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Background: There is currently a proposal for a new Math Teaching site that will be entering private beta once enough people sign up. One question that came up during its question is (basically): Is teaching math significantly different from teaching any other subject? Would it be better to broaden the scope to all education?

I had my own opinions, but I don't have enough experience teaching non-math classes to know. And now I am really curious about variation in teaching methods across disciplines.

Therefore, I have this question:

Is there any evidence (such as refereed sources) to show that teaching mathematics and related fields uses significantly different methods or skills than teaching other subjects?

Conversely,

Is there any evidence that teaching ability and/or techniques transfer across a wide variety of disciplines?

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Look at the suggested questions. How many of them are easily transferable to another fields? (But I have some sort of feeling that all questions there would fit Math.SE or are general education questions or are not good SE questions at all.) –  Piotr Migdal Feb 23 at 12:04
    
@PiotrMigdal A lot of them fit in with some of the MSE community, but many people don't like them on MathSE. It's like the difference between SO and User Experience. –  Brian Rushton Feb 23 at 12:34
    
When it comes to strictly educational questions, it may beneficial to start a broader site (in such topics usually getting critical mass of participants is highly non-trivial (speaking as an ex-mod of now-deceased site). And on broader "teaching/education" site there is no problem in asking questions specifically about math (even if the community is oriented about math and most of questions turn out in this way). But once the site is too specialized, it can dry quickly... –  Piotr Migdal Feb 23 at 13:28
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@EnergyNumbers: your recent edit drastically changed Brian's question by removing the motivation. Moreover you've removed content referred to several times on this page. Finally you describe in your edit this deleted content as "spamming". That seems rather strange: the birth of a new SE site related to education seems awfully relevant to academia.SE. I rolled back the edit. If you feel strongly that this cutting of Brian's question needs to be done, let's discuss it on the meta site first. –  Pete L. Clark Feb 24 at 7:42
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@CharlesMorisset This post was admittedly nothing more than spam (although it is a legitimate question I've had, I asked it with only advertising in mind). I wouldn't be put out at all if the severe editing was restored to preserve community standards. –  Brian Rushton Feb 24 at 12:39

3 Answers 3

up vote 8 down vote accepted

At the University of Georgia we have a program (which is not identical to a "department", but is close enough so that the distinction has always eluded me) in Mathematics Education and thus we have undergraduate mathematics education majors and also mathematics education graduate students (both master's and PhD).

There are certainly close ties with both the mathematics department and other education disciplines -- e.g. the mathematics courses I teach have a substantial population of mathematics education majors -- but such undergraduate majors also take plenty of courses with the name "Math Education XYZW". These courses are split into "content" and "pedagogy" courses. This distinction was very hard for me to wrap my mind around (it literally took me a few years to do so, although obviously I was not working very consistently on it!): see for instance this page, and please read carefully: the courses that they list as Content are actually in the math department (one or two of them are taken mostly by math education majors, but many of the others are also required courses for undergraduate math majors). Rather the distinction between "content" and "pedagogy" -- which are the terms used by UGA students and faculty who talk to me about this -- is a distinction being made between two types of courses in the longish list of Professional Education courses. Thus e.g. compare

EMAT 3800.
Course Title: Connections in Secondary Mathematics II
Course Description: Exploration of secondary mathematics topics related to number and measurement with an explicit focus on reasoning that connects critical topics of secondary mathematics to one another and to problem situations. Sample topics include proportional reasoning, number theory, and probability.

and

EMAT 4800
Course Title: Teaching Secondary School Mathematics I
Course Description: Introductory ideas about mathematics education, including current mathematics standards and policy documents, learning theories, and teaching strategies. Students will explore how secondary students think about and learn mathematics, examine how to select and modify tasks, use appropriate technology, and apply their learning in an accompanying field experience.

This seems to give rather strong evidence that the answer to the OP's first question is yes: Math Education is rapidly becoming distinct enough from Education in general to count as its own discipline. (Obviously there remain many connections and commonalities between Math Education and other kinds of Education, just as virtually any academic field overlaps significantly with others.) In particular, yes, math education students learn math-specific teaching methods. This is indirect, though strong, evidence that there are differences between the teaching methods of various subjects. But my other point is something that is not explicitly in the OP's question: more than just teaching methods, techniques or ability, there is actually additional content that math teachers learn and that other teachers (and students of mathematics who are not intending to teach!) do not.

Let me also introduce you to my colleague Sybilla Beckmann. Beckmann (who was trained as an arithmetic geometer and holds a faculty position in the UGA mathematics department; her office is next door to mine) is truly* one of the very top American experts in the field of mathematical education of teachers. (Beckmann is also largely responsible for my awareness and understanding of the issues presented above. In fact I will contact her and ask her to look over this response to make sure I have gotten things right.) One of her initiatives over the last few years has been to promote the idea of an explicitly identified mathematics teaching community. In this regard, please see this article and this website. Also, Beckmann writes on her webpage "Longer term, we plan for this project to include an electronic self-organizing journal."

tl;dr: Yes, this is definitely a thing. It is a thing which has grown in recent years and is liable to continue to grow in the near future...and everyone seems to agree that we want/need it to grow.

*: So much so that I need not justify it here: just search the web for her and you'll see it right away.

Added: My colleague Sybilla Beckmann took time out of her busy workday [on Saturday!] to quickly look over what I wrote above. She pronounced it "basically accurate" and went on to add the following:

Teaching methods in math are definitely different from other disciplines. Work of Lee Shulman and Deborah Ball on mathematical knowledge for teaching has been transformative for the field in that regard. Some sources to refer people to: the CBMS Mathematical Education of Teachers II on the CBMS website. It refers to various other sources. Math education is a separate discipline with a large body of research amassed over the last 30 - 40 years. It connects to other education research but is its own separate field. At UGA, the math ed program is within the department of mathematics and science education (it used to be a separate math ed department but was joined for administrative reasons some years ago).

I added links to the wikipedia articles on Shulman and Ball, and I recommend at least skimming these. Shulman is responsible for the idea of pedagogical content knowledge, a concept which is rather slippery at first [or at least, it was to me] but really seems to lie at the heart of an answer to the OP's question: it is precisely the material that you need to know as a mathematics teacher that you do not learn in your mathematics courses and cannot learn in non-math specific education courses. To nail it down more specifically than this is beyond my expertise -- e.g. the above two course descriptions were intended to convey this distinction but looking back it seems even more complicated: none of EMAT 3800 would be appropriate material for aspiring teachers of most subjects other than mathematics, and some but not all of EMAT 3900 would.

The two linked wikipedia articles give entry points into the vast body of literature on these matters; people who were interested enough to read this far are encouraged to delve into the literature itself. And when you do, come back and tell me about it! I am an academic mathematician and thus a mathematics educator, but I have no specific training in mathematics education.

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By the way, I didn't comment on the second question because I feel more strongly about the first one and my answer was already long enough. But sure: it would be even easier to point to commonalities in training of educators across different disciplines. Graduate students in the UGA math department receive plenty of math-specific teaching training (thank goodness) but they also take more than one course in non-math specific teaching. –  Pete L. Clark Feb 22 at 18:05
    
This is a great answer. By the way, is she interested in participating in the new site or in sharing it with others? Terence Tao was an important helper in creating Mathoverflow. –  Brian Rushton Feb 22 at 18:50
    
@Brian: I told her in passing about the new site a couple of weeks ago and wrote to her just now about this message. We'll see... –  Pete L. Clark Feb 22 at 18:54
    
@PeteL.Clark the site you link would seem to obviate the need for another math education SE site. –  Suresh Feb 22 at 19:28
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One final comment: at this point math.SE is a mathematics teaching site. (Being a teaching site rather than a Q&A site is again a bit against the SE party line, and there is some tension there, but factually speaking it seems pretty clear that the site is being used mostly in this way: math students ask questions; math instructors answer them; people who are some of both do some of both.) If anyone is worried that the distinction between a mathematics teaching site and a mathematics education site is fine enough to be asking for some trouble: yes, me too. –  Pete L. Clark Feb 22 at 20:21

The methods we use in physics are certainly different from the ones used in math. We have lab courses. Also, there is a huge pedagogical literature on overcoming students' preexisting conceptions of physics, and the literature seems to show that straight lecturing never does an acceptable job of overcoming these preconceptions. The classic paper is Hake, "Interactive Engagement Versus Traditional Methods: a Six-Thousand Student Survey of Mechanics Test Data for Introductory Physics Courses, Am. J. of Phys, 66 (1997) 64, and I believe it's available online.

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This is an important answer because physics is quite close to mathematics in the cosmic scheme of things (e.g. with respect to my answer note that "math education" is a program within the department of "mathematics and science education"), but still there are some important differences. It is a bit sad to think about the vastness of subject-specific educational research out there that is virtually unknown to subject area experts (like me). –  Pete L. Clark Feb 23 at 21:58

One evidence that some teaching abilities/techniques transfer across a wide variety of disciplines is the existence of the UK Professional Standards Framework (UKPSF), which "provides a general description of the main dimensions of the roles of teaching and supporting learning within the higher education environment".

I'm currently attending a training course at my university to obtain some qualifications for this framework, and this course is attended by people from many disciplines (from maths to history, including medicine or economy), and the teaching techniques we are learning do not depend on the field (and the people in charge of the course are explicit on that fact).

Of course, some particular aspects can be specific (for instance, techniques specific to teaching in a laboratory with potentially dangerous equipment might not be relevant to mathematicians), but for instance, learning how to conduct an interactive exercise can be done similarly in most fields.

Now, perhaps the proposal in question looks for techniques for very specific topic, for instance, how to teach Pythagoras theorem, or some nice examples of matrix operations.

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While certain commonalities across disciplines certainly exist, in no field apart from mathematics is a substantial proportion of incoming students predisposed to dislike and fear the subject. –  vadim123 Feb 22 at 16:01
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@vadim123: I totally disagree (unless you want to say that a substantial fraction of students who sign up for a maths degree dislike maths): it is very common across a broad range of subjects that students who have to do the course (e.g. chemistry for medicine students) intensely dislike it. Also this isn't restricted to natural sciences: natural scientists may have to take language courses which they both dislike and fear. (Not to talk of historic examples like the compulsory marxism-leninism courses in the GDR) –  cbeleites Feb 22 at 16:18
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@vadim: As someone who has a lot of experience with and allegiance to academic non-mathematics (e.g. my parents were both college English teachers), let me say that I believe in mathematics's exceptionality among academic disciplines, but I do not believe that it is exceptional in its exceptionality. Or less preciously: substantial portions of students dislike and fear writing, computer programming, painting, dance [I am now very scared!].... What changes is the subset of the students which have these negative feelings and the way these feelings manifest. –  Pete L. Clark Feb 22 at 17:58

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