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I have seen a number of questions that ask if we should avoid certain types of questions, and who is welcome here. Let's ask each other the biggest question we can: What is your vision for this community? What would help you in your work? How sort of community would help you be a better math educator?

We make the community ourselves. It's name is Mathematics Educators. If you are a mathematics educator, you are part of this community. What would you like it to look like?

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    $\begingroup$ As you say, this is your site, so I'm not going to answer directly. However, I think I sum up most of my hopes on another question. As a non-expert, I'd love to see a site that, when I look at questions, makes me feel like I walked into the wrong bar. Not that the community should unwelcoming by design, but rather as a consequence of being a site for experts. $\endgroup$ – Jon Ericson Mar 15 '14 at 0:53
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My vision:

Teachers and other math educators at all levels can find useful information here, including answers to specific questions. (Math educators include leaders of math circles, homeschooling parents, anyone who is trying to help someone else understand mathematical ideas.)

Because teaching is not a science, people here will respect different philosophical stances. We will all do our best to document, through specific experiences, or research, what we suggest.

My own philosophy starts here: The term 'educate' comes from the Latin 'to bring forth'. We are not pouring knowledge in; we are bringing forth understanding from our students, helping them to build mathematical concepts in their minds. The more we can help students recreate mathematical ideas themselves, the stronger their learning will be.

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I'd like to see answers include references to empirical research, when possible. There has been a tremendous amount of research done on math education at both the K-12 and university levels. Let's make use of it.

I say this because many of my intuitive feelings about how math should be taught do not seem to be empirically supported. I would hate to unknowingly give useless or counterproductive advice, and I hope other answerers will be similarly conscientious.

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    $\begingroup$ Potato, I have seen much research that is flawed. Something as nebulous as education can be defined in many ways. Your definition will lead you to certain assumptions in your experiments. I'd be happy to give specific examples. Also, even good research often shows that one method helps a certain percentage of students, while some other, quite different method might help another percentage of your group. I feel sure that our experiences can tell us much of value, sometimes more than any research. $\endgroup$ – Sue VanHattum Mar 14 '14 at 21:16
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    $\begingroup$ @SueVanHattum I'd love to see some examples! Ideally, research provides a reality-check for our intuitions. I'm wary of purely anecdotal answers because many people on this site are very talented mathematicians, and their experiences may not generalize to the majority of students. But I think you're right that we should respect the experiences of professional educators. $\endgroup$ – Potato Mar 14 '14 at 21:29
  • $\begingroup$ Another thing to keep in mind is that the tension between internal validity ("the study is controlled, but probably outside the classroom") and external validity ("the study is inside an actual classroom, but more qualitative than quantitative") in education research is probably going to be a re-occurring thing we see in our community. I think we should be on the watch for it, because qualitative, quantitative, and anecdotal evidence all have their place here. $\endgroup$ – adamblan Mar 15 '14 at 17:07
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My vision for MathEducators.SE is that we have a good place to ask quality questions and receive quality answers. I hope that this can be the place where people go to find answers for their questions relating to mathematics education. I would like to see questions/answers on topics like (just some random examples)

  • methods of teaching
  • research in mathematics education
  • questions about introducing various topics
  • good examples that teach a certain concept
  • theories of learning

It is clear that even in this list of topics we will have different opinions. And so I believe we need to find a good way to deal with differences of opinions.

And I believe that everyone is welcome. We would not discriminate against anyone. It is not about who you are, it is about how you contribute.

That said, a core philosophy of Stack Exchange is:

We welcome questions that are clear and specific, representing real problems that you face; Stack Exchange is not the place for conversation, opinions, or socializing.

I think and believe that we have to respect that. We have to acknowledge that Stack Exchange is not just another forum where anything goes. We want to be inclusive, but we shouldn't accept all questions/answers. I think a this philosophy is one of the key reasons that Stack Exchange has become such a success. As I have seen it discussed on math.SE new users might feel like they are not welcomed when their questions or answers are closed or even deleted. From their point of view they are just trying to contribute. But if we want to be respected for the high quality, then that necessarily means we can't accept just anything.

I am afraid that if we allow answers that rely too much on personal anecdotes and experiences we end up just starting discussions and arguments. The stronger users will then end up running the whole site and we end up turning professional educators away.

Also, if we do not obey by this general philosophy, I would be afraid that Stack Exchange would shut the site down for us. But maybe one of the higher level moderators could address this for us.

But again, education will depend heavily on experience and personal stories. This is certainly much of my approach to teaching. I base my philosophy on what I have actually experienced. But I also acknowledge that when providing an answer I need to do more than just say " I feel like ...", "In my experience ...". I need to be more objective. And this all starts with having questions that are well-defined. Questions that have as definite answers as we can.

One way we can get good answers would be to require (yes require) that the answer is based not just on opinion. The answer always should contain objective information that contributes to answering the questions. So this could for example be citing research in mathematics education. I agree with Potato that there is a ton of good research out there. And we could probably all learn a lot from studying some of this.

This is a site for mathematics educators and people interested in mathematics education. By forcing ourselves to have to support our position with objective data, then that will increase the quality of the answers.

Yes, this means that it will take a bit longer to write an answer. But if we get better answers, maybe that is OK?

So, my vision is to see quality questions that have quality answers that make you have to think. Answers that encourages further study and though about the question.

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I don't necessarily disagree with anything the other posters have said, but if it becomes the norm that answers should be accompanied by references to studies in mathematics education, then I should exit this site eftsoons and rather speedily. The things I can bring are my years of experience teaching college math, and my collection of good examples that seemed to have worked in inspiring various and sundry students. Having worked on both sides of the pond, I hope to also be able to add some multicultral flavor to the site, but that is by no means my primary objective.

I would just like to compare notes with other math educators: what works, what does not? Exchange ideas and such things rather than try to defend/rebutt the hottest trends in education. Having read the other answers I realize that the SE software is not necessarily ideal to that end, because such questions do tend not to have any definite answers. But questions of that nature have been rather popular (at least in terms of answers and upvotes) in Math.SE.

I have been relatively active in Math.SE, and it is a live possibility that the questions I am most interested in will continue to appear there as opposed to here. We shall see. The boundary between this site and Math.SE will be fuzzy for a long time. And it may be best not to attempt to define it very precisely too soon.

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    $\begingroup$ May be on this site I should be asking questions as opposed to answering them? That might actually be better! $\endgroup$ – Jyrki Lahtonen Mar 25 '14 at 17:26
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    $\begingroup$ I doubt a "should" in the sense towards must or that is expected will or should happen throughout. I think your vision of the site is not at all a minority opinion and academia.SE shows that it can work for an SE site. $\endgroup$ – quid Mar 25 '14 at 17:35

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