Computational Math Crisis!

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Tegan
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Post by Tegan »

I've got a question for players only. I need to write a case in the case manual, and I am torn as to how to write it. Now that a forum exists, I would like to hear from the players:

Situation:
Math toss-up....the answer is: "natural log of 3"

Player buzzes in: "natural log of 3 minus natural log of 1". Moderator refuses to accept the answer based on the fact that it is an understood rule that all computation answers must be in simplest form. The question did not state "give in simplest form", and I have never heard of this rule.

The rules state that a player may give a single piece of additional correct information, and is not just applied to creator-creation situations.

As I see it, there are two options:

1. New rule: All computation answers must be give in simplest form, unless the question calls for another form. I think some old timers think this really is a rule already (it is not).

2. Use the rule as written to apply here. In other words, if the answer is "2", an answer such as "2 plus zero" is acceptable, or if the answer is "5", an answer such as "six minus 1" would be acceptable.

What do you think?

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Post by dtaylor4 »

Nice double post, egan. I played for the team whose travels instigated the ban, and the philosophy of that team is this: games aren't won by playing them, they are won during the days and weeks before. These teams still see the team (and me when they played against us) almost as a deity. For example: when we got the brackets for a local tournament this year, we saw that we would be playing against someone who had played for us the year before. Apparently he had been boasting that without the sophomores (who were busy at the Loyola JV tourney), his team could take us. We went on to hold them to 65 points in a 24-tossup match, 5 of those in the second half. We went on to win our bracket (a whole four teams), claim the top seed, scoring about 500 more than the 2 seed, and repeat as champions. It's so bad that one team just wanted to forfeit to us.

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Irreligion in Bangladesh
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Post by Irreligion in Bangladesh »

In response to the math prompting rule....no.

Long answer...math that is not simplified is not done. If a question asks for circular distance in feet, and you give the answer in radians, both answers may be right, but only 1 would make sense to a moderator without math background.

Your examples show something that would not be logical for this case...if someone answers a log question with ln 3 - ln 1, they would have to be able to compute logarithm questions, and would know that ln 1=0 and to further simplify. The same goes with the other two examples as well.

Anything that would require computation by both player and moderator shouldn't be considered. What if someone gave "The square root of (1 - cos^2 x)" for an answer of "sin x"? The moderator would have to know trig identities...yes, you could ask someone in the room, but then matches get drawn out for extraneous reasons.

Perhaps in some other cases, it could be used, but not in what you have listed. Because of this, it would have to be done on a question by question basis, and would not warrant a rule, only a mention in the manuals.

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Post by Trevkeeper »

I agree. Even if it is not stated in the question, an answer should be in simplest form.

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Post by potato0328 »

While we're somewhat-discussing math question writing, I wanted to bring up my biggest pet peeve of all: math questions that ask you to answer in approximated decimal form. (For example: Find the area of a circle to the nearest hundredth). Ask ANYONE that knows anything about math, and they will tell you that multiplying huge decimals is about the most unpleasant thing in mathematics (especially under a time limit). Could someone inform the powers-that-be that finding the square root of 104 has no place in a scholastic bowl match?
directly from Fremd High School...

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Post by Tegan »

DaGeneral wrote:Nice double post, egan. I played for the team whose travels instigated the ban
Hey, I caught myself and edited that second post into an entirely original post! :oops:

Actually there were a few teams downstate that used to travel regularly, though I forget all of their names.

BUT...that's all changed now!

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Post by Tegan »

styxman wrote: Long answer...math that is not simplified is not done. If a question asks for circular distance in feet, and you give the answer in radians, both answers may be right, but only 1 would make sense to a moderator without math background.
Just to clarify: if the question states: give the answer in feet, and you give the answer in radians, then that is a wrong answer, no questions about it.

My teacm got caught on this. There was no rule anywhere that says the answer must be in simplest form. The question didn't ask for it (even though many questions do). I still believe the rules, as written, were on my side.

That being said, after mulling it over for a few days, I began to realize that there could be a benefit to making it a rule, and removing any future grey areas. If the thought is "simplest form rules, then there needs to be a rule change. If not, I can write a case to interpret the current rules to allow for math to be covered (for those interested, the rule in question is 4-C-2). I tend to think that this should be a rule, but wanted to run it past the informed before deciding how to word things.

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Post by popculture »

[/quote]Player buzzes in: "natural log of 3 minus natural log of 1". [quote]

I remember a question from regionals that went like:
Evaluate the integral dx over x from 1 to 3

The problem requires three pieces of information
1. the antiderivative of dx/x is ln x
2. the fundamental theorem of calculus: the integral of a function is the antiderivative of the upper limit minus the antiderivative of the lower
3. ln 1=0

By answering "natural log of 3 minus natural log of 1", the player skips the third step of the problem. He (possibly she, but girls aren't good at math) clearly did not recognize that ln 1 was 0. This was the focus of the question, if the question writers did not feel it was important, they wouldn't have picked a limit that could be simplified.

Since the question supplied the numbers 1 and 3, simply, regurgitating them without thought was definitely not want the writers wanted.

Granted, there may not be a rule explicitly outlining these circumstances, but any math guy knows that you don't say "natural log of 1," you say "0," just as you don't say "5 squared," you say "25."

Now that this circumstance has arisen, a rule should be made. I propose:
"If an answer is given with an operation unperformed, it is incorrect. Exception: if an operation is generally left undone because it is virtually impossible, such as natural log of 3 or sine of 22, it should be left as is. Also, fractions should be simplified, and radicals should be simplified and/or rationalized, unless stated otherwise."

Otherwise, you are inviting goofy answers like 5 times square root of thirty-six times sin 30, instead of just a simple 15. I don't think anyone wants to hear that answer.

Yes, it would be funny if you were talking about a different question and I just gave a random lecture on evaluating integrals. However, the second part of the post is a direct answer to your question. If a rule like this does not exist, it should. If one doesn't I'm never simplifying again.

Maybe we could get Reinstein's "friends in high places" to help us out.[/quote]

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Post by steven-lamp »

popculture wrote:
(possibly she, but girls aren't good at math)
Nice one there, Lawrence.

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Post by jewtemplar »

Obviously, virtually impossible is hard to define. The trig functions of an angle of any integer number of degrees can all be found using the appropriate formulas. In a world of moderators who know math, I think there is no reason for simplified answers to be required. Obviously, if writers require simplest form, then simplest form is all that is acceptable, but the whole notion of simplest form is kind of fuzzy. Sorry for digressing into a discussion about the nature of computation questions, but:
If you are seeking to test knowledge of math, and not what is learned in math class, then simplification just doesn't matter. If the question is about anything but arithmetic, then the knowledge doesn't depend on arithmetic. Standard forms for solutions are arbitrary, nonuniversal, and often counterintuitive. Practical limitations aside, requiring simplified answers is just making a rule for the sake of making a rule. I find that pointless. Obviously, the logical conclusion of such a debate is a call not for stricter rules, but for math questions of higher quality. Just thought I'd pipe in for no reason, although I think this issue has come up before...

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Post by solonqb »

I think the ground rule here should be that the moderator should not need to do any extra thinking to parse the answer given with the answer on the paper (in all subjects, not just math), but for math nothing beyond ridiculously easy simplification (like basic fraction to decimal, etc.). Many moderators nationwide are volunteer parents or students, and we can't expect them all to have taken precalculus or remember their algebra II.

I agree with Sam that simplification can often be arbitrary and counterintuitive (like rationalizing the denominator of radical fractions). That particular case is arguable, but I think the guiding principle above calls for the use of simplest form.
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Post by Irreligion in Bangladesh »

I have found the analogy I've been looking for...

If you buzz in on "Who wrote Innocents Abroad?" with Samuel Clemens, you have given a name, and not the commonly accepted pen name. Will a question provide Clemens or Twain for the answer? In most cases, Twain is universally accepted, and Clemens is accepted as an also-acceptable answer, but only in some question sets. Generally, you could argue that Clemens was Twain, but you could counterargue that the name on the cover is Twain, not Clemens.

For a more obscure question, author of Middlemarch? I haven't heard anyone say Evans yet. 1984? Blair hasn't come up. I could ramble for days on this...

The question sets I've seen don't accept more obscure pen names for authors. Why should more obscure answers, answers that don't necessarily have to do with the question (6-1 for an answer of 5 being accepted when the question is "What is the square root of 25?" doesn't make any sense at all, just a connotation of smug condescension) be accepted simply because math is naturally ambiguous?

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Post by popculture »

jewtemplar wrote:
"In a world of moderators who know math, I think there is no reason for simplified answers to be required."

Good point. I completely revise my stance. This conversation is perfectly acceptable.

Moderator: What are the solutions to 2x squared plus 5x minus 3 equals zero?

Player: [buzz] Minus five plus or minus the square root of the quantity 5 squared minus 4 times 2 times 3 end quantity, all over two times two.

Moderator: Correct.

But not only is this a "world of moderators who know math," but it is also a world where moderators know literature. This conversation should also be acceptable:

Moderator: Who wrote Oliver Twist?

Player: [buzz] The man who wrote Nicholas Nickleby.

Moderator: Correct.

Because these answers are factually correct, they should be accepted. It's a good thing our moderators are so knowledgeable.

Bottomline: Just do the freakin' operation, if you can't do that, don't buzz in.

Dogbert once said, "Sometimes sarcasm makes us think clearer."[/i][/list]

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Post by jewtemplar »

The fact that mathematical computation is naturally ambiguous is a powerful argument for the removal of calculation questions from all distributions. While smug, condescending answers should be discouraged, I don't think an argument could be made for rejecting an answer based solely on that.

And styxman, the inferior question sets you are mentioning don't provide any reason that answers to math questions should be restricted. Failing to accept Clemens or Blair or Evans is simply and inarguably wrong. When asking about a person, the idea is to identify the person, and Samuel Clemens identifies the man just as well as Mark Twain does, whatever the book jacket says.

Maybe what I'm saying is that question writers need to provide as many acceptable alternative answers as possible. With good writers, such incidents rarely occur, and those that do won't take much time to resolve.

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Post by Irreligion in Bangladesh »

Thumbs up to popculture. I believe this settles this argument quite well.

ETA: Illinois questions use calculation questions, and the only steps the IHSA has shown they will take are steps backward. Math calculations are not fair game for college bowl, and in most states, as they are apparently not in the canon (because obviously, mathematics is a subpar field of academics and doesn't deserve to stand in the same room as humanities....just look at the other states' distributions...), they are not fair game either.

Illinois is different, practically isolated from the rest of the nation by problems consisting of a sharp discrepancy of funding between the Northern schools (i.e. Chicago suburbs) and Southern schools. Northern schools have elaborate humanities courses, and sway towards the academics. Southern schools do not have money for extra courses, and put money where it would be used, and is often not in the specific fields Scholastic Bowl benefits from. The schools still compete, but ask for less academic questions, and often receive their wishes. (If you've read page 7 of this thread, you probably skipped that paragraph.)

Math calculation will not leave Illinois Quiz Bowl until the IHSA subsidizes Scobowl to NAQT.
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Post by solonqb »

jewtemplar wrote:The fact that mathematical computation is naturally ambiguous is a powerful argument for the removal of calculation questions from all distributions.
Hear hear. I can only hope someone from NAQT is listening.

I ask again: Which Illinois teams plan on being at NAQT in Chicago in June?

We now return you to your regularly scheduled programming of Illinois prognostication.
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Post by jewtemplar »

popculture wrote:Moderator: What are the solutions to 2x squared plus 5x minus 3 equals zero?

Player: [buzz] Minus five plus or minus the square root of the quantity 5 squared minus 4 times 2 times 3 end quantity, all over two times two.

Moderator: Correct.

But not only is this a "world of moderators who know math," but it is also a world where moderators know literature. This conversation should also be acceptable:

Moderator: Who wrote Oliver Twist?

Player: [buzz] The man who wrote Nicholas Nickleby.

Moderator: Correct.

Because these answers are factually correct, they should be accepted. It's a good thing our moderators are so knowledgeable.

Bottomline: Just do the freakin' operation, if you can't do that, don't buzz in.

Dogbert once said, "Sometimes sarcasm makes us think clearer."[/i][/list]
A factually correct answer is always easy to derive by stating the question in the form of an answer. Implicitly, an answer to a qb question must provide distinct factual information.

All that is required to solve that math question is knowledge of a formula and knowledge of arithmetic. The answer demonstrated knowledge of the formula; if the arithmetic is important to the question writer, say so in the question. Obviously my statements are colored by the fact that I think that questions which require a single application of a well known formula are pointless.

The answer to the lit question is not acceptable because it does not demonstrate that the one who buzzed knows the author's name, which is the only way to unambiguously specify the author, since someone could just have the mental connection between Twist and Nickleby without knowledge of the intervening author.

The math answer unambiguously demonstrates the player's knowledge of the "real" answer, while the lit answer only demonstrates knowledge of a factually correct path towards the real answer. Neither answer is complete, but the link between the quoted formula and the printed answer is clear, while that between nickleby and dickens is not.

If you think the ability to do simple arithmetic that quickly is vital, than I say specify it in the question, so that accepted answers for less inane questions aren't restricted by a general rule.

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Post by Trevkeeper »

solonqb wrote:I ask again: Which Illinois teams plan on being at NAQT in Chicago in June?
The only one I know for sure is New Trier. I'd assume Stevenson is, because they won NAQT state, but they might have conflicts or something.

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Post by popculture »

jewtemplar, I now see where you're coming from (though I still disagree), but there are several points you made that don't make sense (to me):

You say, "All that is required to solve that math question is knowledge of a formula and knowledge of arithmetic. The answer demonstrated knowledge of the formula; if the arithmetic is important to the question writer, say so in the question."
I ask, "If two things are 'required' (formula and arithmetic) why should it be acceptable to do only one of the steps (the formula)?"

You say that the Twist/Nickleby answer is not acceptable, because it does not "demonstrate knowledge" of the "intervening author."
I agree, this answer was obviously not supposed to be acceptable. Demonstrating knowledge is the purpose of every scholastic bowl answer. But when someone answers "ln 3 -- ln 1," they are not demonstrating that they know that ln 1 is 0.

You say that answering "The guy who wrote Nicholas Nickleby" does not unambiguously answer the question like the math formula did.
I say, "Who else wrote Nicholas Nickleby? The guy who wrote Nicholas Nickleby could only be Charles Dickens."

Every team has a "math guy" who does arithmetic really fast. Cliff Chang is on Team Illinois because of this talent. I don't think making arithmetic unneccessary is advantageous to Illinois Schollastic Bowl or evenpossible.

Saying that "mathematical computation is naturally ambiguous" doesn't make sense. Math is the most precise thing in the world. They ask you for a number and you give them one.

All right, I'm tired of this argument. My life is too complicated; I wish someone would simplify it for me.

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Post by Captain Sinico »

Please see http://www.hsquizbowl.org/phpBB2/viewto ... 8639#18639 for the correct solution to this problem (someone already guessed that the real real correct solution is to boot computation... but I'll eat my hat if that ever happens.) Also, please note that mathematics comes-up plenty at the college level and in other states' questions, except in the form of actual quizbowl questions like those on every other subject, not in the form of "Who can multiply these numbers fastest?" Also, please don't bother suggesting that anything like a significant fraction of the questions are anything other than that; my own attempts at computation questions requiring anything other than "I can multiply!" were met with a responses ranging from dead silence to death threats.

MaS

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Post by Tegan »

I expected to get one or two replies from the usual suspects in Illinois (Da General, Styxman, HAHAHA, etc), but never expected a protracted, (and I would say quite intelligent) deep debate on the issue. For the persons hailing from points south and east, thank you for your insight.

Regretfully, this debate has given me a great deal to think about:

1. On the one hand, lack of requiring a simplified answers demands moderators well versed in math (which is not the reality), or a willingness to slow down the match to offer a challenge. In the end, I suspect that this would be a minority of occasions.

2. I agree, and now clearly see the arguement why "ln 3 - ln 1" is not quite an acceptable answer to the question. I am certain my player fast buzzed and was flustered (he knows math quite well).

3. On the other hand requiring a "simplified answer" needs to be thought of carefully....is rationalization equal to simplification? Could there be any moderators out there that would never take a mixed number or decimal because "that's not simplified?" Frankly, in all my years of coaching and officiating, this is the first time I have seen this come up, but I now see how much of a grey area it is.

As for dumping math as a category, as was suggested: If we dump math, we have to dump physics, and if we dump physics we have to dump the rest of science, and if we dump science, I would insist that history (the advancement of which has so much depended on science) be dumped. If there's no history, you might as well dump the arts and literature.

Which would mean we're reduced to a trash tournament. Knowing mathematics is as imortant as any other academic area. We'll plow through with it.

Again, thanks folks!

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Post by Captain Sinico »

Tegan wrote:As for dumping math as a category, as was suggested: If we dump math, we have to dump physics, and if we dump physics we have to dump the rest of science, and if we dump science, I would insist that history (the advancement of which has so much depended on science) be dumped. If there's no history, you might as well dump the arts and literature.
Again, that's just not true. More or less every other distribution doesn't use computational math, yet doesn't see the need to "dump" physics or anything else, really. I'm not sure if you're saying that allowing computational math to be gotten rid of is the first step on a slippery slope that leads to some trash nightmare, or if you think physics questions are necessarily computational, or what. I'm also not sure which of these view is more wrong.
Tegan wrote:Which would mean we're reduced to a trash tournament. Knowing mathematics is as imortant as any other academic area. We'll plow through with it.
Knowing, yes; but knowing is never the issue. The vast majority of the time, math questions come down to who can perform arithmetic the fastest. They don't test knowledge, or speed of recall of knowledge.

MaS

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Post by dtaylor4 »

I'm sorry that I haven't had the opportunity to put in my two cents. When taking a math course, I have always known to leave things such as sin 22 as is unless it is explicitly asked to be simplified. Of course it could be approximated using a difference formula, but that is asking too much in the context of Scholastic Bowl. Those who are the best in the state at math in Scholastic Bowl implicitly know how to answer and do not bother with the ambiguity. If too much time is used in contemplating the ambiguity, you will either not answer in time or someone else will beat you to it. As for humanities, either an author's real name or his/her pen name should NEVER be the only acceptable answer unless it is explicitly asked for. IMO, every humanities expert in Illinois should know how to fish/blitz. For those who have not seen the benefit of this practice, here's an example: "Count Alexei" *buzz* "Anna Karenina by Tolstoy (all in one breath)". By giving the CORRECT author and title, if either is on the paper, they have to deem it a correct response. This can also be done with author's pseudonym/real name. It is the responsibility of the question writer to be able to identify possible ambiguous answers and clarify such situations on the paper for the moderator. Anyone who can find further uses of fishing/blitzing should post them for the benefit of all.

Mr. Egan, with all due respect, when I last posted, I saw a double post, so don't jump down my throat. As per traveling, D Mac usually does, but others rarely do due to the lack of ability or lack of funds. Most teams think that it's just not worth it to travel far away to be thrashed.

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Post by HAHAHA »

Just as a hypothetical situation, what if the question had been the integral of dx/x from 2 to 3?

Would ln3-ln2 be an acceptable answer, since ln2 does not convert easily to a known number? Or would ln (3/2) be the only solution?

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Post by Irreligion in Bangladesh »

HAHAHA wrote:Just as a hypothetical situation, what if the question had been the integral of dx/x from 2 to 3?

Would ln3-ln2 be an acceptable answer, since ln2 does not convert easily to a known number? Or would ln (3/2) be the only solution?
Heh heh...niiiice...

My view: ln (3/2).

My reasoning: ln (3/2) is more simplified, to me, because it has the term "natural log" in it only once. I haven't had logs yet to know exactly which to use, but it seems that ln (3/2) is more simplified. Look at the (square root of 2) times (the square root of 3). You can simplify it to a single square root sign by using the properties of arithmetic. Using the properties of logarithms, ln 3 - ln 2 can be simplified comparatively.

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Post by dtaylor4 »

I think that the simplest answer, in this case ln (3/2), should be deemed the correct answer and if (ln 3) - (ln 2) is given, the moderator should prompt. BTW, what math are you in where you haven't had logs yet? I had them freshman year in 2nd year Algebra.

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Post by Irreligion in Bangladesh »

Are your math classes honors or AP, by any chance?

I had freshman 2nd year Alg, soph. Geo, and now jun. Adv. Alg and Trig. I'm as advanced as I can get without having taken summer classes or extra classes at a community college. We get to logs after spring break, so in 3 weeks (in time for ICTM state :)) or so.

2nd year Alg. has advanced freshmen, who often aren't interested in math so much as they are smart in general and placed in advanced math in 5th grade...normal sophomores, who are middle of the pack in ability to learn and ability to learn fast...remedial juniors, who took 2 years to take 1st year algebra....and, yes, remedial remedial seniors, who took 3 years of 1st year algebra or passed on math class junior year.

We can't go any faster than the slowest person, who is often very, very slow at the Algebra level. In trig, we just finished the trig unit this week. 1st semester acted as Algebra 3...polynomials, conic sections, etc. The review never ends. Technically, if it weren't for my other math class this year, Finite Math/Statistics, I wouldn't have had actual probablity lessons at any point in my middle, junior high, or high school career. We just never got to it in any class. This is what happens at smaller schools, Donald.

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Post by cvdwightw »

DaGeneral wrote:I think that the simplest answer, in this case ln (3/2), should be deemed the correct answer and if (ln 3) - (ln 2) is given, the moderator should prompt.
This makes sense to me. Correct answers should demonstrate clear, unambiguous knowledge of the answer. Therefore the moderator must rule that the answer given constitutes knowledge of the correct answer, and that the answer is unambiguously equivalent to the answer on the page. Answers that fail the first part should neither be accepted nor prompted on. Answers that fail the second should not be accepted but should be prompted on.

I think the issue here may be similar to the issue of excessive underscoring, that is, what the answer on the page deems is necessary to pass the second test is more than what actually should be necessary. That is, the given answer is correct as is, but it is not sufficient to be compared to the answer on the page and ruled unambiguously right.

Essentially, my view for computational math is that the page should state unequivocally all answers that should be considered correct. If a response does not match one of those answers, it should not be considered correct. However, if it is not a completely wrong answer, then it should be prompted on. Disallowing an answer in that gray area can lead teams to thinking it must be that answer, but giving another answer that is not equivalent because "well, the other team already tried that answer." I know this happens in instances where a moderator rejects an incorrect answer, but the other team mishears the response as the correct answer. However, those "gray area" answers do not demonstrate unambiguous knowledge that the given answer is equivalent to what is on the page, so therefore should not be accepted. The easiest, and perhaps only (assuming abolishing computational math is not an alternative) way to alleviate this problem is to prompt on that type of answer.

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Post by Tegan »

cvdwightw wrote: Essentially, my view for computational math is that the page should state unequivocally all answers that should be considered correct. If a response does not match one of those answers, it should not be considered correct. However, if it is not a completely wrong answer, then it should be prompted on.
When I started writing for the state, I tried getting my math writers to do this. Invariably, something gets left out. We could do this with little chance of error, but it would mean that the math would need ot be fairly rudimentary (arithmetic racing).

The solution that we arrived at was to have a longer lead-in to the question asking for a specific answer format. As one player (I think Styxman..apologies if I am wrong) pointed out, this really takes away from the question. Until we find a way to write complex questions that we can be assured cover all the bases, I think we are stuck.

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Post by jbarnes112358 »

Okay, as the resident mathematician, I suppose I'll throw in my opinion. I do not take the extreme view either way. However, I do believe the moderator should accept any "reasonable" form for a math computation, like the Math League or an AP Calculus grader might do. Of course, the trouble with this is that often the moderator does not know what constitutes an equivalent answer or a reasonable answer. Even experts might disagree on what the simplest answer should be. For example, I might think that ln3-ln2 is simpler than ln(3/2), as the former avoids a fraction. Indeed, one of the nice properties of a logarithm is that it converts a division operation into the simpler subtraction operation. As another example, some math teachers insist that fractions be rationalized. This view is a little outdated IMHO. It is an artifact from the days when approximating, say, sqrt(2)/2 by hand was easier than approximating 1/sqrt(2).

Since many moderators can hardly even read some math questions, much less rule on subtle variations in answers, the question writer should list the common variations that might be anticipated. If it is desired that a fraction be put in lowest terms, then the question should say so, as early in the question as reasonable to do so. Though, I'm not sure why it would necessarily be so important to have the fraction in lowest terms, especially if significant knowledge was necessary to arrive at the fraction in the first place. For example, If a question asked for the probabilty of rolling a 5 with a pair of fair dice, I would be happy with an answer of 4/36, since it clearly shows the probabilty knowledge I was after. The extra step of simplification seems almost pointless to what we were trying to accomplish with the question. If the moderator is a total math phobe, and cannot adequately rule on reasonable, equivalent math answers then someone competent with at least basic math skills should be nearby to offer assistance. If the local tournament culture is overly contentious, then I suppose it might be a good idea to attempt to define "reasonableness" in the rules in order to minimize controversies.

I take issue with the poster who said that mathematics was not sufficiently important knowledge for quiz bowl, though I suspect it was offered, at least partly, in jest. The problem is with how the questions are presented, not with the subject itself. Questions that reduce to speed computation are out of character with most quiz bowl questions. That is why so many players groan when they come up. Often, I myself am struggling not to groan. If such questions come up sufficiently often, then teams feel compelled to solicit a speed math specialist for their team. We do have such a specialist, and used him to our advantage in certain tournaments this year. A similar situation arose a few years ago when the local TV competition insisted on including a spelling round. We had to recruit a designated speller to remain competitive, since our usual players were not such good spellers.

I believe it is possible to ask math questions that conform to the overall character of quizbowl tournaments, even using pyramidal structure etc, that require non-trivial math knowledge, and that are not just speed computing. Perhaps, we could start a thread on how to write good quiz bowl math questions. It seems that many tournament writers are struggling with this issue.

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Post by dtaylor4 »

styxman wrote:Are your math classes honors or AP, by any chance?

I had freshman 2nd year Alg, soph. Geo, and now jun. Adv. Alg and Trig. I'm as advanced as I can get without having taken summer classes or extra classes at a community college. We get to logs after spring break, so in 3 weeks (in time for ICTM state :)) or so.

2nd year Alg. has advanced freshmen, who often aren't interested in math so much as they are smart in general and placed in advanced math in 5th grade...normal sophomores, who are middle of the pack in ability to learn and ability to learn fast...remedial juniors, who took 2 years to take 1st year algebra....and, yes, remedial remedial seniors, who took 3 years of 1st year algebra or passed on math class junior year.

We can't go any faster than the slowest person, who is often very, very slow at the Algebra level. In trig, we just finished the trig unit this week. 1st semester acted as Algebra 3...polynomials, conic sections, etc. The review never ends. Technically, if it weren't for my other math class this year, Finite Math/Statistics, I wouldn't have had actual probablity lessons at any point in my middle, junior high, or high school career. We just never got to it in any class. This is what happens at smaller schools, Donald.
At my school (which is in major financial trouble, BTW) we have math ranging from practical math (for the real FDA, the future dropouts of america) to AP Calculus AB. I took algebra 3-4 my freshman year (one of three to do so), then precalculus (which includes a huge section on trig), last year I took AP Calc AB and got a 5 on the AP exam (in my class, out of a dozen taking the class itself, 6 got a 5 on the exam). This year, due to my invovlement with the Scholars & Mentors program here, I was not able to attend a local university to take advanced math. We don't have a stats class here, which I would have taken. For your comment about small schools, a local private high school (St. Teresa, who got 3rd at State) has more AP classes than we do (this year we have 4: Calc AB, Psych, Euro and US History).

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Post by Captain Sinico »

jbarnes112358 wrote:I take issue with the poster who said that mathematics was not sufficiently important knowledge for quiz bowl, though I suspect it was offered, at least partly, in jest. The problem is with how the questions are presented, not with the subject itself. Questions that reduce to speed computation are out of character with most quiz bowl questions. That is why so many players groan when they come up. Often, I myself am struggling not to groan.
If that's my post you're referring to (and I don't see how it could be otherwise; correct me if I'm wrong), I'll just say that's not at all what I said, nor can that be reasonably inferred as my position (and, in fact, it is not my position.) Please read and try to understand posts before attempting to respond to them. In the event that you get tired of beating straw dogs, feel free to respond to what I actually said and we'll discuss this further.

MaS

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Post by Tegan »

ImmaculateDeception wrote: Again, that's just not true. More or less every other distribution doesn't use computational math, yet doesn't see the need to "dump" physics or anything else, really. I'm not sure if you're saying that allowing computational math to be gotten rid of is the first step on a slippery slope that leads to some trash nightmare, or if you think physics questions are necessarily computational, or what. I'm also not sure which of these view is more wrong.

[sic]
Knowing, yes; but knowing is never the issue. The vast majority of the time, math questions come down to who can perform arithmetic the fastest. They don't test knowledge, or speed of recall of knowledge.
I took some time to read your quote, because I too thought a moment that you were placing math on the low bookshelf....I see that is not what you are saying.

I was being sarcastic in saying that getting rid of math would mean gettng rid of other subjects (NAQT all but gets rid of computtaional math, and they do a fine job as question writers). Could it be a slippery slope, maybe, but I would even doubt that.

I believe that every topic has its issues with "alternative answers". Math has a more magnified situation, because instead of one or two alternatives, there are more.

Moderator education would be a great step in the right direction. We are trying in Illinois to get certification off the ground, and the State to sponsor clinics (the IESA already has this!) This would hep greatly in reducing the problems.....too many moderators, when in doubt, push their authority around instead of listening and thinking things through. I am also working on a primer that might cover the motion common situations (though it to will be understandably incomplete).

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Post by iamsam »

jbarnes112358 wrote:Even experts might disagree on what the simplest answer should be. For example, I might think that ln3-ln2 is simpler than ln(3/2), as the former avoids a fraction. Indeed, one of the nice properties of a logarithm is that it converts a division operation into the simpler subtraction operation. As another example, some math teachers insist that fractions be rationalized.
That is definitively right. Like with trig identities, is sin2x or 2sinxcosx more simplified, when it comes to functions in math, there really is not an universally agreed upon answer. And this is essentially what Sam said earlier:
Obviously, if writers require simplest form, then simplest form is all that is acceptable, but the whole notion of simplest form is kind of fuzzy.
This argument is pointless in some respects than, because there are going to be so many exceptions to rules, like, obviously simple arithmetic and multiplication should not be convoluted with superfluous functions, and at times, when the questions ask for answers that include "sin22," converting that into a decimal/fraction answer would not be reasonable because of time limits. As for the analogous relations with literature, that can't verily be said, because they are similar in even though they have a similar core principle, it is like comparing apples and oranges (even though they are both fruits). I personally would have accepted that answer, because when one is pressed for time, doing that final step doesn't really prove that the person knows how to integrate the function. The player already proved that by I'm assuming integrating 1/x to lnx from 1 to 3. My Calc BC teacher messed up half of the classes quizes because he got ln1 going to zero and ln0 going to negative infinity mixed up. If the question wanted to prove whether the person knew logarithms, then the question should indicate that (i.e. "to one term"). Now this gets into the nature of the questions, which Sam already discussed, so I won't further clog the thread with a repeat. Basically, there is not going to be a unilateral decision on this, even mathmeticians don't fully agree on this matter of simplification. The question should be better written so that the players can be told whether or not the question is asking for a "more simplified" answer.
Last edited by iamsam on Mon Mar 21, 2005 8:58 pm, edited 1 time in total.

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Post by dtaylor4 »

The reason that I said that ln (3/2) was simpler than ln3-ln2 is because typically in quiz bowl, the fewer terms, the simpler (at least that's my perspective except when it comes to factoring a trinomial or something similar.

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Post by iamsam »

except
This kind of thinking is exactly why there can't be a definitive rule for math.

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Post by Howard »

ImmaculateDeception wrote:Please read and try to understand posts before attempting to respond to them. In the event that you get tired of beating straw dogs, feel free to respond to what I actually said and we'll discuss this further.

MaS
Dude: you're being rude to someone who doesn't deserve it, and, in fact, deserves our respect. While I understrand you have some frustration, you would do better to direct it away from those who have significant influence on the shape of quiz bowl. Because you're being rude, what you've done is encourage one of the most intelligent quiz bowl coaches I've ever met to NOT post. Leaving out the quote above (except for the offer of further discussion) would have accomplished the same level of understanding, AND wouldn't have been rude, AND would have promoted further intelligent discussion.

And since I've been a frequent critic in the past, I'll reiterate that except for this instance, that you've been doing a fine job with your moderator/admin duties. Fair is fair. I just thought this one was out of line.
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Post by jbarnes112358 »

If that's my post you're referring to (and I don't see how it could be otherwise; correct me if I'm wrong)
Immaculate: I was not referring to anything you said, in particular. I found most of your comments insightful and I agree with them. In looking back, I was responding to Tegan's allegation that dumping math had been suggested by someone, and to Styxman's comment about math being a "subpar field of academics...".

If nobody here is actually advocating the dumping of math, then I'm glad to hear it. Part of the confusion is that people are blurring the distinction between mathematics and computation. I am actually hearing much agreement that the quality of math questions needs improvement, generally. I am also hearing a consensus that questions that are simply computation races might be better suited for some other venue besides quiz bowl, just as spelling questions should be reserved for spelling bees. I am in agreement with both of these points.

We don't need to remove all computations from quiz bowl questions, but any computations should be secondary to the larger concepts or factual information inherent in the question.

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Post by Captain Sinico »

Alright then. I agree with you; sorry for the confusion and for any (non-vicarious) offense given.

MaS

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Post by Matt Weiner »

I hope we can all get along....anyway, I don't see anyone presenting the solution that many high school tournaments have already adopted: Eliminating calculation tossups and relegating calculation to the bonus in order to preserve it for those who want it. That gives the writer the freedom to put in as much info as needed to specify exactly what sort of answer is sought. Furthermore, it puts the focus entirely on understanding concepts rather than racing the other team on arithmetic.
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Post by jbarnes112358 »

Matt, putting computations in the bonus would help some, especially in regards to specifying answer format. But, it doesn't completely solve the problem. It still requires speedy computation skill to beat the clock. Furthermore, if the tournament has bouncebacks, the other team can actually steal the points if they have the speed computing specialist and you don't.

Some tournaments give more time for computational questions, or read the questions twice. (Virginial High School League does this.) But these measures slow down the game. It would seem to be a better solution to minimize the computational aspects of math questions. Any computation should be reasonable, and ancillary to the main thrust of the question. Ten seconds is not much time to do certain computations. In other cases, it is more than adequate time, especially if you know the right trick. The tournament director should be sensitive to the time issue. Testing the questions before the tournament would be helpful.

By the way, computations are not just relegated to mathematics. Often physics, chemistry, and other science questions contain computational aspects. My comments about reasonableness apply in these cases as well.

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Post by First Chairman »

As much as "handout rounds" are not in character with quiz bowl, it is probably the only way aside from putting it in bonus questions to preserve calculation questions. I will agree that there is still a time element in handouts and bonus questions, but it's much better than speed calculations on tossups. Either that or change the rules so that the clock is extended up to 30 seconds for all math questions.
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Post by Tegan »

Matt Weiner wrote:I hope we can all get along....anyway,
I as well...I was looking for some input, and I am afraid that I touched off a tiny jihad. That was not my intention. I do like to hear all sides, and as I stated earlier, I hearing the diversity of opinion gave me a great deal to think about.....I hope we can all give and take opinions in the spirit of a scholarly debate.
I don't see anyone presenting the solution that many high school tournaments have already adopted: Eliminating calculation tossups and relegating calculation to the bonus in order to preserve it for those who want it. That gives the writer the freedom to put in as much info as needed to specify exactly what sort of answer is sought. Furthermore, it puts the focus entirely on understanding concepts rather than racing the other team on arithmetic.
In the Illinois state series (and in the rounds that I write), This is done for both toss-ups and bonuses. I will being the toss-up with language like: "Give your answer as a reduced, improper fraction", or "Give your answers in descending power order" Quite a few players don't like this, and I see their point, but it is a way to make sure that the moderator can't screw up and deny a team points for giving a potential correct answer. We decided years ago to always put this information as the lead in, rather than the last words of the question. It is far from perfect, but it eliminates a vast majority of problems.

The problem I have with eliminating computational math in toss-ups is that (my opinion only), gives major strength to the humanities portion of the questions. I think it makes it that much easier for "on person gangs" to run roughshot through a tournament. Math, being much more specialized (having to quickly recall the tricks and relationships that make a math player great), forces a team to have one or two really good math players. I think it is (albeit, perhaps an artificial one) a way of having a more balanced team.

Also my opinion, if we are really testing academic (vs. trivia) knowledge, I think math has earned a place alongside the other areas. I like to listen to my colleagues who run mathletes and spelling bees, and they brag how tough their competitions are....I know that in this competition, our players have to be as strong in spelling as a spelling champion, as good in math as the better mathletes (actually, often the same players), know as much geography as the NGS bee winners, etc. Our players are the most rounded academically, and I (again, my opinion) don't like to see them limited. [/quote]

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Post by dtaylor4 »

I'm sure that a lot of players in quiz bowl are involved in mathletes and wyse, but for those activites/competitions, you have a lot more flexibility in terms of doing better. In WYSE (I'm not commenting on mathletes since we don't have it here), the math is 40 questions in 40 minutes, and someone taking the test can skip around and do the stuff they know first, or wait till round two and ask about some of the questions. In quiz bowl, you have to be able to recall the "tricks" Egan refers to at the drop of a hat and still be able to nail your specialties.

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Post by Matt Weiner »

Tegan wrote:The problem I have with eliminating computational math in toss-ups is that (my opinion only), gives major strength to the humanities portion of the questions. I think it makes it that much easier for "on person gangs" to run roughshot through a tournament. Math, being much more specialized (having to quickly recall the tricks and relationships that make a math player great), forces a team to have one or two really good math players. I think it is (albeit, perhaps an artificial one) a way of having a more balanced team.
Formats that do this still have conceptual math and science tossups. If your math person can't keep up on those then I think he was probably an "arithmetic person" in reality. In the PACE NSC we've had calculation in the bonus only for the past several years, and I've never heard anyone say we don't have enough science. A few people even said we have too much.

Personally, I do agree with those who suggest eliminating calculation entirely in favor of conceptual math questions. Collegiate quizbowl has done this and there's still plenty of math people getting questions in their area. However, I know that some high school regions are very wed to the idea of calculation, so some way of preserving it without the unfairness of most calculation tossups is needed.
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Post by kevinatcausa »

How many math questions per match do those formats that eliminate computation have? I don't know if it's changed or not, but when I played in High School there were 5-6 math tossups per match. Combine that with the more limited scope of answer choices for high school matches, and it could be rather difficult to eliminate computation without making major changes in distribution.

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Post by dtaylor4 »

In Illinois format, it's 20% math (6 out of 30 in the State tourney), and for the State tourney, the specific categories are general math, algebra, geometry, trig, calculus, stats, and math history (I think, Tegan will correct me if I'm wrong), and there are no repeats of categories of tossups in the same match, i.e. two calculus tossups in one round.

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