A quarter century ago, the National Council of Teachers of Mathematics (NCTM) published the first Handbook of Research on Mathematics Teaching and Learning (Grouws, 1992); 15 years later, they published a Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007). Now, in anticipation of its centenary in 2020, NCTM has published the Compendium for Research in Mathematics Education. The replacement of Handbook of by Compendium for in the title, though originating as an issue associated with copyright permission, also represents a kind of progress. The word handbook was originally used to mean something like “small, easily consulted pocket reference,” which certainly did not apply to the first two publications. In his preface, Cai quotes the dictionary definition of compendium as “‘a collection of concise but detailed information about a particular subject’ that has been ‘systematically gathered’” (p. vii), and he emphasizes that the three components of “concise,” “detailed,” and “systematically gathered” characterize the compendium at hand. Perhaps even more significant is the change from of to for. That change was made, according to Cai, to signal a shift from a static, backward-looking collection of observations about research in our field to a resource that could be used to move that research forward. To service that shift, the authors of all the compendium chapters were asked to speculate on future directions for research in light of the research they were reviewing.
A century ago, mathematics education research, like education research itself, was just beginning to emerge as a field of scholarly inquiry. Today, it has acquired many of the trappings of a scientific field, including theories, methods, and (a mountain of) scholarly literature, as well as a considerable infrastructure of organizations, media, and events to promote research activity and disseminate research findings. Mathematics education research still, however, falls short of being scientific in either its processes or its products. Writing in these pages, Steen (1999) called research in mathematics education “a field in disarray, a field whose high hopes for a science of education have been overwhelmed by complexity and drowned in a sea of competing theories” (p. 236).
During the last half century, school mathematics in North America has undergone two major waves of attempted reform: the new math movement of the 1950s through the early 1970s and the standards-based movement of the past two decades or so. Although differing sharply in their approach to curriculum content, these reform efforts have shared the aim of making mathematics learning more substantial and engaging for students. The rhetoric surrounding the more recent movement, however, has been much more shrill, the policy differences more sharply drawn, the participants more diverse. The so-called math wars of the 1960s (DeMott, 1962, ch. 9) were largely civil wars. They pitted advocates of rigor and axiomatics against those promoting applied, genetic approaches and were conducted primarily in journal articles and at professional meetings. Today's warfare ranges outside the profession and has a more strident tone; it is much less civil in both senses of the word.
One of the most popular yet poorly understood terms in today's educational discourse is pedagogical content knowledge, an expression introduced by Shulman (1986) to characterize teachers' knowledge of those “aspects of content most germane to its teachability” (p. 9). He distinguished teachers' pedagogical content knowledge from their subject matter content knowledge and their curricular content knowledge, claiming that “it represents the blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction” (Shulman, 1987, p. 8). The term was promptly adopted by mathematics educators, who have used it to describe phenomena that extend well beyond any sort of content knowledge—everything from teachers' ability to prepare lesson plans to their awareness of cultural influences on learning.
The 1980s, so we are told, are to be the decade of “problem solving.” Ready or not, we are apparently destined to have problem solving as the “focus” of school mathematics for the next ten years or so. Toward this goal, the NCTM's An Agenda for Action recommends the organization of the mathematics curriculum around problem solving. How can one argue with such a sensible agenda?
Jeremy Kilpatrick and Laurie Hart Reyes
The National Council of Teachers of Mathematics has been instrumental in making mathematics educators more aware of the special problems faced by members of minority groups in learning mathematics. The Council has a long history of involving members of minority groups in its activities, but its sponsorship of the Core Conference on Equity in Mathematics, held at Reston, Virginia, in February 1981, began a new phase of concern and positive action.
Jeremy Kilpatrick and Alice Hart
Edward A. Silver and Jeremy Kilpatrick
Our task in preparing this article on the occasion of the 25th anniversary of the Journal for Research in Marhematics Education (JRME) was to look ahead to the future of research in the field and to identify and discuss issues that might be important for the next decade or two in the life of the journal. Rather than merely offering our own opinions and speculations. we decided to interview a number of other researchers, some from the United States and some from other countries, to sample their views regarding the current state of research in mathematics education, the issues that may affect the future of the field, and the role of the JRME in the current and future scene. In particular, we asked these researchers to identify examples of work they considered significant and to comment on its imponant characteristics. We probed their definitions of the field by asking them to identify the types of work (e.g., empirical studies, historical or theoretical analyses) they judged could legitimately be called research in mathematics education. We explored their visions of the future of research over the next few decades. And we questioned them about the role and place of the JRME in the research community and about its impact on the field. In addition, we participated in a conference on Research in Mathematics Education and Its Results in May 1994 that was part of a study conducted by the International Commission on Mathematical Instruction (ICMI). The discussion document framing the study (Sierpinska et al., 1993) and many of the presentations and conversations at the ICMI Research Conference should be acknowledged as sources of ideas for the article. Naturally, we have included our own opinions, analyses, and perspectives.
Mary Lindquist, Joan Ferrini-Mundy and Jeremy Kilpatrick
In two spirited, well-attended sessions at the research presession of the annual NCTM meeting in Minneapolis in April, colleagues shared with each other and us their thoughts about perspectives from theory, research, and practice that ought to serve as the basis for revising the NCTM Standards documents. As the December 1996 NCTM News Bulletin detailed, the Commission on the Future of the Standards is overseeing a recasting of the current documents into a single entity for the twenty-first century that will strengthen relationships among the curriculum, teaching, and assessment standards and that will address new challenges in these areas. Writing teams have been assembled and are meeting this summer. A draft document is scheduled to be released in the fall of 1998, with the final document (possibly available in an electronic format) scheduled for release in 2000.
Nicholas A. Branca and Jeremy Kilpatrick
To validate and extend the results of previous research by Dienes and Jeeves, 100 adolescent girls were given 3 games to learn in individual interviews. 2 games had the structure of a Klein group; the third had a network structure. Subjects' retrospective evaluations of the group tasks conformed to the relative frequencies and hierarchical order found by Dienes and Jeeves, but evaluations were not related to strategy scores derived from the sequence of moves. Evaluations and performance showed some consistency across tasks, but strategies tended not to be consistent, probably owing to inadequacies in the strategy scoring system.