
“How old is the shepherd?” – The problem that shook school mathematics - fjmubeen
https://medium.com/@fjmubeen/how-old-is-the-shepherd-the-problem-that-shook-school-mathematics-ad89b565fff#.7wxk6psys
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harperlee
I don't think it reflects the fragility of the student's mathematical
reasoning behaviour so much as their ability to play the meta-game of the test
itself. They know they are expected to provide answer, and that they don't
know how to reach for it - so they play the odds. I for one have used this
technique, exploiting for example the fact that in school, correct answers
tended to be round numbers, as an heuristic, for example.

I believe if "insufficient data" was stated as a possible answer (which the
student's are not accustomed to), they would state that.

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mc32
Exactly. Students say to themselves, "while questions can be tricky, they are
seldom so tricky that no answer is expected. As far as I can recall even for
tricky questions, an answer was ascertainable, I must be missing something,
this is all I got, so here goes. A remote chance is better than no chance
(answer) and at least I tried and didn't give up".

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StefanKarpinski
The obvious way to improve this is to make "insufficient data" a somewhat
common answer to problems (others have mentioned this). Despite the apparent
flippancy, I think this is a deep change, since despite its simplicity, it
forces students to think about the problem solving process itself.

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rossdavidh
I think that, if they were trying to determine this outside the context of
"here's a math problem from a teacher-type person", they would realize there's
no way to know more easily. But, this still makes an important point, that the
way we teach math doesn't look much like how we use it, which raises the
question of whether we are really preparing students to use the math they are
allegedly learning.

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robocat
> Yesterday 33 boats sailed into the port and 54 boats left it. Yesterday at
> noon there were 40 boats in the port. How many boats were yesterday evening
> still in the port?

Solvable: solution is a range.

All problems become unsolvable if you allow unknowns to creep in: "I have one
apple in two hands. How many apples do I have?" is completely unsolvable
unless you make assumptions about absolutely everything.

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fallingfrog
Yes, minimum zero, maximum 73..

I don't know if it's really a bad thing for students to assume that their
teachers are not going to mess with them by giving them an unsolveable
problem, doesn't that just indicate that they trust their teacher? In the case
of real world problems, there may or not be a specific correct answer, and I
think students know that on some level. Maybe a better way to ask that
question would be, "Suppose you know that there are 125 sheep and 5 dogs in a
flock. Your friend Amelia asks you, 'How old is the shepherd?' What would be
your response?" That way the hypothetical nature of the question is more
obvious.

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perilunar
Obligatory link: A Mathematician’s Lament

[http://www.maa.org/external_archive/devlin/LockhartsLament.p...](http://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

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nitwit005
If you want to know how a student will confront a real problem, you need to
create a context where they won't try to outsmart whoever wrote the question.

It's entirely possible to solve a math problem using psychology instead of
math, because math problems are made by people. We've all done a horrifying
amount of schoolwork, and thus have a pretty good data set in our head from
which to extrapolate.

Suppose I tell you that an algebra textbook question includes the numbers 32,
4 and 64 in the problem text. What's the answer? I'd bet most of us would
guess 2 or 4.

