Too long; didn’t read: Many questions could as well have been asked from the perspective of a self-learner and also the learner’s point of view can be beneficial to some answers. Therefore I would welcome self-learners.
It does not surprise that we have a fair amount of questions about the content (in a very broad sense) that is presented during education, for example:
- What are good ways to illustrate or motivate some subject?
- What proof of a given theorem is best from a didactical point of view?
- In what order should stuff be learnt?
- Why is the curriculum the way it is?
- What book tackles a given subject with certain techniques?
Such questions and their answers are relevant for both, self-learners and teachers and usually only differ slightly in their point of view when being asked. Therefore I think that it is not an issue, if self-learners ask such questions. Moreover, answers to such questions are likely to benefit both, self-learners and teachers.
From another point of view: If we banned self-learners, they could still ask certain questions (see above) here, if they would only hide the fact that they are self-learners. One likely way to do this is to provide little background to the questions to obfuscate the lack of knowledge. This would result in questions which are not very well asked, but also far from closeworthy. Therefore I consider it better to openly accept certain questions from self-learners.
Also, there are a few questions here which might benefit from the learner’s point of view, like “Is $e^iπ+1=0$ a good motivation for introducing $e$ or $i$? Why (not)?”. One issue brought forward here was that complex exponentiation is very unlikely to be introduced at that point, which could as well have been spotted by a learner – and I can imagine similar cases in which only the learner would spot this. In general, I would be very surprised, if none of the contributors had reflected their first impression of this formula, i.e., the learner’s point of view. Moreover the questions here were:
Is it a good motivation […] for the students if you tell them about the
formula above […]? Or is such a thing distracting or even unhelpful since you overload the students with stuff they don't know at that point (and maybe don't care)?
So the question is directly asking for the student’s point of view. An elaborated explanation from a student why he considers this motivating or not could actually be a helpful answer here.
For these reasons, I think that questions from self-learners should be welcome here, as long as they are about the “process of teaching or learning mathematics” (to quote the original proposal) – other questions should be deleted or moved to the Math SE. Narrowing down criteria for such questions is however something we better do (if at all), when such questions are actually asked.
For answers from self-learners, I would distinguish two cases:
- Questions that ask for arguments: A self-learner’s answer should be well reasoned (like any answer) and should be judged by its arguments and not by its author.
- Questions that ask for experience (e.g., with teaching some technique): A self-learner’s answer should tell its point of view (as should any other answer to such a question).
Should this be agreed on, I suggest to change the subtitle (“Mathematics Educators Stack Exchange is a question and answer site for those involved in the field of teaching mathematics.”) of the site to include self-learners (as the original subtitle did). But that would be another discussion.