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I wonder if such questions should be avoided at least at this early beta stage, if not "for all time". I do not think this is the kind of question that experts ask each other, as the reasonable things to consider when beginning to deal with such a question are: "why is it important to teach students who do not have the background?" and "why don't the students have the proper background if this is important to them?".

Could we instead shift our focus slightly by instead asking: "What background knowledge is helpful for enabling students to understand <concept>?".

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  • $\begingroup$ are you pointing to a particular question? If not, you are doing the same sort of thing that you are asking us to avoid - framing something in the negative. If so, please point to the question at issue. $\endgroup$ – Sue VanHattum Mar 14 '14 at 13:31
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    $\begingroup$ Why the downvotes? While I don't agree with the proposal of the OP, I do think that this question is somewhat important. $\endgroup$ – Roland Mar 15 '14 at 8:30
  • $\begingroup$ @Roland: re downvoting on Meta, see also meta.matheducators.stackexchange.com/questions/294/… $\endgroup$ – J W Apr 15 '16 at 4:21
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I think that this kind of question deserves appreciation on its own, and it should not be avoided.

Sometimes, teachers have a certain curriculum to teach, which they haven't chosen completely on their own. The questions outlined by you (e.g. Any tips in explaining the central limit theorem in statistics?) are valid questions of how to teach math.

The comments you are mentioning ("why is it important to teach students who do not have the background?" and "why don't the students have the proper background if this is important to them?") will help to understand the concrete teaching situation in a better way, and giving specifics will help to provide better answers.

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    $\begingroup$ I agree. This question presupposes that the students that we teach are in math class because it is important to them. We don't all teach classes that students actually choose to take. $\endgroup$ – jbaldus Apr 25 '14 at 5:14
  • $\begingroup$ @jbaldus, it is mostly that somebody else decided that <some math> will be important to them in some (indeterminate) future, the students themselves usually have no clue what the matter is all about. Particularly at high school or as beginning undergraduates. $\endgroup$ – vonbrand Jun 17 '14 at 13:32
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Another reason for allowing and even encouraging such questions is that they are very relevant to another group of math educators: instructors at enrichment programs such as math circles and summer camps. Often in those situations one wants to introduce students to an exciting idea for which they don't have the usually-required background, not with the goal of deeply learning the material but rather with the goal of conveying excitement about mathematics and an appreciation for what is out there beyond what they see in school.

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  • $\begingroup$ Exciting somebody with something they can't really understand sounds quite strange... $\endgroup$ – vonbrand Jun 17 '14 at 13:33
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    $\begingroup$ @vonbrand Isn't that what popular science writers do for a living? $\endgroup$ – Mike Shulman Jun 18 '14 at 14:33
  • $\begingroup$ Yes, but the good ones are far in between. If I had that talent, I'd better not waste it on textbooks... $\endgroup$ – vonbrand Jun 18 '14 at 15:06
  • $\begingroup$ @vonbrand I don't consider good textbooks (or teachers) a waste. $\endgroup$ – Mike Shulman Jun 18 '14 at 15:38
  • $\begingroup$ It's just that you'd probably make more writing a book for wider audiences... $\endgroup$ – vonbrand Jun 18 '14 at 15:45
  • $\begingroup$ @vonbrand Well, the topic here is about teaching, not about making money. $\endgroup$ – Mike Shulman Jun 19 '14 at 16:16
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I have some small experience in reading of such 'non-standart' courses: I had to read some short basic course in statistics for students in social science (PR). Of course most of these students has no enough mathematical or technical background.

Reading of such courses has some aspects that will not present in classical courses. E.g. some topics should be given using another (possibly simplified) approach, etc.

So such questions are valid questions of how to teach mathematics and increase area of interest for our cite.

Therefor we should not avoid such question. However, may be it will reasonable to mark such questions with some 'special' tag.

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  • $\begingroup$ What tag do you propose? "missing-prerequisites" or something like that? $\endgroup$ – vonbrand Jun 17 '14 at 13:34
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Should these be avoided? Absolutely not. If math has taught me anything, it's to study the edge cases, the situations that push the boundaries of my assumptions :-)

But these types of questions might also need to be tagged with some kind of signifier. I wouldn't turn to the answers of such a question to structure an entire course, but I would certainly turn to them to figure out how to work with a particular audience, or how to tailor material to a particular kind of student.

Might I propose the tag "extremity", or "potential problem", or even "edge case", to flag these kinds of questions?

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