Timeline for What number is the sum of two roots
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| Jun 20, 2017 at 18:48 | comment | added | R.P. | @DanielR.Collins: Also, there is no single optimal answer to a why-question, because different mathematicians may have developed different perspectives on the same piece of mathematics, and there's no way of telling which is better, except on the grounds of taste. To say that "there is no why to X" is really just a different way of asking: "why would you have supposed X is true in the first place?" I really don't see what is so wrong about that, as long as you're not dismissive of the question. | |
| Jun 20, 2017 at 18:45 | comment | added | R.P. | @DanielR.Collins: I do not agree with your assumption that the "why" of a statement is answered by giving the proof of the statement. Why-questions ask for vaguer things, they are a sort of meta-questions. 'Why can't we integrate exp(x^2)?" The answer is not: "here's a proof", but it could be: "because differentiating functions tends to make them more complex (i.e. the number of symbols needed to write them down tends to increase), while integrating makes them simpler, and there are fewer simple functions than complex functions". | |
| Jun 20, 2017 at 18:23 | comment | added | Daniel R. Collins | @René: Because of course there is a "why" to it. Saying "there is no why" is telling a student that they'll never understand math, that it's arbitrary and mysterious, and something that they simply have to submit and obey to some capricious authority. It's the worst, and most false, of all possible explanations. The whole point of math is deducible explanations from simple, accepted axioms. | |
| Jun 20, 2017 at 17:05 | comment | added | schremmer | @JessicaB René's "So you will have to treat the question as a moment where the student is discovering something that they won't be able to really get their head around unless they're going to do some serious mathematics. And it's not a bad thing if they decide not to do that." is the reason for my "Good question and I don't really know the answer." And of course I don't drop the issue. The idea is acknowledge the worth of the student's question rather than to humiliate her/him. We can then work through an answer satisfactory to the student ... even if probably not to "good teachers". | |
| Jun 20, 2017 at 16:48 | comment | added | schremmer | @René I already accepted mweiss' answer and I still think it is a good answer but if I had wanted to answer my question, your answer is exactly what I would have written because you see the student and consider what your response to the student is likely to do to the student. That is extremely rare as teachers are too fond of teaching to pay attention to the students. | |
| Jun 20, 2017 at 15:33 | comment | added | R.P. | @DanielR.Collins: Why is that? | |
| Jun 20, 2017 at 15:19 | comment | added | Daniel R. Collins | "I would start by saying that there is no why to it, it is simply that way and no other." -- This is my least favorite of all possible explanations. | |
| Jun 20, 2017 at 14:23 | history | edited | R.P. | CC BY-SA 3.0 |
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| Jun 20, 2017 at 14:14 | history | edited | R.P. | CC BY-SA 3.0 |
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| Jun 20, 2017 at 13:47 | review | First posts | |||
| Jun 21, 2017 at 4:37 | |||||
| Jun 20, 2017 at 13:47 | history | answered | R.P. | CC BY-SA 3.0 |