**Author**: Clement-Bishop-Kertel-Kipatrick-Leung

**Publisher:** Bukupedia

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Abstract The four major sections in this Third International Handbook are concerned with: (a) social, political and cultural dimensions in mathematics education; (b) mathematics education as a field of study; (c) technology in the mathematics curriculum; and (d) international perspectives on mathematics education. These themes are taken up by 84 internationally-recognized scholars, based in 26 different nations. Each of the Handbook's four sections is structured on the basis of past, present and future aspects. The first chapter in a section provides historical perspectives ("How did we get to where we are now?"); the middle chapters in a section analyze present-day key issues and themes ("Where are we now, and what recent events have been especially significant?"); and the final chapter in a section reflects on policy matters ("Where are we going, and what should we do?"). An overview of the major common recurring themes and issues in the Handbook is presented. It is argued that mathematics education research has a vitally important role to play in improving mathematics curricula and the teaching and learning of mathematics. As a result of the expertise, wisdom, and internationalism of both authors and section editors, this Handbook provides an invaluable, state-of-the-art compendium of the most recent, and promising, developments in the field. Keywords Globalization and mathematics education • History of mathematics education • International Handbook of Mathematics Education • Mathematics education research • Mathematics education policy • Social tum • No Child Left Behind • Technology in mathematics education There are a number of facts about this Third International Handbook that should be made clear at the outset. These are: • All 31 chapters were specifically written for this Handbook. There is no chapter in this Handbook which appeared in either the first International Handbook of M. A. (Ken) Clements Illinois State University, Department of Mathematics, Normal, IL, USA v ~' J vi Clements Mathematics Education (Bishop, Clements, Keitel, Kilpatrick & Laborde, 1996) or the Second International Handbook of Mathematics (Bishop, Clements, Keitel, Kilpatrick & Leung, 2003). • Although authors were expected to pay special attention to developments in scholarship, and in practice, that have occurred since the publication, in 2003, of the Second International Handbook, this Third International Handbook should not be seen merely as an update of the earlier handbooks. From the beginning, the editors aimed for a state-of-the-art compendium that identified and examined four major dimensions of contemporary mathematics education. • The contents of this Third International Handbook are consistent with the inclusion of the word "International" in the title. Altogether, there are 84 authors who contributed to the 31 chapters, and at the time the chapters were written (between September 20 I 0 and December 20 II), the authors were working in a total of 26 nations: Australia, Austria, Brazil, Canada, China, Colombia, Czech Republic, Denmark, France, Germany, Hong Kong, Iran, Israel, Italy, Japan, Malaysia, Mexico, New Zealand, Portugal, Singapore, Spain, Sweden, The Netherlands, UK, USA, and Venezuela. Although we would have liked the Third Handbook to have been even more international than it is in its outlook, we recognize that given that there were to be only 31 chapters, it would not have been realistic, or prudent, to have attempted to have more nations represented among the authors. • In July 2010 the editorial team met for a week to discuss the structure, likely chapter emphases, and authors for the Third Handbook. The first decision made, at that time, was that there would be the following four sections: Section A: Social, Political and Cultural Dimensions in Mathematics Education; Section B: Mathematics Education as a Field of Study; Section C: Technology in the Milthemlltics Cmric111nm; ilnd Section D: International Perspectives on Mathematics Education. We recognized that these sections did not cover all of the important areas of mathematics education-but we chose these major themes after reflection on what we thought offered the best follow-up potential to the Second Handbook, in terms of developments between 2003 and the present. • It was also agreed that each section would be structured on the basis of past, present and future aspects. Thus, the first chapter in each of the four sections is concerned with analyses of historical antecedents ("How did we get to where we are now?"); the "middle" chapters provide analyses of present-day key issues_and themes ("Where are we now, and what events since 2003 have been especially significant?"); and the final chapter in each section reflects on policy matters ("Where are we going, and what should we do?"). As far as we know, this Handbook is the first major mathematics education publication to adopt, consciously, this past-present-future organizational structure. • Each author was selected, jointly by the editors, on the basis of her or his recognized excellence and experience in relation to the theme that needed to be addressed in a chapter. Past, Present and Future Dimensions of Mathematics Education ... Major International Developments in Mathematics Education Since 2003 vii I have read each chapter in this Handbook several times. One cannot read the chapters carefully without beginning to recognize the pervasiveness of certain influences on the field of mathematics education. It is not my intention here to comment on each chapter in the Handbook-the section editors will have the opportunity to do that in their own introductions, placed at the beginning of the sections. Rather, I wish to draw attention to several major developments, and sometimes associated tensions, over the last decade. · The "Social Thrn" Versus Control Groups, Random Assignment, and Randomized Trials The first major development has been in relation to what Lerman (2000) called the social turn in mathematics education research. Many of the authors (especially of chapters in Sections A and B of this Handbook) draw attention to the increasing use of socio-cultural theories in the field. Some see the selection, use and refinement of such theories as the main way by which mathematics education is developing into a discipline in its own right. This emphasis on the social, cultural and political aspects of mathematics education has resulted in many of the traditional assumptions in mathematics education, about who should study what mathematics, and why, being problematized. In relation to issues associated with the call for "mathematics for all," traditional concepts of "disadvantage" have been questioned and re-defined, and traditional classroom discourse patterns have been subjected to scrutiny, especially from vantage points offered by different theorists. Issues associated with the role of assessment have never been far away, and the matter of what should constitute the most appropriate forms of assessment in. a given context is widely discussed. There has also been much discussion and research on the concept of teachers as research- / ers, and on what collaboration might mean in different areas of mathematics teaching and mathematics education research. Globalization tendencies have been, and continue to be, scrutinized from various theoretical perspectives. An inter~sting feature of the last decade has been the roles and status of mathematics education researchers in the USA, where the 200 I Federal Education initiative No Child Left Behind (NCLB) Act heralded a series of significant reforms which sought to improve student, teacher, school, and system performance in mathematics through test-based school accountability (Learning Point Associates, 2007). The NCLB Act called for education policy to rely on a foundation of scientificallybased research which employed rigorous methodological designs and techniques, including control groups, random assignment, and randomized trials. National Science Foundation (NSF) grant applicants were strongly advised to strive for randomized designs, and the Department of Education's 2002-2007 strategic plan (see viii Clements Shavelson & Towne, 2002) stated that, by 2004, 75% of new research and evaluation projects funded by the Department which address causal questions should use randomized experimental designs. Mathematicians, as well as mathematics educators, were expected to be included in mathematics education research teams. The tension between those _r~q!Jirements and the spirit of Lel1)1an 's (2000) social tum is discussed in several chapters in this Handbook. ' Technology Some of the authors in this Third International Handbook make it very clear that these days the world of mathematics education is changing very rapidly, and that technology is a major factor influencing the directions of change. Writers in Sections C and D of this Handbook emphasize that recent technological developments are challenging traditional views on curriculum, teaching, learning, and assessment. What forms of curriculum, teaching, learning, and assessment are the most appropriate given the rapid technological developments? How can teachers keep up with developments and, simultaneously, cope with their often-too-heavy teaching loads? Given recent developments, what should algehra, geometry and calculus curricula look like in the future? What should proof in school mathematics look like? What technological aids should students be allowed to use in examinations, and what are the implications of that question for those responsible for developing policies with respect to assessment and evaluation? Given the rapidity of ongoing technological developments, and the increasing reach of new technologies into even remote areas of the world, one cannot help wondering whether in 20 years time, say, there will be an agreed internation,al mathematics curriculum. Many writers committed to the need to link curricula and teaching to social and cultural factors view such a possibility as extremely unwelcome. Issues associated with online and other distance forms of mathematics education arc frequently discussed, and there is a concern that despite the socializing potential of new technology, an international mathematics curriculum would result in mathematics . education becoming even more separated from local aspects of culture than it is now. Globalization and Internationalization of Mathematics Education When the Handbook editors initially met to work out the Handbook structure, chapter titles, authors, etc., it was agreed that it would be wise to try to avoid unnecessary repetition. In particular, it was agreed that we should try to restrict, to just a few chapters, discussion of the influence of the International Association for the Evaluation of Educational Achievement's (lEA's) "Trends in Mathematics and Science Study" (TIMSS), and the Organisation for Economic Co-operation and Development's (OECD's) "Programme for International Student Assessment" (PISA). Despite the best efforts of our editors, we failed in this regard, largely . ~= ·. . ~= . ·. Past, Present and Future Dimensions of Mathematics Education ... ix because many authors recognized the huge impact that TIMSS and PISA (and other international studies such as the Learner's Perspective Study-LPS) have had during the past decade. There is a concern that TIMSS, PISA, and other international testing programs will have a standardizing effect on school mathematics that will cramp promising developments arising from the "social tum" in research. But some authors have argued that despite this potential danger, these international studies have drawn attention to well-performing nations like Japan, Singapore, Hong Kong, and Finland and have more or less forced researchers and policy makers to face the question: "Why have the students in such nations performed so well-and why have students in some extremely well-resourced nations performed considerably less well?" This has given rise to additional questions like: "How can we make mathematics education research more responsive to national needs, as those needs are perceived by politicians and education policy makers?" The possibility that influential policy makers do not regard the results of much mathematics education research as useful has been raised. Who Should Read This Handbook? As I read the draft chapters of this Third International Handbook I often found myself thinking that all mathematics educators, including mathematics teachers at all levels, should read some or all of the chapters. Then, when teaching graduate classes, I often thought that all of my graduate students would benefit from reading some of the chapters. I certainly intend to use this Handbook as a text for my future graduate students and, of course, I hope that other persons teaching graduate mathematics education students will do the same. Various Handbook authors have drawn attention to the tendency for much mathematics education research to be carried out in teams that include school teachers and mathematics educators normally based outside of schools. Every person involved in collaborative studies of this type would likely benefit from becoming aware of what authors in this Handbook have said. Chapters in this Handbook can provide important insights into how teachers and researchers around the world are working towards providing answers to issues that can no longer be ignored. For example, we need to answer questions such as: "What can a school do if it wants to engage all of its students actively and productively in relevant mathematics learning?" And, "What about those outside of the normal school and college system (many adults, for example) who want to learn mathematics?-What should we be doing, for them, to facilitate top-quality, and satisfying mathematics learning?" This Handbook is the most-internationalized of all mathematics education handbooks that have been prepared thus far. Its chapters provide up-to-the-minute, stateof- the-art reviews on major themes; invariably, there has been an attempt to make readers aware of the international spread of opinion, methodologies, research and practice. The Handbook provides much insight, not only from researchers in the ,, ' X Clements traditional European and North American nations but also from researchers in many other parts of the world. Throughout, any suggestion that the best mathematics education research wisdom has largely emanated from "the West" has been problematized, and basic questions-such as: "Why have Confucian-based cultures generated such productive forms of school mathematics?"-have been carefully considered. Authors charged with the responsibility of presenting historical perspectives (and authors of some of the other chapters, too) have deliberately argued from international, global, vantage points rather than from distinctly Western vantage points. Whither Mathematics Education? I have been privileged to work on the three Springer/Kiuwer international handbooks on mathematics education. For almost all of my professional career I have worked in the field of mathematics education, and it has been a matter of principle for me to be able to say why I believe, strongly, that mathematics education is a cruc~ally important field of endeavour. Mathematics is one of the few areas in an individual's life in which she or he is required to spend hetween three anrl five homs pf',r week (:mrl, in ::1rlrlition, more honrs on homework or with a tutor), for between 10 and 12 years (at least) studying a curriculum defined by others. What a waste of everyone's time, energy, and money, if students do not learn school mathematics as well as they possibly can, so that they develop an interest in the subject and an appreciation of its power to help them deal efficiently with important everyday problems. Furthermore, I believe that success with the subject is likely to be associated with greater satisfaction in later life (because successful students are more likely to take up vocations of their choice, or gain entry to a wider range of courses in higher education institutions). From a national perspective, the benefit of having a mathematically-competent citizenry is, it is oftP-n assertP-d, likP-Iy to result in strong economic performance (or, at least, stronger than would be the case if most citizens were not mathematically competent). Thus, it is important that research be conducted which will take into account students' attitudes towards mathematics, as well as their mathematical problem-solving and problem-posing performances. But if mathematics education research is important, then how well are we doing in fostering the highest possible quality of mathematics learning as a result of our mathematics education research? Let us not put our heads in the sand on this matter. There is certainly a lot of room for improvement! The nation which has the most qualified mathematics education researchers is probably the USA-yet, many indicators (including results on international comparative studies) suggest that many US students fail to learn mathematics well. How could that be the case, considering the amount of research that has been conducted, and published within the USA, over so many years? It is well known that many students, in most nations (perhaps all nations), experience difficulty in understanding fractions, the four operations with integers, and elementary algebra. We need to face the reality that many learners experience much difficulty in mathematizing situations for which mathematical approaches to problem solving would be informative and efficient. Why has there not been a marked Past, Present and Future Dimensions of Mathematics Education ... xi improvement, given the large amount of mathematics education research conducted around the world, and over a very long period of time, with respect to such fundamentally important curriculum matters? Should our standard curricula and teaching approaches be problematized and reconceptualized? Various chapters in this Third Handbook consider issues such as these. I could say much more-but perhaps, now I have succeeded in stimulating your interest and arousing an argumentative spirit within you. I should leave the core of what is said in this Third International Handbook to our team of very competent authors. As you read each chapter. I urge you to rellect on the basic question: Whither mathematics education? Acknowledgments As many readers might imagine, it has been an honour and privilege to work with a teum of such outstanding editors. It hardly needs to be said that Alan Bishop. Christine Keitel, Jeremy Kilpatrick and Frederick Leung are world-class mathematics educators and researchers. And I can say, sincerely, that each has expended a huge amount of effort, and time, on this project. I would also like to thank the authors, who have worked hard to meet demanding deadlines. Together, twhe editors and authors for this Third International Handbook have provided enormous experience, expertise and wisdom on key mathematics education issues. Has any other hook in the field of mathematics education ever had such a wide-ranging and authoritative international set of authors? I would also like to thank the large number of professional reviewers of chapters. Every chapter has been read by at least four people-the appropriate section editor, at least two especiallyappointed external reviewers, and myself. None of the Handbook's 31 chapters appears in the form in which it was first submitted. Always, authors were willing to respond professionally to suggestions for improvement. During the period in which the Third Handbook was being prepared I was based at Illinois State University's Department of Mathematics. I would especially like to thank Dr George Seelinger, Head of the Department of Mathematics, for his encouragement and support. Throughout the planning and manuscript preparation process, Harmen van Paradijs, Editorial Director. Human Sciences, for Springer, was supportive, wise and understanding. We also profited from the knowledge and cooperation of Melissa James and Natalie Riebom, Springer's Publishing Editor, and Senior Editorial Assistant, respectively. We could not have asked for a better relationship with our publisher. References Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (Eds.). (1996). International handbook of mathematics education (2 vols.). Dordrecht, The Netherlands: Kluwer Academic Publishers. Bishop, A. J., Clements, M.A., Keitel, C., Kilpatrick, J., & Leung, F. (Eds.). (2003). Second illlernational handbook of mathematics education (2 vols.). Dordrecht, The Netherlands: Kluwer Academic Publishers. Learning Point Associates. (2007). Understanding the No Child Left Behind Act: Mathematics and science. Chicago, IL: Author. Lerman, S. (2000). Social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19-44). Palo Alto, CA: Greenwood. Shavelson, R. J., & Towne, I. (Eds.). (2002). Scientific research in education. National Research Council, Committee on Scientific Principles for Education Research, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academies Press.