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Mathematics education research is generally very different than mathematics research. I am interested in collaborating with mathematics education professors at my next institution, and possibly transitioning into mathematics education as my specialty.
What examples are available of successful transitions from mathematics research into mathematics education research? What common challenges did these individuals have to overcome in the process?
As an earlier comment (How can a research mathematician transition into a mathematics education researcher?) indicates, I speak from the perspective of someone who has done a smidgen of math-education research, but not in any sense as an expert.
With this caveat, I think that it is important to realise that math-education research is much closer to science research than to math research, in the sense that it is necessarily an experimental science. As such, gathering experimental data is research, and this is something that we do every day, as teachers. (I believe that the usual term for this is 'practitioner research' (https://en.wikipedia.org/wiki/Practitioner_research ).) This is not the only kind of research that one can do, but it is a legitimate and valuable kind, and it is one that is accessible to you with only a little bit of extra training.
I have heard a math-education teacher literally say "I had an interesting experience in class today. I wrote a paper about it." While I am not sure that this is the kind of mentality that one should seek, it at least shows that writing a practitioner-research paper is not necessarily the huge and time-intensive process that writing a mathematics paper seems to me to be.
I also strongly recommend working in concert with an existing math-education researcher, collaborating informally (discussing ideas together) if not formally (writing a paper together). Such a person will be able to tell you whether questions you have are interesting; to suggest ways to elaborate on, expand, and research them; and to advise you on how to write up results or discoveries that you might find. (A tip: don't try to transfer your knowledge about writing mathematics papers directly to writing math-education papers. The latter are much closer in structure (I think) to papers in the social sciences.)
One example may be Roger Howe, who is a distinguished mathematician at Yale University, most recently at Texas A&M. He has written widely on education topics, including this article on 1st-grade math and the U.S. "Common Core":
(1) "Three Pillars of First Grade Mathematics." (PDF download.)
and this conference presentation on teacher preparation:
(2) "The Mathematical Education of Teachers." CBMS National Summmit. (weblink.),
in which he says, "I want to emphasize the possibility of greater involvement of university mathematicians in K-12 education."
Course content is taken [by many] as given, so the research problem is how to teach it most effectively. This approach [...] has produced valuable insights and useful results. However, it ignores the possibility of improving pedagogy by reconstructing course content.
is an especially difficult road to take because:
a. It requires (much) mathematical thinking of a very different nature than that necessary in research. Briefly, in reconstructing course content, one must think globally, that is one must constantly try to take as many mathematical relationships into consideration as possible and then decide which to deal with. You might call this the problem of organizing the "content architecture" and/or that of providing a "story line". (Very rewarding.)
b. One then has to write the materials to be used by the students. (A lot of work.)
c. One then has to cope with one's department. (Likely a lot of grief.)
Anyone curious as to what experience I am basing this opinion on might want to check FreeMathTexts
Best of luck.
Felix Klein is well-known as a mathematician, and in later years became very involved in mathematics education.
Around 1900, Klein began to take an interest in mathematical instruction in schools. In 1905, he played a decisive role in formulating a plan recommending that analytic geometry, the rudiments of differential and integral calculus, and the function concept be taught in secondary schools. This recommendation was gradually implemented in many countries around the world. In 1908, Klein was elected president of the International Commission on Mathematical Instruction at the Rome International Congress of Mathematicians. Under his guidance, the German branch of the Commission published many volumes on the teaching of mathematics at all levels in Germany.
Although I am not aware of any mathematics education research that he did, his name is highly regarded in the mathematics education field.
The Felix Klein Award is given by the International Commission on Mathematical Instruction to honor a lifetime achievement in mathematics education research.
The Klein Project, which "aims to support mathematics teachers to connect the mathematics they teach to the field of mathematics, while taking into account the evolution of this field over the last century," is "inspired by Felix Klein’s famous book, Elementary Mathematics from an Advanced Standpoint, published in 1908 and 1909."
