think of a much better way to write them. As for bonuses, bonuses that repeat the same calculation multiple times can get quite boring after a while, but are quite easy to write. Math bonuses that I like to write involve doing successive calculations in multiple parts to come up with some final answer in the last part. The ladder example above could have been written as a bonus, having the first part be determining the volume of a rung, the volume of the entire ladder, and ultimately the time it takes for the ladder to burn completely. This particular example isn't the best bonus but I like computation bonuses more along those lines.
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Post by Matt Weiner » Sun Jul 22, 2007 5:27 pm

I guess my major problem with math questions is the lack of variety. When you have between 15/15 and 30/30 computational math in an NAQT-style set (let alone 50/50 or more in an Illinois-style set), and you're paying attention to the advertised time and difficulty limits of the tournament, then you're basically just going to check off a list of problem types with the numbers changed slightly each time: probability of drawing marbles from a bag, finding the area of a triangle the quickest way, remembering the formula for interior angles of a regular n-gon, etc. Certainly, the elite teams have figured this out regarding NAQT's IS and HSNCT sets and prepared accordingly. It would be boring and somewhat pointless to memorize the same 30 history answers for every single tournament, so why do we put up with it in math?

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Post by First Chairman » Sun Jul 22, 2007 5:49 pm

I suppose the reason is because you can't write more complex math questions than that in a reasonable amount of "quiz bowl" time. The more complicated the math question (akin to an SAT math question), the more time it takes, and the less "quiz bowl" compatible the question.

The thing is that it is so surprising the non-elite teams do not do better with math questions. If it is so predictable, it should be easy to do these types of math questions in a competition context. Instead, computations go completely dead time after time. Shouldn't these be "easy points" in a game context?
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Post by STPickrell » Sun Jul 22, 2007 9:14 pm

In the first couple years I organised VHSL competitions, the math questions were 'dead air.' (I use we from here on as I have not been the regular math writer since 2002, but the math writer follows my directives.)

To get them converted we ended up having to pander to the lowest common denominator (heh, thanks Dr. Barnes.)

I believe in pyramidal math tossups. While it is far from ideal, it is certainly better than seven-word tossups which is what would occur otherwise. We are not going to get rid of computational math from the IHSA, MSHSAA, VHSL, and other distributions, or more accurately, the amount of effort needed to eliminate them would be better put elsewhere.

For VHSL competition, we will attempt to make tossup questions more pyramidal. I have given credit to the TJ and Gov teams as the ones who put everything in place for me to realize things. The era of 'What is 38 times 63?' being the entirety of a tossup is over. If we get the Missouri contract the same thing will occur there.

The directed questions (think bonus questions with bounceback) will be much the same but hopefully for 2008-9 we can start allowing 10/20/30 seconds for math directeds, expanding the realm of what is askable.

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Post by Deviant Insider » Sun Jul 22, 2007 9:57 pm

I agree that computational questions should not have students begging for calculators. I do not agree that they should be written like pyramidal questions.

If you take the JIAT triangle example, any reference to Heron's Formula is not helpful in any way. You're basically saying that some student who isn't good enough in math to draw the altitude of an isosceles triangle should be able to figure out the square root of 18*8*5*5 once they generate those numbers. (I know it can be done by grouping and cancelling factors, or by multiplying each number by the five first, but I don't think it can be done by students who don't know how to draw an altitude of an isosceles triangle.)

It's the math equivalent of:
This President lived in Galena. He had the same last name as the guy who finished 2nd on Wheel of Fortune for the show that aired June 12, 2004. Name this man who was also a successful Union General in the Civil War.

Basically, the more you ignore the middle clue, the better off you are. It doesn't matter whether you mention Heron's Formula by name or describe it, it isn't particularly helpful--the student who gets the answer first is almost certainly going to be someone who draws the altitude. That's not the way it's supposed to work. I don't mean to be particularly harsh with that question, but it's a trap you get with supposedly pyramidal math questions. I would rather just give the question and let the students figure out what the best method is--good students know shortcuts and know when to apply particular methods.

One reason that math questions sometimes go dead is that writers and editors underestimate the amount of time it takes to do math. If you read the JIAT example over several times, you could convince yourself that anybody could do it in two seconds: Everybody knows 5-12-13 triangles, and everybody knows .5*12*10 is 60. In reality, however, such questions much longer: you think about drawing the picture, you make sure you drew it right, you make sure you multiplied correctly, etc. A few students could do it in two seconds, but they are as common as students who can regularly get lit tossups from the first sentence.

I'll also point out to Shawn something he probably already knows. 'What is 38 times 63?' is a bad question not because of its lack of pyramidality--it is a bad question because of its subject matter. It's bad for the same reason that lit questions about Shel Silverstein are bad. I like Shel Silverstein, and I think that multiplication is an important skill, but high school quiz bowl is not the time or place. Quizbowl math primarily should be about algebra (including what is usually in Algebra II and Precalc), geometry, trig, prob/stat, and calculus. Computational questions should measure to at least some extent conceptual understanding.

The best reason I can think of to limit noncomputational math is that the answer space is limiting. Otherwise, it would be fine to have more of it in place of computational math. I do think that there is a good variety of questions that can be asked using computational math.

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Post by jrbarry » Wed Jul 25, 2007 2:28 pm

I think what Mr Reinstein has posted above (in both of his posts) reflects closely to what I think. In that, I will ditto what he said.

I will once again attempt to suggest to the members of this community what someone outside this community might think when looking at this thread. NOTE: THIS IS NOT AN ATTACK ON ANYONE HERE ALL OF WHOM HAVE MADE GREAT DISCUSSION POINTS, IMO, ON THIS THREAD. Nor is this an attempt to shut anyone up on any topic.

Every high school in the US teaches mathematics and most players are going to take 4 years of it in high school. This, of course, is a generalization, but nonetheless I believe it to be true and relevant. So, it MIGHT seem odd that we here are discussing whether computational math has a place in high school quiz bowl or not, or to what degree should we use competational questions. Of course computational math should be included in tournaments.

Now, as several of you have done here, let's figure out two things: (1) How to teach folks to write good math questions or, at the very least, the best ones we can write if some of us already think no really good math question can be written. And (2) the discussion about how many per round/match could continue.

On my (1), I will leave that to people whose expertise exceeds mine both in computing and in questionwriting. (Most of you on this board fall into that community, I am sure.) On my (2), I would say 2 computational tossups and 2 computational bonuses in a 20 T/B set sounds fine to me. That is 10% of the questions in that type of match.

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Post by grapesmoker » Wed Jul 25, 2007 3:46 pm

I would argue that strict computation has no place in a serious math high school curriculum in the first place, much less quizbowl. There's a reason you don't do much actual computation in most physics and math classes; you spend most of your time focusing on applying and understanding concepts. I don't see any good reason why we shouldn't have a computation that applies Heron's formula be replaced with a tossup whose answer is Heron's formula.
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Post by Captain Sinico » Wed Jul 25, 2007 3:53 pm

One thing I want to say is that, while I said earlier that I understood why people would want computation, I don't think the fact that a course or body of courses are widely or even universally taken makes them a slam dunk to show up in high school quizbowl, especially if there are other factors at play. For example, most everyone everywhere takes drivers education and a foreign language, yet not many places have questions on those topics. While not all the reasons those topics aren't asked apply to computational math by direct analogy, some do hold.
Also, questions about important math concepts, techniques, history, and other non-computational topics are (or, at any rate, ought to be) just as germane to the math classes offered in high schools as computational questions are. Thus, exclusion of computation is in no way tantamount to exclusion or trivialization of math itself.
There is something that tips my own preference against computational math tossups and that is the fact that computational tossups as currently written do not test knowing/understanding what something is or knowing/understanding how something works as most all other questions do; rather, they test how quickly and accurately one can do something given that they know how to. Further, the bar of things one needs to know how to do is set very low, so the emphasis is very nearly entirely on speed. As I said earlier, though, I don't think this necessarily has to be so; I think math questions can be written that very strongly emphasize knowing how to do the computation and only secondarily reward the speed with which one can actually do it.
So, basically, I see strong arguments for both sides of the issue of including computation, with the (to some extent) open question of whether computation can be made into fair tossups perhaps trumping the pro, at least as far as tossups go.

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Post by Captain Sinico » Wed Jul 25, 2007 4:03 pm

grapesmoker wrote:I would argue that strict computation has no place in a serious math high school curriculum in the first place...
While that may be your position, Jerry, I think you would have to agree that it represents neither the normative actual state of things nor the only consistent positive ideal for them. It seems to me wrongheaded to argue "I believe things should be this way so, though they're not, I say we must all act as though they are." Consider the fates of the various other quizbowl arguments that fit this pattern that various people have made throughout the years.
Also, to make an aside, as a fellow theoretical physicist, I know as well as you do how de-emphasized hand numerical computation is in the world of discourse where math is actually used. I for one walked away from high school feeling that I was at best mediocre at math because the courses I took emphasized computation almost entirely. Given the arc of my career thus far as compared to those of my fellow graduates, I would have to say I was not mediocre at math in the final analysis; I was instead slow and inaccurate at hand numerical computation, a fact which became less and less important as I mastered more and more mathematics. All that said, however, I do not and cannot completely deny the utility of computation, especially as a pedagogical device at lower levels of instruction.

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Post by grapesmoker » Wed Jul 25, 2007 4:52 pm

ImmaculateDeception wrote:While that may be your position, Jerry, I think you would have to agree that it represents neither the normative actual state of things nor the only consistent positive ideal for them. It seems to me wrongheaded to argue "I believe things should be this way so, though they're not, I say we must all act as though they are." Consider the fates of the various other quizbowl arguments that fit this pattern that various people have made throughout the years.
I think you're reading too much into that statement. All I'm saying is this: I've seen plenty of arguments, many in this thread, about why computational math doesn't make for good quizbowl. I've seen no credible arguments for why it should other than that "some teacher might come along at some point and say, 'we teach computation in high school and therefore this should be in quizbowl.'" I'm not saying that teaching people how to do practical computation is bad or wrong, but I am assuming that most people who play quizbowl are probably not the kind who are in remedial math courses or need to be tested on the kind of simple computation that's appropriate for quizbowl questions. Moreover, once you get into a decent high school math curriculum, emphasis on computation drops off quite a bit. My geometry and trig classes weren't actually about computing sines and cosines, they were about mastering the concepts behind those terms.
Also, to make an aside, as a fellow theoretical physicist, I know as well as you do how de-emphasized hand numerical computation is in the world of discourse where math is actually used. I for one walked away from high school feeling that I was at best mediocre at math because the courses I took emphasized computation almost entirely. Given the arc of my career thus far as compared to those of my fellow graduates, I would have to say I was not mediocre at math in the final analysis; I was instead slow and inaccurate at hand numerical computation, a fact which became less and less important as I mastered more and more mathematics. All that said, however, I do not and cannot completely deny the utility of computation, especially as a pedagogical device at lower levels of instruction.
Well, I'm hardly a theorist; in fact, I routinely need to compute things on a regular basis, frequently without access to a calculator. Most of these computations are basic operations, which anyone in high school could do just as well as I could. Also, yes, So I don't deny their utility, I'm just saying that I don't see a compelling reason to make computation part of a non-remedial high school curriculum, and by extension, of quizbowl. I think that space in the distribution would be better utilized by asking about the concepts involved in the computations rather than asking people to figure out Pythagorean triplets or remember what the cosine of pi/3 radians is.
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Post by Deviant Insider » Thu Jul 26, 2007 2:25 pm

I understand the arguments that Michael and Jerry are making. I agree that computation drops off as you get into more advanced math and physics courses, and I understand why it is not a part of the college game. High school math and physics resemble college engineering more than they resemble college math and physics.

However, if you want to test somebody's understanding of area, the computational problem given upthread does a better job than a question whose answer is Hero(n)'s Formula. The computational question tests your understanding of the relationships between parts of a triangle and how that relates to the Pythagorean Theorem, whereas a noncomputational question would test your knowledge of the name of the formula, perhaps with some early clues likely to go dead that might test advanced knowledge of its history or relationship to similar formulas.

Even though I panned one aspect of the question before, it is a good question overall and tests mathematical understanding better than a noncomputational question would.

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Post by BuzzerZen » Thu Jul 26, 2007 2:40 pm

I think the people who are saying things like "computational math should have a comparable distribution to history because high school curricula focus on those things" are begging the question. It hasn't been established by any means that good high school quiz bowl should parallel the high school curriculum. In fact, it demonstrably does not do so in many instances, and I don't think it needs to.
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Post by Frater Taciturnus » Thu Jul 26, 2007 3:15 pm

BuzzerZen wrote:I think the people who are saying things like "computational math should have a comparable distribution to history because high school curricula focus on those things" are begging the question. It hasn't been established by any means that good high school quiz bowl should parallel the high school curriculum. In fact, it demonstrably does not do so in many instances, and I don't think it needs to.
I have to agree with Evan here. I don't think many of us have high schools that cover trash, among other things. I'm not the biggest fan of computational math, but I do believe it has a place. I'm fine with the use of good, well-written computational math. If said math is what is being used, I have no problem with it. The ones where students such as Palmer, from Gov, are struggling to the end to find an answer, or worse even have a clue of what to do, are the parts that I take issue with.

Perhaps instead of 5/5 decent computational math, going towards 1/1 or 2/2 good computational math would be a viable solution.
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Post by Saiem » Thu Jul 26, 2007 3:50 pm

As someone else said in a previous post, my problem with the compuational math questions is the lack of variety. If you memorize how to do the 15 or so odd math questions that they love to ask, you can proclaim yourself a quizbowl math expert. Don't worry, we'll all applaud. There are a number of computationally simple topics that could be used in quizbowl. Theres such a great emphasis put on combinatorics and probability or simple geometry. Personally, the computational math heavily benfits me and my team. Quiz Bowl is my second passion. I was far more involved with math and Mu Alpha Theta (math competition.. really big in FL). I am a USA Math Olympiad qualifier and it is utterly ridiculous how question writers have no grasp on what is too difficult or too easy to do in ten seconds. I do my best, and I'll convert about 4/5 of all the computation tossups (whether science or math) with a large percentage of those being powers. However, I'll often find myself more confused by the probability questions, because they are far too wordy. What concerns me is that on those particular questions there is next to no pyrimadality.

Topics I think ought to be included in computational math:
Calculus (Slope of the tangent line, Newton's Method, Find the nth derivative, etc)
Analytic Geometry (i.e. Find the area of the ellipse, Find one of the Foci, Find the length of the Latus Rectum, Find the Eccentricity, etc.)
Matrices/Linear Algebra (Cramer's Rule, Systems of Equations, Find the sum of the trace, Find the determinant of special matrices [Jordan-Block, Vandermonde, diagonal, upper triangular, etc], there are many many questions you could ask about Matrices)
Number Theory (Find the number of factors, Find the sum of the factors, Find the number of positive solutions to this diophantine equation, Find the mod 11 of this number, Base conversion, number of zeros at the end of 99!, etc.)
Set Theory (Find the number of subsets, Cartesian product, etc.)
Discrete (Some really interesting logic question, alot of theory type things, etc.)
Sequences/Series (These are the most intuitive types of questions, they're both usually not computationally intensive, and relatively simple conceptually)
Trig/Polar (pretty easy stuff, just not well tested. Conversion wouldn't be that hard)

There are some questions that for computation's sake are pretty interesting. i.e. What is 92*88 = (90+2)(90-2) = 90^2-4^2 = 8100-16=8084

Thats just pure thinking over brute force.

However, as much as I love to complain about the quality of math questions, I like the current distribution in NAQT to about 1/1 or 2/2 of Math Computation. I could definitely use alot more variety. I feel like my talent is being wasted on buzzer beating questions as opposed to where I could get the question powered while it would take the other team the full 10 seconds (since they wouldn't know the immediate way to do it). A few more interesting theory questions would be fun.

Comp sci: Pet subject of mine. I don't see it having a significant place in HS quiz bowl.

I assure you all, I am not bragging about myself being good at math, but I really don't appreciate doing the same problems over and over again. More often than not, getting math questions is more about practice than knowing math. I'm pretty disappointed that more teams say "Skip the math, I suck at it" When its very well true that they just don't care to practice it.

EDIT: I think people could try to add to the canon by writing questions that are trivialized by relatively off the normal track theorems for mathematics, but still doable by regular methods. It'd really reward someone who is really good at math on a level much higher than Quiz Bowl.

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Post by Gautam » Thu Jul 26, 2007 4:35 pm

SaiemGilani wrote:If you memorize how to do the 15 or so odd math questions that they love to ask, you can proclaim yourself a quizbowl math expert. Don't worry, we'll all applaud.
I am in total agreement with that.
SaiemGilani wrote: it is utterly ridiculous how question writers have no grasp on what is too difficult or too easy to do in ten seconds. I do my best, and I'll convert about 4/5 of all the computation tossups (whether science or math) with a large percentage of those being powers
I will agree with that, too. Trevor and I managed 75% conversion (maybe more) and a lot of the times, there were really silly "find the product of these two numbers" or "volume of a cube" blah blah questions, which were very easy powers.
SaiemGilani wrote: However, I'll often find myself more confused by the probability questions, because they are far too wordy. What concerns me is that on those particular questions there is next to no pyrimadality.


I find myself in the same position. Trevor gets a lot of the probabilty stuff, but then again, he's pretty good at it. I get lost trying to understand what's being said, and like the saying goes, I am bad at English (i.e. I misunderstand the clues). That said, I thought there were way too many probabilty/combinatorics questions at HSNCT this year, and I grew tired of them after the second round. The only question I remember powering at the HSNCT was one with 37 miles as the answer, which was pretty ridiculously written. I basically predicted the question by the 2nd clue whereas one would need the third clue to actually compute the answer. Also, most of the times the questions were read so fast that i couldn't even make mental notes of the facts provided. I do much better on untimed rounds where there isn't a giant gorilla chasing the reader (do others have the same problem?). I feel like NAQT should make 22 tossup rounds a standard, and do away with the 9 minute halves to better accomodate the math questions.

Topics I think ought to be included in computational math:
ANYTHING that can be asked in the first 15 questions on the AMC 12 or the first 2 questions on the AIME that doesn't require a toooo much thinking.

I would like to see tossups that invoke more geometry theorems and trig stuff. There were more of them in the 2002-03 and 03-04 packets, if I remember correctly. Using Euler's phi-function makes for a good tossup, I think, but it's never been used before AFAIK. Two thing that should be done away with: ANYTHING that involves making decimal approximations and EVERYTHING that involves logarithms and decimals. Those questions are so stupid that I have answered them by guesswork most of the times.

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Post by Bigfoot isn't the pr » Fri Jul 27, 2007 6:33 pm

Warning: I am not a big fan of computation.

However, that does not mean that I do not like math. I have computation tossups. If its anything outside of level 1 packets the works "Pencil and Paper Ready" translate to "Lay back and hope that one of your teammates gets it". I greatly prefer tossups on theorems or mathematicians or concepts like that. I love (and have a decent chance of getting) questions about the four color map theorem or traveling salesperson problems. Mind you those examples only demonstrate a small portion of what could be part of a "math" topic.

I would prefer a distribution of something like 1/1 (or even 2/2) "math" per packet. "Math" would include computation, questions about mathematicians, questions about theorems, concepts, all that math jazz. Now I know that won't be popular, but that would be my ideal distribution of the math business.
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Post by The Atom Strikes! » Sun Jul 29, 2007 6:34 pm

I would say that computation should be generally decreased, and that questions should use non-calculator numbers, as Quizbowl is really a game to test knowledge (ie: understanding concepts), rather than g, or raw computational ability.
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Post by gonzagaeagleahy » Mon Jul 30, 2007 12:53 am

This is a poesronal jount thosugh but i havete having probaltily problems. I want more calucsulsu.
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Post by DumbJaques » Mon Jul 30, 2007 1:14 am

Dan you should go to the pet store and get a new Leahy this one drunk posts
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Post by Sen. Estes Kefauver (D-TN) » Mon Aug 13, 2007 1:23 am

So I certainly want more calucsulsu.

Anyway, I was thinking today as I was editing some questions and I'm trying to decide how much time a math calculation warrants. My teammate submitted tossups that all said "you have 15 seconds" which is the Missouri state length, but I know some places that do 5 or 10 or even 30. I'm inclined towards 10, but how much do you think math should get?
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Post by Saiem » Mon Aug 13, 2007 10:27 am

10 if you know the question before the question is over. I like alot of NAQT style where they ask the question, and then tell you how to solve it, allowing you to still potentially get power if you know how to solve it.

Otherwise, I'd go with 15. Just a personal opinion.

If the question is like "28 is an awesome number. It holds alot of special attributes. What is the sum of the positive factors of 28?"

A question in that style should warrant 15 seconds if it isn't completely stupid.

However a question like "Billy wants to find the cosine formed by the two vectors <3,4> and <5,12>. Billy can do this by taking the dot product of the two vectors and dividing by the magnitudes of both vectors. For ten points, What is the cosine between the two vectors?"

This would warrant 10 seconds since a person who knows whats going on will be done by the word magnitude, and anybody who knows math will be able to get 10 points at the end of the question.

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Post by theMoMA » Mon Aug 13, 2007 10:55 am

SaiemGilani wrote:However a question like "Billy wants to find the cosine formed by the two vectors <3,4> and <5,12>. Billy can do this by taking the dot product of the two vectors and dividing by the magnitudes of both vectors. For ten points, What is the cosine between the two vectors?"

This would warrant 10 seconds since a person who knows whats going on will be done by the word magnitude, and anybody who knows math will be able to get 10 points at the end of the question.
Sums up everything wrong with computational quizbowl right there?

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Post by Irreligion in Bangladesh » Mon Aug 13, 2007 10:58 am

Illinois allows 30 seconds, and as a result we've seen questions on things a lot tougher than you'd expect elsewhere. One reasonably written tournament that I've been to has featured tossups on volume of a solid of revolution and area between two curves - both concepts I can't see, say, NAQT doing with 10 seconds unless they're purposely easy (volume of a sphere, area between a curve and a horizontal line that isn't the x-axis).

Those questions are really the only times I've seen all 30 seconds used by a good math player. Generally speaking, if a good math player is in the game, they'll get an Illinois math tossup within the first 10 or 15 seconds, if not instantly. If nobody's good at math quizbowl, it doesn't matter if you give them 2 minutes, they'll just sit there, not caring, for the most part.

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Post by theMoMA » Mon Aug 13, 2007 11:19 am

The last two posts warrant a response. Math quizbowl not only fits into the format of the game poorly, it's also often very poorly written. When I said that a previous post sums up everything wrong with math quizbowl, I wasn't joking. The post directly preceding this one merely proves it's no anomaly.

The problem is that people write hard math, then assume that "anybody who knows math will be able to get 10 points at the end of the question." The cold, data-supported fact is that there just aren't a whole lot of people who are going to be able to do the easiest dot product in 15 seconds, even if you tell them they have to do it. Hell, if the question elucidated exactly how to do a dot product it would still go unanswered at a far greater rate than every other question category at the tournament.

The notion that--regardless of the objective fact that math questions are converted at a pitiful rate compared to every other part of the distribution--giving teams an extra 15 seconds allows you to ask "tossups on volume of a solid of revolution and area between two curves" is downright insane.
Last edited by theMoMA on Mon Aug 13, 2007 11:19 am, edited 1 time in total.

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