I'm impressed that the student thought it through, but people are giving the grader too much of a hard time. If the question was instead, "If a machine can produce 2 cars in 10 minutes, how long does it take to produce 3 cars?" the teacher would be correct. If you've ever taken a standardized math test, it's easy to assume that the question is just a variation of that classic question. If I were a third-grader, I wou…
Yes, if it was a different question then the teacher might have been right.
Kidding aside, this is probably a good demonstration of how shoe stringing our education budgets might not be the best idea.
If I cut myself shaving in two places with one motion of my razor, how many cuts have I made?
The answer to this question is open for debate. You see you didn't specify whether you cut all the way through resulting in two halves of a person with one cut on one of them. And which one!
My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.
You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.
In grade school I had an argument with my science teacher about wheels. She said that a point along the outside of a wheel moved faster than a point nearer to the center (which is absolutely correct). However, she followed that up by saying that the outside of the wheel makes more revolutions than the inside. I tried to correct her, but she wasn't having any of it. So I grabbed my bike from outside, brought it into the classroom and tied two pieces of string onto one of the spokes on the bike: one near the axel, one near the tire. A few spins of the wheel had her convinced, but I can't believe I actually had to do it.
The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only…
My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.
In high school geometry, I remember my teacher making some assertion that was plainly false - I think it was that 3 planes always intersect in a line. After arguing with him for like 15 minutes, I walked to the front of the class and wrote a proof on the board. I spent the rest of the class period sitting outside.
It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007
If it is ambiguous, there is no answer. There must be an answer. Therefore, it cannot be ambiguous. The answer given is the only one it is possible to give. Therefore, it must be the correct one. The context isn't so much "third grade" as it is "math test", and very, very few math tests allow "Question ill-formed as posed" as a valid answer. Maybe more should.
That's actually a great idea. If I were a math teacher, I would teach my class that IFQ is a reasonable answer to a question, and I'd throw in a few plainly ill-formed questions just to keep them on their toes. Actual thinking > correct answers.
I would've arrived at the teacher's solution, but the question allows different interpretations and both answers are correct assuming different interpretations. The correct answer would be "I do not know, this problem is under-specified."
Can you explain why you think it has two correct interpretations? I obviously thought 15 min when I first read it and my brain didn't want to accept any other solution until I read the post below where it said 20 min and explained it as 2 pieces = 1 cut = 10 min, 3 pieces = 2 cuts = 20 min. And now I can't see why my first thought was correct. Did you come up with some good rationale as to why it should be 15 min or…
Perhaps it's a really long stick and we are cutting off small pieces. Cut off one small piece: 1 cut. Cut of 2 small pieces: 2 cuts. Etc.
Perhaps the teacher or the author of the question understood the problem differently – we are cutting off small pieces from a long stick. So to cut off 2 pieces, we need 2 cuts, not 1.
You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very ted…
I agree with this. I think it's a pretty decent example of the fundamental attribution error. The context of the problem clearly sets it up as one of those "everyone gets this wrong, so make sure you think a second" situations (I had to think a second, anyway). I'd extend that to the publisher as well, though (or at least it's individual employees creating the book). First off, assuming the answer key has "15", I'm n…
On the topic of how math textbooks are created, you might like this commentary from Richard Feynman when he served on a school-math-textbook recommendation committee: