A “simple” 3rd grade problem • Hacker News Board

Re: A “simple” 3rd grade problem

#11

Post by gbaygon » Sat, May 04, 2013, 4:03 PM UTC

jostmey wrote: post #3

The story is a wonderful illustration that the human brain is not perfect. It seems that most people when first reading the math problem get it wrong. Our brain is designed to first jump to conclusions before seriously thinking about the problem. The human mind may be the highest form of intelligence on the planet, but that does not mean that there are not serious design flaws. The human brain was born out of a proce…

The problem is not if the humar brain is/isn't perfect (compared to what?).

The matter here is that the question is not mathematically strict and so the reader is free to interpret it as he pleases, and multiple solutions spawns naturally.

The teacher is very mistaken trying to assert a unique solution.

Re: A “simple” 3rd grade problem

#12

Post by redblacktree » Sat, May 04, 2013, 4:03 PM UTC

hmottestad wrote: post #8

kaeluka wrote: post #7

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…

If you were to cut off two pieces of the board from an unknown source, you'd require two cuts. Three pieces would require three cuts (with the rest remaining behind). I don't think the wording really allows for this interpretation, but that is the only way I could explain the alternative answer.

Re: A “simple” 3rd grade problem

#13

Post by viraptor » Sat, May 04, 2013, 4:05 PM UTC

Oh the "simple" questions... reminds me of the fragment from Cryptonomicon where Lawrence Waterhouse answering the usual trivial math question about boat going from A to B with some speed X while the water moves with speed Y. He failed, even though he decided the answer cannot be that trivial and wrote a long solution involving analysing the flow of the water using partial differential equations (later published in a paper).

Re: A “simple” 3rd grade problem

#14

Post by bayesianhorse » Sat, May 04, 2013, 4:05 PM UTC

The problem at hand is "what are you supposed to do" vs the actual problem at hand.

At first I had a difficulty seeing why 20 should be wrong, but then it dawned upon me: The teacher set out to create a word problem for a specific mathematic solution strategy. Students probably were inundated with this strategy for weeks before the test, so for them it is very clear what they were supposed to do.

Re: A “simple” 3rd grade problem

#15

Post by downandout » Sat, May 04, 2013, 4:05 PM UTC

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 marked the answer wrong (which could have just resulted from looking at a publisher-provided answer key) but actually wrote down a completely incorrect justification for the teacher's incorrect answer is rather disturbing to me. Also, this did not occur in a vacuum. Either no other students answered the question correctly, or the teacher saw the question being answered correctly by others and repeatedly marked it wrong with the same justification. Either way, it causes concern about the teacher.

Re: A “simple” 3rd grade problem

#16

Post by [deleted] » Sat, May 04, 2013, 4:06 PM UTC

[deleted]

Re: A “simple” 3rd grade problem

#17

Post by jamessb » Sat, May 04, 2013, 4:06 PM UTC

moioci wrote: post #6

Who was it that said the biggest problem in programming is concurrency and off by one errors?

Well, Phil Karlton said that "There are only two hard things in Computer Science: cache invalidation and naming things".

Some people list off-by-one errors as the third hardest thing.

Re: A “simple” 3rd grade problem

#18

Post by buttscicles » Sat, May 04, 2013, 4:07 PM UTC

kaeluka wrote: post #7

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."

>but the question allows different interpretations and both answers are correct assuming different interpretations.

There is only one logical interpretation (though you'd have to actually think past the conclusion your brain jumps to), the question was perfectly clear about the board being cut into two pieces.

Re: A “simple” 3rd grade problem

#19

Post by alexvr » Sat, May 04, 2013, 4:09 PM UTC

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 would have probably answered "???". So kudos to this kid.

Re: A “simple” 3rd grade problem

#20

Post by auctiontheory » Sat, May 04, 2013, 4:16 PM UTC

A friend of mine teaches school in rural North Carolina - here's what she tells me.

Her school has to meet certain percentage-based "standards" - I forget the exact numbers, but let's say 75% is the cutoff. So now when Joey gets 5 answers right out of 10, the resulting 5/10 is defined as "75%."

We're doomed.