Special Interest Group of the MAA
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Undergraduate Mathematics Education

ARUME Guidelines Committee Report, January 21, 2000

The ARUME Guidelines Committee has initiated the writing of a document to define standards for mathematics educators in departments of mathematics, standards for Ph.D. programs in departments of mathematics and the role of the research literature in undergraduate mathematics education. Our discussions resulted in the formulation of these three major topics and 7 separate categories, with our discussions producing detailed statements for 3 of the 7 categories of the document (A.1, A.2, C.1).

The current draft of the document includes the following 7 categories:


A.1 Educational background of mathematics education faculty hired in departments of mathematics.

A.2 Scholarship of mathematics education faculty housed in departments of mathematics.

A.3 Teaching assignments, including the potential benefits of varying these assignments to promote professional growth.


B.1. Coursework and standards needed to complete a Ph.D. in mathematics education.

B.2 Resources needed to establish a Ph.D. program in a department of mathematics.


C.1 Role of research in teaching and learning in guiding instructional decisions.

C.2 The important role of departments in preparing preservice teachers, including the need to consult the research literature and invest resources for aspiring to excellence in these courses.


In addition, we reviewed the current draft of the MAA Guidelines Document (not a public document) and recommended the inclusion of 5 specific statements, at appropriate places in the document, that conveyed references to our document or information contained in the current draft of the ARUME Guidelines Document (e.g., Mathematics education faculty should hold a Ph.D. in either Mathematics or Mathematics Education and possess minimally a Master's level background in mathematics and a strong background in education, including publications in mathematics education research journals.) or information agreed upon by the ARUME Guidelines Committee members. Prior to forwarding these suggestions to the MAA Guidelines Committee, our guidelines document and suggestions were forward to the ARUME administrative committee for their approval.


The current draft of the ARUME Guidelines Document follows:

ARUME Guidelines Document--Working Draft-December 21, 1999


A.1 Educational background of mathematics education faculty hired in departments of mathematics.

Mathematics education faculty in a department of mathematics should hold a Ph.D. in either mathematics or mathematics education, while minimally possessing a Master' level background in mathematics. A strong background in education is required, but can be obtained in a variety of ways. The individual should be knowledgeable of the educational research literature in the area of specialization. If the person will be required to do research, then he or she should have some background in doing educational research (e.g., Ph.D. in math ed, post doc in math ed, significant research in math ed). If the person is going to be responsible for preservice education (including math for elementary teachers, math for secondary teachers, math methods, supervision, etc.) the person should have some knowledge of the current state of school math curricula and knowledge of relevant research in the appropriate age range (elementary, middle, secondary or combinations thereof).


A.2 Scholarship of mathematics education faculty housed in departments of mathematics.

Mathematics education faculty should be held to the same standards of quality and quantity of scholarship as other members of their mathematics departments, but their scholarly work should be in mathematics education rather than mathematics. In assessing such scholarly work, it is appropriate to consider not only traditional research publications, but also other forms of creative activity, just as it is in the case for art or music. There are two main reasons for this:


(1) Mathematics education has a major practical component (with practitioners, i.e., teachers) which provides opportunities to produce original "products" (expositions of research results, research-based pedagogical software, curricula, assessment instruments, etc.) which are useful beyond one's own teaching or research.
(2) Mathematics education differs from mathematics in depending on less precisely defined ideas and on physical evidence, sometimes provided by several independent researchers. Thus the field as a whole moves forward and is coordinated and focused partly through writings (e.g., synthesizing or analyzing research results), which for example may be published as chapters in books, rather than the traditional kind of research paper. The kind of intellectual creativity that results in research papers in mathematics often finds a wider expression within mathematics education.

Compared to pure mathematics, most research in mathematics education is immediately applicable and implementable. Such implementations often involves externally funded programs for teachers or students that can provide opportunities for more research, even when research is not the ostensible goal of the implementation. Because of this and because external funding of research may be essential (for data collection, transcription, etc.), grant proposal writing is often an integral part of a research program in mathematics education. Thus grant proposal writing should be considered in assessments of scholarly work.

If a specialist in mathematics education is encouraged to perform extra service (e.g., lead TA training, direct curriculum revision of large enrollment courses, conduct workshops), release time should be provided in other areas. If this has not been possible, the time disadvantage should be considered in assessing the quantity, but not the quality, of scholarly output. Also, since some research projects in mathematics education require collecting and processing considerable amounts of data (in addition to the overall analysis), delays in publication should be expected. As a result, when assessing scholarship produced during periods of only a few years, works-in-progress should carry significant weight.

Mathematicians unfamiliar with the mathematics education research literature who are assessing scholarly work in this area should obtain qualified advice (and inform those advisors of their institutional standards). In order to reach a wide audience, researchers in mathematics education often publish in a variety of journals and volumes. These may have widely differing refereeing and editorial policies. For example, acceptance rates can vary from quite liberal to around 10% and some volumes and conference proceedings (e.g., PME, PME-NA) that mathematicians might expect were not refereed, actually are refereed.


A.3 Teaching assignments, including the potential benefits of varying these assignments to promote professional growth.

(work in progress)


A.4 Establishing mathematics education communities in departments of mathematics, including recommendations for addressing the problem of isolation which is common for many mathematics education faculty.

(work in progress)


B.1 Coursework and standards needed to complete a Ph.D. in mathematics education.

(work in progress)


B.2 Resources needed to establish a Ph.D. program in a department of mathematics.

(work in progress)


C.1 Role of research in teaching and learning in guiding instructional decisions.

Research in mathematics education provides information about what students know and can do, how they construct mathematical concepts, how they solve problems, how various kinds of mathematics teaching affects learning, how students read proofs, etc. It also provides concepts and a vocabulary for analyzing instances of teaching and learning, and communicating research findings. Educational research may provide valuable insights to guide both curriculum developers and instructors. As a result, curriculum developers and classroom teachers, at all levels, are encouraged to consult the research literature to assist them in making curriculum and instructional decisions.

All faculty should be encouraged to regularly assess the effectiveness of their instruction and should regularly make adjustments based on both the results of their evaluation and new research information.


C.2 The important role of departments in preparing preservice teachers, including the need to consult the research literature and invest resources for aspiring for excellence in these courses.

(work in progress)

Submitted by:
Marilyn Carlson
Chair, Guidelines Committee


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