*By Priscilla Bremser, Contributing Editor, Middlebury College.*

In the past nine months, I’ve heard colleagues at three different meetings—an AMS sectional meeting in Louisville, the Joint Mathematics Meetings in Baltimore, and the Contemporary Issues in Mathematics Education workshop at the Mathematical Sciences Research Institute—identify a need for journals focused on publishing useful refereed articles for mathematicians about mathematics education. This raises several questions that get at fundamental issues in the complicated and sometimes uneasy relationships among research mathematicians, mathematics education specialists, and those with interests in both areas (I put myself in the last category).

To begin, why might we need such journals? The most obvious answer is that good work in mathematics education should be identified (hence a refereeing process) and shared in a way that is accessible to mathematicians. Trained as a mathematician, I found some of my first readings in mathematics education research to be inaccessible — full of unfamiliar vocabulary and references to social science research methods that I felt unqualified to evaluate. Naturally this triggered my instinctual skepticism. I have certainly found some writing about mathematics education research to be clear, convincing, and useful to me as a mathematician who teaches and works with teachers. Elise Lockwood’s earlier post on this blog is exemplary, as are [1] and [3]. I’ve also gotten more familiar with the methods and conventions of mathematics education researchers; Alan Schoenfeld’s article [4] from 2000 is a fine place to start. Still, I would appreciate collections of articles about mathematics education that are written with speakers of my native language in mind.

Another answer to the “why” question is that many mathematicians are doing important work in mathematics education, and that work might not get the attention and validation that it deserves from other mathematicians unless it’s being certified by mathematicians. We who teach future teachers, investigate how students learn to write proofs, provide professional development to K-12 teachers, and so on, should have ways to present what we’ve learned in venues that are recognized by the larger mathematical community. As Sol Friedberg, chair of the mathematics department at Boston College, put it at MSRI*, “The coin of the realm in the evaluation of faculty is what? Publications.” The first round of evaluation for a mathematician is in the mathematics department, where skepticism is a professional requirement. Recognition by mathematicians beyond our own campuses might help.

The influence on performance reviews of a mathematician’s activities in math education may be limited, though, even if publications result. Another speaker at MSRI, Steven Rosenberg of Boston University, was blunt on this topic: “We look for math publications; we look for funding in math. So if you have a great love of math education, please wait until you’re tenured. For those of you in math education, when you go to approach colleagues in the math department, please keep that in mind. Is work in math education respected within a research math department? The short answer is, yes, if it’s funded, and even in that case, maybe not as much as research in pure and applied math or statistics.”

At the same MSRI session, however, Brigitte Lahme, a mathematician at Sonoma State University, reported that her department values work in teacher education and professional development, and has revised its tenure criteria accordingly. A contribution to mathematics education, she said, “can’t be just an add-on.” Clearly there is significant cultural variation among mathematics departments. Further, as Lahme added later, “we can challenge the status quo… In my department, it used to be that [publishing] papers was the coin of the realm, and we changed it, and the world has not ended.”

In response to concerns about untenured mathematicians putting themselves at risk by engaging in math education activities, the last word of the session was provided by Bill McCallum: “I think it’s time for us to embrace the contradiction between (a) calls for culture change and (b) our desire to protect everybody. Culture change isn’t going to happen without a certain amount of pain, and I think younger faculty who want to get involved in math education should be encouraged to do so. They’re grownups. Let’s all stop worrying too much about the pain that’s going to be caused; we can all share it, and let’s stand up for the culture change.” Wherever we stand on the question of culture change, mathematicians would do well to examine the cultures in our own departments and institutions.

A second question is this: what journals are already out there for this work? The *International Journal of Research in Undergraduate Mathematics Education* (Springer) will begin publication in 2015. There’s also* PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies*. For those willing to explore the discipline of mathematics education, the *Journal for Research in Mathematics Education *and *Educational Studies in Mathematics* are respected by practioners. Then there’s the related but distinct area of SoTL: the Scholarship of Teaching and Learning (see [2] for an introduction to SoTL and its publication venues).

Beyond journals, there are conference proceedings as well as edited volumes such as those in the Mathematical Association of America Notes Series. These lack the validation of a fully refereed journal, however, which calls for caution on the part of both writer and reader.

Perhaps we should consider the demand side. Thus my third question: what sorts of papers about mathematics education would mathematicians like to see? I suspect that many mathematicians who teach would like to learn about various approaches to improving student learning, provided those approaches are backed up by evidence that is plausible to them, if short of rigorous proof. Having developed a Math for Teachers course at a small liberal arts college, I’d like to read about math courses for future teachers that integrate pedagogy and math content. I’d like to read about professional development programs for practicing teachers that work by some reasonable measure. I’d like to read about what happens when mathematicians spend time in K-12 math classrooms. I’d like to read more articles that address mathematicians’ skepticism about social science methods used by math education researchers.

It seems to me that there is indeed room for more places to publish peer-reviewed papers on math education for an audience of mathematicians. There’s a lack in particular of outlets for articles on mathematicians’ involvement in K-12 education. This brings me to the last questions: what other venues exist for papers of this type? Are there any new journals in the works? If more journals of this type are available, what are the best ways to bring them to a broad audience? Please respond in the comments section!

*A video recording of this session at MSRI is available here.

Many thanks to Ben Braun, Elise Lockwood, and the Department of Mathematics at Middlebury College for helping me develop the ideas here.

**References**

[1] Ball, D., M. H. Thames, and G. Phelps, Content knowledge for teaching: what makes it special? *Journal of Teacher Education* 59, no. 5 (2008), 389-407.

[2] Bennett, C. D. and J. M. Dewar, An overview of the scholarship of teaching and learning in mathematics, *Primus : Problems, Resources, and Issues in Mathematics Undergraduate Studies* 22, no. 6 (2012), 458-473.

[3] Hill, H., The nature and predictors of elementary teachers’ mathematical knowledge for teaching, *Journal for Research in Mathematics Education *41, no. 5 (2010), 513-545.

[4] Schoenfeld, Alan H., Purposes and methods of research in mathematics education, *Notices of the American Mathematical Society* 47, no. 6 (2000), 641-649.

Great post! Two years ago, I was hired in my current position with the expectation that I would engage in scholarship in both pure mathematics and math education/scholarship of teaching and learning at the undergraduate level. I feel blessed that I have such a position. Yet, despite the official support I have from my institution, I often feel that the work I do related to SoTL is undervalued. The good news is that I think things will improve over time, not get worse.

About a year ago, there was a small movement (http://www.change.org/petitions/arxiv-org-add-math-ed-mathematics-education-category-to-arxiv) (instigated by me, I suppose) to get an official math education category on the arXiv (http://arxiv.org), similar to the one for physics education (http://arxiv.org/list/physics.ed-ph/recent). When I came up with the idea, I never thought for a moment that it would be met with resistance. However, the folks over at the arXiv weren’t exactly in favor of the idea (at least not in the way I envisioned it). To be fair, they voiced legitimate concerns. In addition, there were some trained math educators that were opposed to the idea. This blew me away. To get a flavor for the kind of opposition I encountered, here is a short blog post that captures a conversation I had on Twitter about the topic: http://danaernst.com/a-twitter-conversation-about-math-ed-on-the-arxiv. For more history of the movement to get math ed on the arXiv, check out the blog posts http://danaernst.com/mathematics-education-on-the-arxiv/ and here http://danaernst.com/an-update-mathematics-education-on-the-arxiv/. I put the pursuit of a math education category on the arXiv on hold when I become concerned that I could end up putting a lot of time and energy into it and not have it work out. As a pre-tenured assistant professor, I have to be careful about the battles I choose to fight.

On a related note, Robert Talbert recently wrote a blog post titled Grand challenges for mathematics education (http://chronicle.com/blognetwork/castingoutnines/2014/06/28/grand-challenges-for-mathematics-education/) in which he addresses a survey by the NCTM asking users to submit their ideas for “grand challenges” for mathematics education in the coming years. Talbert’s 4th grand challenge was “Create an online repository for preprints in mathematics education.”

Thanks for the comment, Dana. FYI, I did some minor editing so that the hidden links are visible, since for some reason our system doesn’t allow the use of “a href=…” tags in comments (in fact, I had to change the < symbols to ” just to get it to display). I think the issue of online preprints in math ed is really complicated in part, and you might be alluding to this with your comment about opposition by trained math educators, because many math ed publications use double-blind peer review. I think this is much more common in education and the social sciences than in pure and applied math. While I understand and respect this position, I still feel that for work that is more in SoTL, rather than Math Education Research, an online preprint server is a good idea. This would be especially useful for high-quality research surveys, informal reports regarding promising classroom practices, reports regarding the history of certain curricular movements, etc.

Ben, thanks for fixing the links in my comment.

A few comments about accounts of education research intended to be accessible to mathematicians:

If you expand “refereed journal” to include “collection of refereed articles” then you can include the CBMS book series Research in Collegiate Mathematics Education. This was a precursor for the International Journal of Mathematics Education. It was initiated by Ed Dubinsky, Jim Kaput, and Alan Schoenfeld, and the first volume was published in 1994. (For some history of this connection, see http://www.academia.edu/2316847/A_Home_for_RUME_Plenary_Presentation_RUME_Conference_February_2011)

The RCME editorial policy says: “Papers published in these volumes will collectively serve both pure and applied purposes, contributing to the field of research in collegiate mathematics education and informing the direct improvement of post-secondary mathematics instruction. The dual purposes imply overlapping audiences and articles will vary in their relationship to these purposes. The best papers, however, will interest both audiences and serve both purposes.” (The rest is here: http://cbmsweb.org/Issues/rcme_policy.htm)

There are seven RCME volumes. I was the managing editor for volumes III and IV, and I know that we worked hard to make the articles accessible with respect to writing style.

Between 1996 and 2005, Annie and John Selden edited a “research sampler” for mathematicians: http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/teaching-and-learning/research-sampler. The September 1997 column includes a description of the findings in a RCME II article on expert problem solvers.

Another edited volume addressed to mathematicians is Alan Schoenfeld’s Assessing Mathematical Proficiency, published by MSRI in 2007. This includes discussion of research, also policy and related issues, e.g., the WTIWYG phenomenon (“what you test is what you get”). That can be downloaded here: http://www.msri.org/people/staff/levy/files/Book53/book53-all.pdf

For lighter reading . . . Education researchers sometimes publish short articles about their research that are written for teachers. (These are not refereed research articles themselves but about the findings of such articles.) These appear in AFT’s American Educator. (The author index for American Educator is here: http://www.aft.org/newspubs/periodicals/ae/authors4.cfm) Such articles used to appear in NCTM’s Mathematics Teacher, Mathematics Teaching in the Middle School, and Teaching Children Mathematics—and may still for all that I know (I don’t claim to stay up to date on everything). NCTM also has online “research briefs”: http://www.nctm.org/news/content.aspx?id=8468. The research briefs may not be as accessible as a mathematician might want them to be, but they are at least brief.

Thanks, this is awesome!

Thanks for the thoughtful response, Dana. Having taken the “wait until after the tenure review” path, simply because I got drawn into mathematics education mid-career, I appreciate the challenges you face and the care and mindfulness you bring to those challenges.

Cathy, your citations are extremely helpful. Thank you!

As someone who just went through a tenure review last year, I’m happy to say that (unlike some reports I’ve heard from faculty at other institutions) my SoTL work was not viewed as a negative in the process. While I’m certainly in a position where my pure mathematics research is the dominant factor in tenure decisions, I got the impression that my two SoTL publications were valued at my institution. I think that many of these challenges are highly dependent on the specific department/institution where the tenure decision is being made.

We have founded the Journal of Humanistic Mathematics (http://scholarship.claremont.edu/jhm/) partially for this purpose. JHM provides a platform where mathematicians who wish to understand the work of mathematics education researchers and mathematics education researchers who wish to communicate with mathematicians can come together, along with historians of mathematics and philosophers of mathematics and many others who are interested in mathematics but are not trained in all the various ways of understanding mathematics. Traditionally in academia, disciplinary communities gather together around common interests and concerns (which is great as it encourages rapid and unhindered progress and offers mutual support), but then these go on to isolate themselves and exclude others (which is not always all too great). This is not to underestimate the value of disciplinary work or platforms but to underline the need for cross-disciplinary communication and collaboration. And to point out that JHM, too, along with many other journals already mentioned above, offers a welcoming place for just what the blog post is emphasizing the need for: places to publish peer-reviewed papers on math education for an audience of mathematicians (and others who want to listen and join in the conversation).

Thank you, Gizem, for the reminder about JHM, and its emphasis on “all the various ways of understanding mathematics.” Thanks also, of course, to you and your co-founders for launching it. I’ve just subscribed to the email list!

You may also want to look at the online journal Mathematics Teacher Educator for more practice-oriented work on teacher education (http://www.nctm.org/mte). It is a joint publication of the National Council of Teachers of Mathematics and the Association of Mathematics Teacher Educators. AMTE is a great resource for mathematicians interested in teacher education, especially the content preparation of teachers.