Stupid quiz question

[go_team]

Okay, so one of my students is a high school sophomore taking algebra and geometry in one year to catch up with her class. We're about halfway through the algebra course and she's got a quiz due tomorrow that she's going to submit online. One of the questions, though, has us both stumped --- mostly because it's so poorly worded. So here's the question, and a poll so you can tell me what you think the answer is/should be.

The formula for questions 14-16 came from the police department. They use this formula to determine the speed at which the car was going when the driver applied the brakes, by measuring the distance of the skid marks. So when you get to #16, it is referring to what a person would interpret the situation if the skid mark was zero distance. So, if the skid mark distance equaled zero, that would mean, the speed of the vehicle, r, was zero, or that the car was able to stop instantly.

For problems 14 through 16, the equation d = .05r² models the distance, d, in feet traveled by a car moving r miles per hour (r is the speed of the car) after the driver begins to stop the car.

[Poll #200387]

I thought about adding a fifth possible answer, "This is a really stupidly vague question, and all of these answers might be right since the wording of the problem is so bad", but I decided to give you guys the option of choosing multiple possible correct answers instead. Just to confuse you some more, my student chose C, I chose A, and I just emailed the independent study people to say "What the fuck?" and ask if answer D is a typo and it's meant to say "Both A and C are possible..." although that's not very satisfying, either.

Argle-bargle. She's hoping to submit this quiz tomorrow. Hopefully I hear back from somebody in independent-study land before then. Sigh.

Comments

[chocolatesmudge.livejournal.com]

Yuck, that IS awful! I couldn't even bring myself to choose one, though I'd probably go with A if you held a gun to my head. Seems like they want you to pick D though. Yeesh, who knows?

[cubetime.livejournal.com]

I'd like to hold a gun to the head of whoever wrote that question.

I think that they're trying to give the answer away in the first paragraph of the preamble. They give two options of how to interpret a distance of zero.

There is also the fact that they don't clearly state their assumptions relating the length of skid marks to the distance traveled by a braking car.

[goteam.livejournal.com]

Yeah, I'd be much more certain if it weren't for that stupid preamble, which is what my student is basing her answer on and I can't really blame her for it. I think the stuff about skid marks is made up so that students don't ask "but how do we know the stopping distance?" but really it just confuses stuff more.

Physics

[msmithma.livejournal.com]

Can't be anything but A,

B implies no skidding = no distance traveled but anybody with ABS gets optimum braking, no skidding, and the stopping distance is non-zero

C Non-physical => an infinite frictional force between the brakes and the wheels as well as the ground and the tires, not even the fanciest race car with super sticky tires could do it.

D Disqualifies itself by the inclusion of B (as you noted)

Re: Physics

[msmithma.livejournal.com]

Now I'm confused, I re-read the question and it talks about skid-mark distance, pig fuckers! Measuring a zero skid mark distance means Jack and Shit about initial speed, honestly you get better braking without skidding anyways. I vote that the answer is E The car had ABS and the pigs are too entrenched in their empirical formula to get a clue.

[goteam.livejournal.com]

See, I think the business about the skid marks is made up to stop students from asking "so how do we know stopping distance again?" but that doesn't make the problem much better. It feels like this problem is trying to test whether the math you learned in this chapter can overcome your physical intuition about a situation, but that's just evil. There's plenty of ways to stop without skidding, like you said, so then answer B starts looking better again, but ugh!

[olstad.livejournal.com]

I said D and here is why...
As a math person, it seems obvious the answer is A and in a math class, I would expect this to be the answer, however, lets for a minute suppose we are not in a math class, instead we are in science and/or forensic class.
In that case, "showing no skid marks" means that there were no skid marks, not that it didn't take some distance to stop. Which, I must admit, the problem implies there was no distance traveled, not that there were no skid marks. (Very badly worded) After all, in the real world, most of the time you don't show skid marks when you stop. Therefore B is in my opinion the MOST correct answer to a badly worded problem. Now then, C is a possibility (think- crashed into a telephone pole or something). It is not very realistic that someone would crash into a telephone pole without first applying the brakes, but it *could* happen, in which case the car would have stopped "instantly." (or at least without showing skid marks.) Therefore answer D must be correct.

Back to answer A, why isn't it correct? I'm just not sure.

But this <em>is</em> a math class!

[goteam.livejournal.com]

I agree that A and C aren't very realistic if you're thinking in real-world terms, leaving B.... but I'm trying to use only the data given in the problem and that suggests A... or maybe C.... or I don't know! Ack! Stupid, stupid problem-writers!

[boojum.livejournal.com]

I think they must be assuming "driver jams on brakes" for the measuring component; I stop my car plenty of times without leaving skidmarks, even from high speeds, because I'm stopping gradually.

If the question really means "distance travelled after brakes", not "skidmarks left from travelling after brakes", then I'm tempted to say that C and A are both true, but A is a special case of C.

I think that, popping out of common sense land (where all the answers make the same amount of sense) and into let's apply formulae without thought land, they want A, because that's the plug-the-numbers-in answer.

This rather reminds me of a children's intelligence test question I read about: "Giants are a) scary b) big c) going to kill people d) mean."

[amoken.livejournal.com]

Ugh. That's horrible. The answer is really: the car did not skid noticeably (perhaps due to external interference, like oil on the road), the car was already effectively stopped, or there was something other than the brakes which interfered and caused the car to stop. This is a horrible question and answer set, but if you ignore external factors and pretend we only have the car-road system with no complications, A is really the only reasonable choice.

[cubetime.livejournal.com]

Well, at least we know that A is A.

[pmb.livejournal.com]

Stooped so low as to begin baiting objectivists, eh?

[nuclear-eggset.livejournal.com]

I think the answer is E.

"This question cannot be answered at all due to the endangered spotted owl.*

*The answer to this question would require detailed the excessive assumptions in the problem statement, testimonial from police officers as to the day-to-day application of the "rule", and numerous sets of data demonstrating actual car tire/pavement behavior during brake application in all cases (elderly driver, young driver, dry road, wet road, blizzard, wind gusts, fresh asphalt, cracked asphalt, ABS brakes, disc brakes, drum brakes, various choices of driver shoe wear, etc.). Additional evidence and discussion would be needed to point out the numerous flaws in the alternative answers' statements, including all possible interpretations (including the cessation of the basic laws of physics on the macroscopic scale), and why said interpretations are inappropriate for the given problem statement. This would require so much paper as to endager the spotted owl's natural habitat, and divert badly needed funds from the conservation effort for this beautiful creature."

[iainuki.livejournal.com]

I can come up with plausible reasoning for all of those responses, most of which has been covered by various people already.

Briefly:

A) Literal application of the equation yields this.

B) If you interpret "distance" as "length of skid marks" this makes sense.

C) Unphysical, but if it did happen, this description is correct.

D) C is unphysical ("not realistic"), but both B and C could technically be right.

This problem sucks. My test-taker's intuition would say A, if it weren't for D and the wording in the preamble; as it is, I suspect with you that D should have said "A and C," and that D is the right answer.

[kuddliphish.livejournal.com]

I'm guessing because it's a math test that they want A, to prove that you know 0 times anything is 0. But mostly it is weird to have this kind of non-mathy guessing game on a math test. The real answer is that the officer looks to other evidence at the scene to find out what happened since the skid-mark test was useless (and probably does NOT conclude A, since there is an accident discussed, which strongly implies a moving car.)

[maxemulien.livejournal.com]

I agree that they're probably looking for A. However to my understanding, in most traffic accident investigations, considerations other than skid marks are used to determine if a vehicle was moving. In this context, the most likely interpretation would be that the driver failed to brake, and estimates of speed would probably have to be gathered by analyzing the wreckage.

Upon re-reading the question...

[cubetime.livejournal.com]

If the distance the car traveled after applying the brakes equals zero, what does that mean to the officer investigating the accident?

The question that is being asked is what does that mean to the officer investigating the accident?

• The distance the car traveled after applying the brakes equals zero means to the officer that the car was stopped when the driver applied the brakes.
  True, but not exclusively true. It could also mean that the car had just collided with an immovable surface.
  
  
• The distance the car traveled after applying the brakes equals zero means to the officer that the car was going so slow that there was no skidding when the driver applied the brakes.
  True, in the limited sense that you don't skid if you're already stopped. If the car moved zero distance after brake application, then (appealing to physics) it must have been stopped at the time of brake application. This is not a reasonable interpretation by an officer. If the officer knew that the car did not move after the brakes were applied, the officer would not think that the car was moving slowly. It was not moving. As stated in the problem.
  
  
• The distance the car traveled after applying the brakes equals zero means to the officer that the car stopped instantly when the brakes were applied.
  False. No officer would interpret a zero stopping distance to mean instantaneous stopping. However, this is true vacuously if the car is already stopped. Still, that's not what it would mean to an officer. Maybe to a math geek.
  
  
• The distance the car traveled after applying the brakes equals zero means to the officer that both B and C are possible, even though one or both are not realistic.
  Again, false, since a zero stopping distance would not cause an officer to think that C is possible. It might be enough to make a math geek think that C is possible (though not realistic).

Thus, the only reasonable meaning to an officer is A. This, however, has little to do with math, and more to do with unstated assumptions about police officers.

Let me rephrase the question that was asked: What would it mean to an officer if a car didn't move at all from the moment the brakes were applied? It would mean the car was already stopped.

I'm gonna bitch some more...

[cubetime.livejournal.com]

Things the problem doesn't say:

• Whether or not there were skid marks.
  
• How long the skid marks were, if there were any.
  
• How the officer knows that the distance the car traveled after applying the brakes equals zero.
  
• Whether or not the car was on an incline.
  
• Under what conditions braking results in skidding (if any).
  
• Whether or not the car was already skidding when the driver applied the brakes.
  
• Whether or not the car started spinning when the driver applied the brakes.
  
• Whether or not the car was already spinning when the driver applied the brakes.
  
• Whether or not the car was on some sort of conveyor belt system.
  
• The officer's mathematical and scientific background.
  
• The intelligence level of the person who wrote the question.
  
• And a host of other things...

[leech.livejournal.com]

Kill!

[stereotype441.livejournal.com]

You know, what really impresses me about all the responses you got, Tracy, was that in spite of how horrible the question was, a bunch of people actually put serious consideration into what the correct answer is. And they went above and beyond just trying to figure out what the teacher wanted to hear.

The sad thing is, none of these insightful answers would have gotten any more points than a lucky guess.

I think one of the most valuable things I got out of my education (including both K-12 and college) was an ability to take problems seriously and apply my whole brain to them, not just the figure-out-what-the-teacher-wants-regurgitated-to-them lobe.

I hope you show this discussion to your student. I think it's tremendously educational to see everyone's perspective on the problem...and how stupid it is.

And by the way, my FOWTTWRTT lobe says the answer is A, because A matches the formula, and all the rest of the answers sound like the teacher was trying desperately to come up with red herrings to fill out the test. :-)

[175560.livejournal.com]

This is the stupidest goddamn fucking multiple choice question I've ever seen -- and this is coming from an ex Calc teacher who once wrote deliberately devious multiple choice questions for his midterms. However, in contrast to the unfortunate test-writer that we're discussing here, I always made sure that the wrong answers were just that: WRONG.

Oh, and I agree with pub's FOWTTWRTT lobe.

(The spell checker says:
FOWTTWRTT: FETTERED, FITTEST, FOOTREST, FUTURITY, FORTUITY, FRITTER, FORTRAN, FATTEST, OTTERED, FOSTERED, COTTERED, FATTIEST, POTTERED, TOTTERED, FEATURED, FODDERED, FEDERATE, FERRET, FITTED, FLATTERED, FLUTTERED, FORTRESS, FRITTERED, FETTERING, GETTERED, TROTTER, DORETTA, DORETTE, FLORET, FRETTED, FLORETTE, FILTRATE, FOOTNOTE, FEATEST, FETTLED, FRAT, FRET, PORTRAIT, TROT)

[goteam.livejournal.com]

There should at the very least have been an option that involved the car slamming into an immovable object without braking, and thus leaving no skid marks. But I feel like I've won some kind of moral victory by getting them to admit that the available answers included a typo.