3 ms·

Yes, there are many poorly written problems, but on the other hand, even well-written problems can have little basis in reality. Spherical cows in vacuum, and

by yongjik 13y ago

Yes, there are many poorly written problems, but on the other hand, even well-written problems can have little basis in reality. Spherical cows in vacuum, and all that. When a question asks "You throw a ball at 80 km/h at 45 degrees, how far does it travel?" you could argue endlessly about air friction, the exact height of your hand when you let the ball go, Coriolis' force, curvature of the earth, and the fact that you can never throw a ball that fast... but you are not being critical. You're just being obtuse. The point of the question is not to indoctrinate students that air resistance is negligible. It's to let students practice their knowledge of Newtonian dynamics so that they can later proceed to more complex problems (hopefully with air resistance) if they want. Context matters. So what about the original problem? I agree that the students' expectation that "there must be an answer" played a role, but I don't think the expectation is necessarily a bad thing. There's a reason that all the textbook problems (are supposed to) have nice answers: it actually makes it easier for the students to practice and internalize the concept they're learning.

pbhjpbhj 13y ago
>* ... but you are not being critical. You're just being obtuse.* // I disagree. One is being critical. If however you try to use that as an excuse not to perform the calculation then you're definitely being obstructive. It is absolutely right for a student performing such calculations to realise there are issues with it not being realistic. They should understand that it's an approximation and understand that even in a perfect, flat, frictionless world it's still an approximation [relativistic mechanics are not being used] but that nonetheless it's a useful model the result produced by Newtonian mechanics is useful. Indeed I'd say the realisation and ability to express the limitations mark out a student as capable of analytical thought. >it actually makes it easier for the students to practice and internalize the concept they're learning. // I fear you're making the calculation the end in itself (we have computers for that!) and not the subject of critical analytical thinking which IMO defines mathematics.
- yongjik 13y ago
  > I fear you're making the calculation the end in itself (we have computers for that!) Well, I have to disagree. Of course it's rather silly to make the calculation the goal in itself, but one needs to have a decent "feeling" of what would happen in a given domain. In math (up to college freshmen) or physics, that involves a lot of number-crunching. Until you get familiar with it. It's same as CS students implementing quicksort, merge sort, heapsort, etc., even though when they graduate they will all use libraries. You can't really grok quicksort by reading the textbook and say "Hmm, I see."
  - pflats 13y ago
    You can grok most sorting methods remarkably well, though, by lining up a bunch of office junk on a big table and working through the sorting algorithm physically.

by yongjik 13y ago

pbhjpbhj 13y ago

>* ... but you are not being critical. You're just being obtuse.* // I disagree. One is being critical. If however you try to use that as an excuse not to perform the calculation then you're definitely being obstructive. It is absolutely right for a student performing such calculations to realise there are issues with it not being realistic. They should understand that it's an approximation and understand that even in a perfect, flat, frictionless world it's still an approximation [relativistic mechanics are not being used] but that nonetheless it's a useful model the result produced by Newtonian mechanics is useful. Indeed I'd say the realisation and ability to express the limitations mark out a student as capable of analytical thought. >it actually makes it easier for the students to practice and internalize the concept they're learning. // I fear you're making the calculation the end in itself (we have computers for that!) and not the subject of critical analytical thinking which IMO defines mathematics.

yongjik 13y ago
> I fear you're making the calculation the end in itself (we have computers for that!) Well, I have to disagree. Of course it's rather silly to make the calculation the goal in itself, but one needs to have a decent "feeling" of what would happen in a given domain. In math (up to college freshmen) or physics, that involves a lot of number-crunching. Until you get familiar with it. It's same as CS students implementing quicksort, merge sort, heapsort, etc., even though when they graduate they will all use libraries. You can't really grok quicksort by reading the textbook and say "Hmm, I see."
- pflats 13y ago
  You can grok most sorting methods remarkably well, though, by lining up a bunch of office junk on a big table and working through the sorting algorithm physically.