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Proposal: Mathematics Learning, Studying, and Education Proposal: Education

This question was originally about Math Teaching being a duplicate of Mathematics, but the discussion turned to comparing Math Teaching with Education.

I thought it might be worthwhile to discuss the two proposals so no surprises happen when it is time for beta.

Let's compare the two proposals:

  1. Education: Proposed Q&A site for professional educators and education researchers, K-12 & higher ed teachers, vocational teachers, school administrators, school faculty, education psychologists, education historians, education theorists and philosophers, non-profit educationists. The scope of this site certainly includes mathematics and much more. The site was proposed roughly a year ago. There are 87 followers, with 16% from MathSE and only a trace amount of MO. There are 9 upvoted questions.
  2. Math Teaching: Proposed Q&A site for math educators, enthusiasts, students, professors. This site has a much more narrow scope. It was started 29 days ago. It has fulfilled its first stage and has 85 commitments. More than half of users are active on MathSE, and more than one in four are active in MO.

In my opinion, Education is a better site concept than Math Teaching. However, I believe that it is easier to get a Math Teachng site going than Education. I feel this way because many professors and students in math identify as mathematicians more than as educators, even if their primary interest is teaching. I think it will be easier to establish an active userbase in math teaching.

I also believe that Math Teaching will have many, many questions on how to teach specialized mathematical concepts like groups, and answers will require an extensive mathematical background.

Given the vagaries of Area51, Math Teaching may very well stall and be overtaken by education. Perhaps the mods will request a merger. I think we should see if Math Teaching can make it.

I'd like to hear anyone else's opinion.

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One education site for all levels and all subjects seems too broad and too heterogenous to be a good idea.

I could imagine (to participate) a general site on tertiary education, somewhat along the lines of Academia but on teaching, so including content-related questions plus general aspects (that might somewhat overlap with academia, in fact). [Note: I single out tertiary education, since this is what concerns me personally, this might also be feasible for other levels.]

Yet, I also see some merit in having all math levels together, since those in tertiary education often teach those that will do secondary (or even primary) education. So, there is some merit in being aware of issues for teaching on a different level.

In addition, this proposal has quite some traction, I think we should try to follow through now and see how things progress. We could still broaden the scope (say include CS, physics, engineering as subjects) latter if we see we have too little traffic with just math.

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    "I also see some merit in having all math levels together": I agree. I have taught from 5th grade to Ph.D. students, and have experienced useful cross-fertilization in both directions. – Joseph O'Rourke Feb 22 '14 at 13:59
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    I would add, personally, I would avoid a site which was primarily about education in general. On the other hand, a site which is primarily about ways to link mathematical ideals to forge a deeper core math, well, for that I have interest. – James S. Cook Feb 26 '14 at 3:15
  • @JosephO'Rourke, I'd love to discuss those over a beer or two... – vonbrand Mar 4 '14 at 13:17
  • @vonbrand: It will have to be a virtual beer, given how far apart we live! :-) – Joseph O'Rourke Mar 4 '14 at 17:10
  • @JosephO'Rourke, I was afraid of that :-( – vonbrand Mar 4 '14 at 17:14
  • @JamesS.Cook, I might dip into a "general education" type forum now and again, but as I'm primarily interested in computer science (and, farther out, science and engineering), I hope to see most relevant discussions here. – vonbrand Mar 4 '14 at 17:17
  • @vonbrand I actually intend my words here. I would literally avoid it if at all possible. Of course, others are free to do as they wish... but, to gain the voice of folks like myself who care more about math specifically than education in general, we need this site. – James S. Cook Mar 4 '14 at 20:12
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I do not see a big conflict between Math LSE and Education. Sure, there is some overlap, but there are enough distinct topics for both sites to coexist peacefully.

Education is about general concepts of education which delve at most slightly into the topic that is being taught. Some example questions to illustrate this:

  • Is "transfer of learning" proven to occur?
  • What value has been found in using interactive-whiteboards alongside experiments and activities in science classrooms?
  • How can I incorporate Wikipedia editing into a middle school English curriculum?
  • Is Plato's "Meno" and specifically the idea of "anamnesis" in any way relevant to contemporary pedagogies (like Montessori)?

Now consider the following example questions for Math LSE:

  • What are some pedagogically good examples to motivate the teaching of the inverse function theorem?
  • How can I show intuitively that 2⁰ should equal 1?
  • What are ideas and strategies on improving at discovering counterexamples?
  • Is there a good reason to insist that students memorize the sines and cosines of 30, 45, and 60 degree angles?
  • How can I incorporate computer algebra assignments into my course without spending a lot of time debugging students code?

I do not think that such questions would be received well by the community of Education and even if, they might not find the audience which can provide good answers to them (and I am not blaming anybody for this).

In contrast to the teaching of most (if not all) other subjects, teaching math raises a lot of questions that apply to teaching math only (and which cannot be answered from didactical experience only). The reasons for this lie in the nature of the subject. And these questions are what Math LSE is mainly for in my eyes. Now, other subjects have their special didactic issues too, but I think those require more general didactic and less subject-specific experience and also the overlap is bigger, e.g., a lot of issues concerning experiments in physics will apply to chemistry as well. Therefore, I do not think that, e.g., Physics LSE would be feasible (one could however think about Science LSE or Languages LSE).

  • "I'd like to talk about different infinities. How can I present Cantor diagonalization without it being too abstract?" – Kevin O'Bryant Feb 28 '14 at 21:02
  • Be careful. We are teaching math, know it (and its pitfalls) intimately (and by painful personal experience, as we were subjected to it). Presumably we know less of other subject matters (and in particular, almost nothing about teaching them). What is far away looks small and fuzzy... – vonbrand Mar 4 '14 at 13:21
  • @vonbrand: I can only guess that you are referring to my evaluation of a hypothetical Physics LSE (and others). Actually, I am a physicist and I have teaching/tutoring experience in both, math and physics. So it’s not certainly not far away to me. And I can assure you that teaching physics has far less subject-specific issues, despite physics arguably being the subject closest to math (except maybe for computer science). – Wrzlprmft Mar 4 '14 at 13:42
  • @Wrzlprmft, you are talking about education in general. Have you ever taught, say, English, or Medieval Italian Poetry? I'm sure each of those has its own snags, preferred methods and examples, and stuff students infuriatingly just don't "get." Just as math, but we see it everyday in our area(s). – vonbrand Mar 4 '14 at 13:51
  • @vonbrand: What about my statements about general education are you referring to? Also, I do not deny that other subjects have their special, subject-specific issues, too. – Wrzlprmft Mar 4 '14 at 14:35
  • @Wrzlprmft, you are talking about this proposal in contrast to the general Education proposal that runs in paralell. Or did I misunderstand something? – vonbrand Mar 4 '14 at 14:43
  • @vonbrand: I am talking about the general Education proposal; I am contrasting it to the Math Education proposal; I certainly do not oppose it. I quote myself: “I do not see a big conflict between Math LSE and Education. Sure, there is some overlap, but there are enough distinct topics for both sites to coexist peacefully.” – Wrzlprmft Mar 4 '14 at 15:21
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I'll answer with another question. How many philosophies on Education consider Mathematics to be one of the pillars of education? Anyone who has studied Education more than cursorily may not have an exact answer but will know that it's the vast majority. I am also a student and a teacher of Physics and I would feel less confident justifying a separate site for Physics Education and probably consider a more general site for Science Education as more appropriate. I'm undecided on that idea. In the above mentioned philosophies, Science as a whole is just as often considered one of the pillars of education alongside Mathematics.

PDF: 2010 Mathematics Subject Classification

The sheer vastness of the area of mathematics speaks for itself in terms of the potential for discussion just about mathematics education. Click on the above link if you're not sure just how broad and deep mathematics has become.

Of course there are overlaps in the practice of education across all subjects, but that in itself is not an argument against specialisation. Solving physics problems and applied maths problems has significant areas of overlap but no-one is questioning the logic of the separate existences of Math.SE and Physics.SE - are they?

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This topic is still relevant even now.

Education has been parceled into Maths Educators,Computing Science Educators and Academia. Both maths and computing science are struggling in their beta phase with not enough questions to keep the group going.

I would argue that Academia has enough questions and a strong enough community to include Maths Educators and Computing Science. I would also argue that Academia should change to Education/Academia to conclude these communities and the broader K-12 spectrum.

I am happy to create a new question to address this but I thought this question and subsequent comments really outline the issues well.

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