The SIGMAA on RUME Guidelines Committee has developed a draft document, "Guidelines for Programs and Departments in the Mathematical Sciences Concerning Mathematics Education Specialists in Mathematics Education: The Undergraduate Program." It has been posted to the listserv. Members' comments should be sent to John Selden (js9484@usit.net) by January 31, 2001 for forwarding to the Committee. After these guidelines are submitted to the Executive Committee, the Guidelines Committee expects to start work on guidelines for graduate programs in undergraduate mathematics education.

John Selden and Marilyn Carlson, Co-chairs

DRAFT

GUIDELINES FOR PROGRAMS AND DEPARTMENTS IN MATHEMATICAL SCIENCES CONCERNING MATHEMATICS EDUCATION AND SPECIALISTS IN MATHEMATICS EDUCATION

THE UNDERGRADUATE PROGRAM

These guidelines were approved by the Executive Committee of the Association for Research in Mathematics Education (ARUME), a Special Interest Group of the Mathematical Association of America on [date]. They were developed by the ARUME Guidelines Committee during the years 1998 - 2000. Additional guidelines, including guidelines for graduate programs in mathematics education, are being developed.

1. Educational background of mathematics education faculty 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's level background in mathematics. They should have a strong background in mathematics education, but such a background can be obtained in a variety of ways. They should be knowledgeable of mathematics educational research literature. If such faculty will be required to do research, then they should have some background in doing mathematics education research (e.g., a Ph.D. in mathematics education, postdoc in mathematics education, significant published research in mathematics education). If they will be responsible for preservice teacher education (including mathematics for elementary teachers, mathematics for secondary teachers, mathematics methods, supervision of interns or student teachers, inservice teacher education, masters courses for experienced teachers, etc.) they should have some knowledge of the current state of school mathematics curricula and of relevant research in the appropriate age range (elementary, middle, secondary or combinations thereof).

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

Mathematics education faculty should be held to standards of quality and quantity of scholarship comparable to 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 scholarship. There are two main reasons for this:

1. Mathematics education has a major applied component (with many practitioners, i.e., teachers) and this provides opportunities to produce original, research-based and research-generating "products" (expositions of research results, research-based pedagogical software, curricula, assessment instruments, teacher education courses and offerings, etc.) which satisfy traditional definitions of scholarship.
2. Mathematics education differs from mathematics in being concerned with the actions of people and the contents of their minds, e. g., how students learn, remember, or understand mathematics. Some of its concepts depend on descriptions of such phenomena and are inherently less precise than mathematical definitions. Gradually the community may alter or sharpen these concepts. Observations may also be reconsidered from new points of view. 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 research in mathematics, most research in mathematics education is applicable in the sense that it offers teaching guidance, insights, etc., (not necessarily in the stronger sense of producing detailed diagnoses of difficulties or prescribing detailed teaching methods). Such research can lead to implementations involving externally funded programs for teachers or students that provide opportunities for more research, even when research is not the ostensible goal of those programs. 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 faculty member with a specialization in mathematics education is encouraged to perform extra service in addition to normal teaching (e.g., lead TA training, direct curriculum revision of large enrollment courses, conduct workshops), compensatory release time should be provided. While a faculty member with a specialty in mathematics education research may have interests in these types of activities and bring special expertise to these endeavors, her or his areas of scholarship may not be in these areas. These activities may not be part of her or his scholarly interest and therefore not a part of her or his research program. It is unjust (and sometimes unethical) to expect this work to be done without compensatory release time. 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), the publication process can take several years. As a result, when assessing scholarship produced during periods of only a few years, works-in-progress should be evaluated carefully. Such works-in-progress usually involve data, documents, and perhaps interim reports. They are thus easier to assess than many mathematical works-in-progress which may consist mainly of attempts to prove theorems that will be documented only on the completion of the proofs.

There are several professional meetings that mathematics educators attend, and these range from selective research conferences to large meetings for teachers. In some cases talks are invited (although the prestige associated with being an invited speaker is not necessarily what it is in the mathematics community). Mathematics educators also present papers at conferences not specific to mathematics (e.g., American Educational Research Association) that are highly selective, and these papers are archived through the ERIC Documentation Service. Such paper presentations differ from presentations given at meetings of the AMS or MAA and should carry considerable weight -- perhaps judged partly according to acceptance rates of proposals for these meetings.

Mathematicians unfamiliar with the mathematics education research standards, traditions, and literature who are assessing scholarly work in this area should obtain qualified advice (and inform 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 greatly 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. Even the terminology differs from that of mathematics. A referee's report is often called a review in the mathematics education community and only context distinguishes such a review from something like a book review.

3. Teaching assignments of mathematics education faculty in departments of mathematics.

Faculty members with a specialty in mathematics education have training in education and mathematics and a familiarity with the education literature that makes them particularly suitable for teaching courses populated mainly by preservice (or inservice) teachers. This is so, regardless of their current research interests, which might for example concern the learning of some aspect of upper division mathematics.

Indeed, mathematics courses for preservice teachers should be taught, if possible, by specialists in mathematics education. Such courses should be regarded as partly mathematics education courses because not only their content, but also the way they are taught, greatly influences the later teaching of the preservice teachers. This Guideline is similar to Guideline C.1.b of the in MAA's Guidelines for Programs and Departments in Undergraduate Mathematical Sciences, which says that a course in the mathematical sciences (including mathematics education) should be taught (or coordinated) by a faculty member with a degree in the discipline of the course.

The teaching experiences of faculty members with a specialty in mathematics education are an important source of ideas that can ultimately lead to research publications. Thus greatly restricting the scope of their teaching assignments (e.g., to only courses for preserve teachers) is an impediment to their research production and also limits their contribution to the broader educational goals of a department. Faculty members with a specialty in mathematics education should occasionally be assigned to teach courses chosen from a wide variety of a department's offerings.

4. Establishing mathematics education communities in departments of mathematics.

Wherever a department teaches preservice teachers and size permits, it would be useful to establish a community of several faculty members specializing in undergraduate mathematics education. There are three reasons for this relating to intellectual isolation, research, and service to the department:

1. Intellectual isolation. While the intellectual isolation of faculty members is a common problem throughout the mathematical sciences, it is likely to be especially severe for a specialist in undergraduate mathematics education. Many of the research techniques in mathematics education are adapted from psychology, anthropology, or sociology and may be unfamiliar to most mathematicians. Also much of the terminology of mathematics education is descriptive (often of mental phenomena, e.g., understanding) and cannot be as precisely defined as what one expects in mathematics. Such differences can be overcome, but tend to interfere with intellectual intercourse.
2. Research. Although much research can be done by a single individual, some cannot. For example, one cannot simultaneously teach and record observations on that teaching. Even to collect data on the interactions of a teacher and several members of a class can require more than one observer. Also the primary analysis of some videotapes is best done by more than one observer - different observers may notice different aspects of the same data.
3. Service to the department. A faculty member specializing in undergraduate mathematics education may be called on to do such things as evaluate the effectiveness of a new or experimental course (internal consulting) or oversee some part of the department's teaching (administration). Such duties require considerable time - often more than could reasonably be expected of one person without interfering with teaching or research. In staffing a multi-section course for preservice teachers it may also be helpful to have more than one specialist in mathematics education. Such an individual may have to guard against being perceived by the students as excessively demanding in contrast to other instructors, e.g., in problem solving or conceptual understanding, both of which are important for preservice teachers according to the NCTM Principles and Standards. (Of course, the teaching of all sections should be informed by the mathematics education literature, but the degree to which this can be implemented may vary.) In addition, (as explained above) a faculty member specializing in undergraduate mathematics education should not always be assigned to teach the same few courses and there may simply be too much teaching for one person.

5. The role of research in teaching and learning in guiding instructional decisions.

Research in mathematics education provides information about teaching and 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 for communicating research findings. Although it usually does not offer prescriptions for teaching particular students or topics, it can 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 own instruction and to make adjustments based on both the results of that assessment and new research information.