Hacker News Reader

Comment by jrabone | Hacker News Reader

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

View on HN

It's only open for debate if you're being extremely pedantic. There is even an illustration demonstrating exactly what the cuts look like!

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 agree. If I am the principal and the student protests to me and the teacher gives some bizarre-ass interpretation of the problem to me, the teacher will have a problem with me.

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.

There is a picture of that illustrates the cut that is being made well enough to infer.

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.

Look at the image provided with the question. It shows a saw cutting the board in a way that leaves it unambiguous - the cutting time for that cut would be identical regardless of where each cut took place.

That's not a board...

In reality, it probably was not open for debate. This is third grade math, remember. The student probably spent the last three problems working similar questions covering ratios/fractions. And the student probably spent at least a few weeks of school working similar types of problems on homework. After so long taking these types of classes and tests, if a student answers a question without using knowledge gained from the class and gets the question wrong, well...what did they expect?

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

I would assume that the "*" next to the problem was an indication that this what not a 'time to fill a water bucket' problem and that more thinking would be required than the previous 3 problems.

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 think for most questions that are not very straight forward, IFQ would be a valid answer with only very little argumentation. That's why formal languages are needed.

The first round of the UK Maths Challenge * is multiple choice, and does often include questions with "not enough information provided" as one of the available answers. However, this isn't a mechanism for identifying badly phrased questions.

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

Reply on news.ycombinator.com