NAQT High School Math Questions

[insaneindian]

Do you guys feel pencil and paper tossups in NAQT are too easy? Too hard? A good mix?

I think some of the questions are easy, like the ellipse area and resistance, and are easily powerable for experienced players. The probability questions, I don't like, but I never liked probability in the first place and they are easy for people who know a little bit about probability. Also, the mean test score questions are quite easy. I sometimes whiff on math questions due to stupid arithmetic mistakes I make because I'm trying to work out a problem quickly knowing other experienced players will get them quickly.

I'm all for NAQT making math questions more difficult to reward real math knowledge. I personally think they should include more pencil and paper calculus tossups. I dont ever recall seeing an integral evaluation (i.e. impulse, work) tossup but I have heard a few questions (like finding max and min values) involving derivatives. They ask questions about events that you might learn in AP US or World History and certainly AP Chem and Biology, so why not ask more questions that would come up in AP Calculus?

Thoughts? (I wouldn't be surprised if everybody disagrees )

[solonqb]

I wouldn't mind seeing some chemical equilibrium questions as well, although the ones I wrote were rejected/are languishing in limbo.

As far as I know, the writer responsible for most of the NAQT computation questions is Matt Bruce. I'm not sure whether he wants his email posted online, but I'll be happy to forward anything to him. Alternatively, you could give NAQT feedback directly, at the email listed on their website.

[Byko]

I think the reason they do the math questions the way they do is so that every one of them can be powered. Additionally, the questions can't be too long, and since a "hint" to get some people started is required to make them long enough to be powerable, there are some real constraints on what they can do.

It's a tough area to write considering the NAQT format and guidelines, I think, and frankly, even as a math person myself, I feel that maybe they'd be better off just abandoning math calculation questions altogether.

[quizbowllee]

It's a tough area to write considering the NAQT format and guidelines, I think, and frankly, even as a math person myself, I feel that maybe they'd be better off just abandoning math calculation questions altogether.

I agree. At our NAQT tournament, we will be skipping all of the "Pencil and Paper Ready" questions.

[First Chairman]

In my experience, math calculation questions are the least answered of any tossup question ever given. Unless the mathematics is exceedingly easy (like sixth grade, it seems), very seldom will a category of math calculation tossups (or bonuses) be answered.

In addition, mathematics is not really taught in a way that allows for quiz bowl competition. Not like I've done a hard-core study of questions asked at MathCounts, but even they have 30-45 seconds to do a problem when they're doing it by themselves.

Furthermore, mathematics should not be taught in the same way that all other subject matter is taught. Mathematics is about process, about problem-solving, and about using concepts to get the right answer. Most quiz bowl questions focus on factual recall, not application (or else we'd be writing essays). Identifying the "tricks" in most math problems is the difficult part of those questions, but this is not the same skill as one would use on a "normal" quiz bowl question.

For those out there with much free time, I'm currently reading the book Countdown, which is about competitors at the International Math Olympiad.

[csrjjsmp]

In addition, mathematics is not really taught in a way that allows for quiz bowl competition. Not like I've done a hard-core study of questions asked at MathCounts, but even they have 30-45 seconds to do a problem when they're doing it by themselves.

Probably calculation questions don't mesh well with the typical quiz bowl tossup, but it is possible to write good math questions that test knowledge.
I personally never really minded the calculation questions, mostly because I tended to get them first :) I can see how they'd be boring for a lot of people though, and they probably deserve to be abolished.

[mentalchocolate]

I believe the type of math questions are done well by NAQT although I would also like some calculus to be added...saying that it is very tough to create questions that have an equal oppurtunity of being powered as any other subject, but also not to exceding easy. Some trig questions allow for the player with the most math knowledge to have a chance at powering, but also a less experienced player may be able to still get it correct towards the end of the 15 seconds.

[dschafer]

Quick disclaimer: I do both math team and quiz bowl, so my feelings on this issue are rather biased.

For the Countdown round at Mathcounts (which of all math competitions best resembles quiz bowl), students have 45 seconds from the start of the question, which is projected for them to read onto a screen. The fact that such projections cannot be done in NAQT competition, the need for pyramidal style tossups, and the difficulty of Mathcounts vs. NAQT math questions eliminate most of the math from the countdown round from the pool of potential quiz bowl math questions.

I would agree with what mentalchocolate said about the trig questions; for example, if an identity that a math specialist would know makes the problem much easier, then the question may be powerable; on the other hand, anyone familiar with the material should be able to get it by the end of the 10 seconds after the questions end. Pyramidal math is hard to write, but not impossible, and works just as well as any other style of quesiton when done right.

My feelings on calculus are similar to those of insaneindian: there are plenty of NAQT questions on AP Bio, AP Chem, AP Physics, AP U.S. History, AP Euro, and AP Psych; why not AP Calc? If a pyramidal style question can be written on a concept in calculus, I don't see any reason not to use it. If it were in the playoffs of a national tournament, I wouldn't even think a multivariable calculus question would be unreasonable.

Identifying the "tricks" in most math problems is the difficult part of those questions, but this is not the same skill as one would use on a "normal" quiz bowl question.

I find that when I am doing math questions, it is a quite similar skill that I use. When a question on an artist/treaty/molecule is started, I begin to recognize some of the information that is given, and when I have enough information to answer with confidance, I do so. Math questions add a step: first, the information in the question is given, then the trick/method needed to solve the problem must be identified, then finally the actual math must be done. This additional step (the computation itself) is what I find the extra 10 seconds is for. Additionaly, just like information at the end of a "regular" question gives away the answer, information at the end of a math computation tossup should give away the method needed.

I certainly disagree with abolishing math tossups; they cater to a specific audience, but then again, what type of question doesn't?

EDIT:

I actually read Countdown a few months ago, if it is the book I'm thinking of. It was very interesting; I'd highly recommend it.

[csrjjsmp]

I'm sorry, I didn't mean to say anything like get rid of math questions in general.
Here are two examples of what I think:
Tossups like this are bad:
Two balls are selected at random, one after the other, without replacement from a box that contains three red balls and five blue balls. FTP what is the probability that both balls selected are blue?
5/14

Tossups like this are fine:
It was first explained in Sections 12 and 13 of Book II of Euclid’s Elements and is incorporated in the definition of the dot product. It can be used to compute any angle of a given triangle if all three sides are known or the 3rd side of a triangle if two sides and the enclosed angle are known. The Pythagorean theorem is a generalization of it when big C is ninety degrees. The law states that little c squared equals little a squared plus little b squared minus two times little a times little b times the cosine of C. FTP identify this law which can be used with the Law of Sines to find all sides and angles of a triangle.
Law of Cosines

Conceptual questions can be pyramidal and reward knowledge. Computation questions generally don't, and making them do so is very hard. I've never seen it done well.

[cvdwightw]

The problem with Larry's post is that neither of his sample questions accurately reflects an NAQT computational math question, which is probably the closest to a pyramidal question that high school computational math has. To modify Larry's example, I present the following hypothetical question:

Pencil and paper ready. John selects a ball at random from a box containing three red and five blue balls, and Susie selects from the remaining balls. Jeff wants to know the probability that John and Susie's balls are the same color. He can find this by finding the probability that both of them have a red ball and adding the probability that both of them have a blue ball.(*) For 10 points--find the probability that John and Susie have the same color ball.

answer: 13/28

Why is this roughly pyramidal? Anyone who knows how to solve the problem can start working almost immediately, since all relevant information is given in the first or second sentence. Of those people, anyone who can do the computation sufficiently fast will get 15 points; anyone who can't still has a head start on the competition. Next, there is a sentence or two describing how to do the problem, while not giving it away completely. At this point anyone with rudimentary probability skills should be able to start working on the problem, and probably get the correct answer within ten seconds from the end of the question. Then there is the obligatory for 10 points, which does not actually give any useful information, but at this point there's no need for additional information. Anything else would turn the question into purely who can multiply and add fractions the fastest, which while I understand is popular in Illinois, is not the type of question NAQT is trying to write. Instead, the obligatory last sentence gives players additional time to work on the problem.

Dwight, who is not affiliated with NAQT in any way except for having played and moderated in a bunch of their tournaments

[csrjjsmp]

Thanks Dwight, my exposure to computation questions comes solely from Gaius, not NAQT, so I didn't know their format. That looks much better than the buzzer races I'm used to, but I would still say that questions like those are better replaced with conceptual questions. I don't know about other schools, but my math education started emphasising theory rather than number crunching after first-year algebra, and I always thought it was a pity that the quiz bowl questions I heard didn't reflect that.

[Stained Diviner]

I like NAQT calculation questions, though I agree that there is too much combinatorics at the expense of other topics. It is difficult to pyramid other types of calculation questions, but it can be done. For example, you can explain an integration technique, explain how you would visualize a three-dimensional figure, give away a conic section formula, change a log problem into an exponent problem, etc.

(I don't have to worry about such issues when I write questions because I write for a format that does not include powers. NAQT sometimes writes for this format as well and does include a better variety when they do so.)

Good calculation problems are more about problem solving than actual calculating. For example, a word problem that requires somebody to find 6C3 comes down to multiplying 5x4 if you have a basic knowledge of combinations. I don't see why anybody would have a serious problem with such a question. Problems requiring people to multiply by 3.14 generally only come up in packets written by people who write lots of bad questions. (I don't think you'll ever see it come up in NAQT.)

I also agree that those questions are the most likely ones to be missed, but I don't see that as a serious problems. Tossup conversion on NAQT questions generally is very high, so having some questions that some teams can't do is acceptable.