When grading things, ppl usually face hundreds of copies at a time and it's very tedious. It's easy to scrutinize a single highlighted problem that someone got wrong in hindsight, not realizing the person might've only dedicated 7 seconds to this problem out of 1000 others that were graded correctly.

I personally try to give them the benefit of doubt and assume best case scenario (but I also understand it might not be).

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 not in any way saying it's okay that we have text books teaching clearly incorrect information; I'm also not in the know on how 3rd grade math textbooks are created. That said, I've been in tons of jobs where you're expected to produce a crap ton of work at a breakneck pace and god help you if you want five minutes to check your work for dumb errors, because y'aint gettin it.

Of course, it could also easily be said that this is also the publishers fault for creating a working environment that isn't sufficiently rigorous or overburdens the employees.

http://www.textbookleague.org/103feyn.htm

Oh, yes, been there and I have the video. Don't you work from pre-written and checked marking schemes?

I accept this, but I'm assuming the original algorithm that a creative student produces will pass tests/produce same output as the 'textbook' solution. My understanding of the original article is that a correct final answer was marked wrong.

"Same goes for most college math."

Absolutely. My favourite from 16+ maths (GCSE in UK) is the area of a trapezium. Most find the mean length of the two parallel sides and multiply that by the distance between the parallel sides (so make a rectangle of the same area). About 1 in 15 break the trapezium up into two triangles and add the areas.

In the real world, you can ask more questions and get a more complete picture. On an exam, generally you must accept what you are given.

As it is, this is one case among many (not all about grade schoolers and not all 'stories on the Internet' by a long shot) and the professor doesn't always acknowledge they were wrong. Speaking as an engineer, the work is hard enough when you do understand the math.

Here is another version:

A fence is made using 15 posts spaced equally along a straight line. There are 3m between each post. What is the distance between the first and last post?

When I'm teaching this kind of thing, we go out and walk around the building site opposite with a few 15m measuring tapes. The physical walking out and measuring helps.

Change "There are 3m between each post." to "The distance from one post centre to the next is 3m"

Which illustrates the general point: you need teams working the test and checking their answers against what the writer thought the answers were. You also need English specialists checking the wording of the questions.

Yeah, my hand is firmly down too…

I've also had students in Functional Maths classes just sketching arrangements of posts and counting the spaces.

;-)

The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes.

It's a bad question.

Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considering the illustration. But the keyword there is "interpretation." The question is ambiguous.

(My argument is taken from this answer: http://math.stackexchange.com/a/380007 )

The student chose a ratio of 1,1,1; which is the logical equilibrium point. your image shows 1.5,0.75,0.75; which is the second most logical ratio because it is in the form x + 2y = 3 (which can be trisected an infinite number of ways while maintaining that ratio). The third form would be x + y + z = 3; which can also be trisected an infinite number of ways and would be the least intuitive.

i am agreeing with you, i am just trying to show that it is illogical for it to be 'open for debate'.

There is a game theory term for this type of equilibrium, but i forgot its name. Its the same type of equilibrium as "there are three colors and a number, which one is different?" type sesame street problems.

However, the teacher corrects it by writing "4 = 20". This is plainly wrong and with no possible explanation, since following the above reasoning, cutting in 4 pieces would require: 10 + 10 / 2 + (10 / 2) / 2 = 17.5 minutes.

the problem is poorly formulated. The teacher would have been correct if it had said "it took 10 minutes to cut away 2 pieces from a very large board (thus resulting in 2 cuts, 3 pieces total)", whereas the student's answer assumes a single cut, which is more reasonable.

In the previous edition it was probably something like "Marie works in a factory which makes cars; it takes her 10 minutes to finish two cars. How long will it take Marie to finish three cars?"

And the answer to that would be 15 minutes, and the reasoning in the answer (based on reducing fractions, which is what it's probably supposed to teach) would be correct.

But probably in the next edition the question changed from putting things together to cutting them apart, and the author/editor simply didn't realize that these are not interchangeable. The teacher, meanwhile, probably didn't look too closely at it, and simply applied the answer and reasoning supplied in the teaching materials for the question set.

None of which implies that the teacher can't do the math; rather, it implies systemic problems in the way the materials are produced and in the methods used by teachers to grade the work.

[1]http://math.stackexchange.com/a/380007

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

Yes, if you want to be very nit-picky the question is undefined, but this is a third grade math test and the only reasonable answer is 20min. The student was absolutely correct.

I've seen enough of that in high-school physics where the teacher literally doesn't understand what the hell the problem is asking to piss off the Good Humor man.

Some inferences have to be made, this is a human taking the test not a robot, and it's a 3rd grade test.

Even if the size of the pieces were specified, she could be cutting a different kind of wood or using a different saw or the humidity level could be different, but she's still "working just as fast".

3rd graders would be confused if you attempted to be completely unambiguous with this time of question.

(Not saying I like it, but it's the way it is many places.)

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.

* (the feeder competition for the British Mathematics Olympiad, and then the International one)