Special Interest Group of the MAA
SIGMAA on Research in
Undergraduate Mathematics Education
Guidelines for Undergraduate Programs
GUIDELINES FOR PROGRAMS AND DEPARTMENTS IN MATHEMATICAL SCIENCES CONCERNING MATHEMATICS EDUCATION AND SPECIALISTS IN MATHEMATICS EDUCATION
THE UNDERGRADUATE PROGRAM
These guidelines regarding courses for mathematics education students and the role of faculty specialists in mathematics education are intended to be used in programs and departments in the mathematical sciences. They include advice on hiring, tenure, promotion, assignment of responsibilities, planning, and instructional decisions. They were approved on January 8, 2002 by the Executive Committee of the Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education, SIGMAA on RUME. They were developed during the years 1998 - 2001 by the SIGMAA on RUME Guidelines Committee with input from the membership. Additional guidelines, including guidelines for graduate programs in mathematics education, are being developed.
A. Educational background of mathematics education faculty in departments of mathematics.
education faculty in a department of mathematics should hold a
doctorate 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 (for example,
a doctorate in mathematics education, postdoc in mathematics
education, or 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) they should have some knowledge of the current
state of school mathematics curricula and methods and of relevant
research in the appropriate age range (elementary, middle, secondary
or combinations thereof). The grounding of such knowledge in
experience can be helpful, but is not essential.
B. 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" (e.g., expositions of research results, research-based pedagogical software, curricula, assessment instruments, or teacher education courses and offerings) that 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 guidance and insights for teaching, curriculum development, and planning (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 (e.g., for data collection or transcription), 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, engage in outreach to school systems), 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.
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.
In order to reach a wide audience, researchers in mathematics education often publish in a variety of journals and volumes and attend a broad range of professional meetings. Mathematicians unfamiliar with the mathematics education research standards, traditions, and literature who are assessing scholarly work in this area should obtain qualified advice concerning the acceptance rates, the refereeing process, and the editorial policies of these outlets for research and other scholarly work. Those from whom this advice is sought should be informed of the institution's standards for evaluating scholarship.
The meetings that mathematics educators attend range from selective mathematics education research conferences to large meetings for mathematics teachers. In many cases, talks are invited and even contributed papers are subject to a stringent review process. Mathematics educators also present papers at highly selective educational research conferences, such as the meetings of the American Educational Research Association, AERA. Proposals to speak at these meetings pass through a rigorous review process and the papers presented are archived through the ERIC Documentation Service. Such paper presentations should carry considerable weight.
rates for journals and other volumes can vary from quite liberal to
around 10% of the submissions. Some volumes and conference
proceedings 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.
C. 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 normally 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 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. However, this is not meant to suggest that interested non-specialists should never teach courses for preservice teachers. Collaboration between non-specialists and specialists can be helpful in such teaching.
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 preservice 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 also be assigned to teach courses chosen from a wide variety of a department's offerings.
D. 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 for School Mathematics. (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.
E. 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.