Self-Learner Considerations

Question

There have been several questions, answers, and comments so far that have mentioned the self-learner on the main ME site as well as the meta site. While it is awesome to see people who are not educators interested in furthering their own education and contributing to the site, I'm not sure if it's beneficial to the focus of the site. However, I'm also not sure if it's an issue. So I would like to hear opinions on the topic.

Question: To what extent should consideration for self-learners influence the direction and focus of the site?

Answer 1

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.

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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.

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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.

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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.

Answer 2

It seems that that should be determined by the users as the site develops. It seems premature to make a specific effort to either accommodate or exclude self-learners. What matters more is their ability to ask good questions. The ability to ask good questions is an especially important skill for self-learners, and something every new user of the SE needs to learn anyway.

Answer 3

I think that we should include self-teachers into the audience, which seemed to be some kind of consensus (or at least popular opinion) in the area 51 discussion.

It would help in the discussion if the OP contained examples of these self-study questions, so we could get a better view on the questions asked and see which kind of questions we'd like to see more of, and which not.

I like to point out that there are questions which don't depend much on the fact if this was asked by a teacher or a self-student, in particular requests for references and/or examples, like What are some great books for exploring mathematics? (not kids' books and not textbooks). Especially this category of questions shows that it might be a good idea to include self-students if the types of questions fall within our focus.

One way to do this is to introduce a tag named "self-study", "self-learning" or "self-teaching", where I prefer the latter since it transports out intentions best.

Answer 4

I don't think that questions from self-learners should be included since the site's focus is about teaching. But what can be relevant is a question from a teacher (then I think mostly at university level) asking how he/she can advise self-learns who will take an exam in his/her class maybe? That would be relevant in my opinion. Or general questions about study's of self-learners could also be helpful here (to have e.g. some arguments and material to convince students to attend your lecture).