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Proposal: Mathematics Learning, Studying, and Education

Teaching mathematics is different from teaching most other subjects in many aspects, one of them arguably being that it is better fitted for the Stack Exchange format, because the possible questions are “harder”. Still, it might be wise to define some softness threhold, not only to avoid overlap with a possible education SE, but also to avoid questions, which are not fit for Stack Exchange at all.

Some example questions, which might be close to such a threshold:

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You raise two issues:

(1) There is potentially some overlap between this proposed Stack Exchange and the proposed Eduction Stack Exchange.

(2) We should be careful about questions that are "too soft".

Issue (1)

For issue (1), I'm not sure this is something we have to worry about unless both of these Stack Exchanges make it to beta. Even in that case I would lean towards being flexible--any question here is being asked in the context of teaching math, and I wouldn't want to migrate a question unless that context clearly had no effect on possible answers. For example, the question

What are the best teaching methods to be a good tutor?

is clearly being asked in the context of math tutoring, which is pedagogically very different from, say, writing tutoring. (I do have some unrelated issues with this question — it seems extremely broad, and it would be better if the questioner could narrow it down a bit.)

The question

How do I deal with one very bright and vocal student who shouts out the answer to every question?

is closer to being perhaps better suited for the Education SE, but even in this case I think this is often a challenge that's specific to math classes. The rhythm of a math class tends to be very different from classes in other subjects — even classes in other STEM fields — in that the whole class often needs to stop and think about a problem for a few minutes. If one student shouts out the answer early, it can short citcuit this process, and the other members of the class don't get the necessary problem-solving experience.

Issue (2)

This is a reasonable concern, but I don't think the questions you mention are any softer than, say, a typical question on the Academia Stack Exchange. The question

What middle and high school topics should be taught in mathematics?

is again quite broad, but if it were narrowed down a bit I think it could be an excellent question.

The questions

At what stage of development should students be first exposed to the notion of a proof?

How do I approach teaching a student who needs math but does not enjoy it?

What role should proofs play in a first calculus course?

seem to me to be reasonably clear and specific, and there might very well be research in the literature about all three of these. It is true that different teachers or professors might have different opinions about these questions — which makes them a bit subjective — but there is still a lot of value in learning the range of opinions that exist, as well as the arguments behind them.

At worst, questions like this should be made "community wiki", and I think we have enough specific, non-soft questions that we fit reasonably well into the Stack Exchange format.

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I thought long and hard about whether to put this here as an answer or add it as another question. It's certainly too long to just be a comment.

One of the major differences between what this site is proposed to be and Maths.SE is that at Math.SE there may be questions with more than one solution, but if they are solutions they none the less have to at least be correct. In Mathematics education, how to go about it is much more opinion based. Discussion becomes a much more appropriate way to go about things than just having questions and answers.

Example In Australia recently, our illustrious federal education department put forward a proposal to get our best researchers more involved in education because according to them, these are the people who can best determine what content should be taught at undergraduate level. To me, this is an extreme view that I strongly disagree with but it's not totally wrong in the mathematical sense. Of course they should play a rôle, but for me the question is how much. My reasoning involves things like (1) the level of specialism involved in research these days doesn't necessarily allow for an overview (2) if they're our best researchers shouldn't they be left to get on with their research and so on.

Plus, the motivation of said government department comes into question: If our top researchers spend more time involved in education then they can spend less money on employing people who specialise in education. These kinds of decisions have forced major changes on university mathematics departments and how they provide mathematics education. End Example

My point is that a significant reason this site was proposed in the first place is due to the difference between handling maths content questions and answers and discussing maths pedagogy. This is a kind of meta site, but it's meta to all of maths education in the world not just meta to how a maths question and answer site should be run on the internet.

It could be argued that my above example is a question that could just lead to heated and unproductive argument but its subject, and decisions made about it, lead to real and significant changes in the real world and impact the lives of many people.

I believe that a site such as this one being proposed should be more about enabling discussion and less about hoping for pat answers to clear cut questions. When I did my graduate diploma in education, the four core compulsory subjects were psychology, philosophy, history and sociology side by side with a mathematics teaching major and a science teaching minor. There were several student teachers who thought the core was too soft and irrelevant to education, but I strongly disagree and that in itself is an important point, there was much disagreement.

If a question is deemed too general then it could be rewritten as a question asking how to refine it. Then, if you have a well formed opinion on how to break it up into sub questions, that could be provided as an answer which then gives rise to a collection of new questions.

In conclusion, I think it's obvious that this new site will need a different set of rules for questions and answers than Math.SE. Perhaps in developing those rules we could learn from a site like Philosophy.SE. Their day to day business is much more discursive than what takes place on Math.SE and how do they go about avoiding such discussions getting out of hand?

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    I think this is very good input. To add on, if one looks at the current questions rated 10 or above, answers to the vast majority depend on the experience of the answerers, and do not have a clear-cut answer. I think this is good, and multiple, potentially completely different, answers will help whoever posed the question to have multiple viewpoints. This should be encouraged, as you say. – Mike Miller Feb 3 '14 at 9:12
  • Just wanted to add to what I believe is the importance of such questions as the example in my answer. What if you're working in a university and you're a member of a body which is going to vote on such a proposal and you want to consider a variety of viewpoints in a more global context than your own and get some ideas on how to bolster or evolve your own viewpoint based on the experiences of other institutions? – Geoff Pointer Feb 12 '14 at 1:23

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