This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.

The second edition continues the mission of bringing together important new mathematics education research that makes a difference in both theory and practice. It updates and extends the Handbook’s original key themes and issues for international research in mathematics education for the 21st century, namely: priorities in international mathematics education research lifelong democratic access to powerful mathematical ideas advances in research methodologies influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development being an important component of all these aspects. This edition also examines other catalysts that have gained increased import in recent years including a stronger focus on the teacher and teacher practice, a renewed interest in theory development, an increased focus on the mathematics needed in work place settings, and a proliferation of research designs and methodologies that have provided unprecedented opportunities for investigating (and ultimately improving) mathematical teaching and learning. This edition includes ten totally new chapters; all other chapters are thoroughly revised and updated.

This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.

Every four years, beginning in 1984, the Mathematics Education Research Group of Australasia (MERGA) produces a review of Australasian research in mathematics education. The authors of the chapters in this volume have summarised and critiqued research conducted during the period 2004-2007.

This book by-passes both psychology and sociology to present an original social theory centered on seeing mathematical learning by everyone as an intrinsic dimension of how mathematics develops as a field in support of human activity. Here, mathematics is defined by how we collectively talk about it. Drawing on psychoanalytic theory, the student is seen as participating in the renewal of mathematics through their contributions to our collective gaze on mathematics as the field responds to ever new demands. As such learning takes a critical stance on the standard initiations into current practices often promoted by formal education. In the field of mathematics education, researchers have moved from psychology where individual students were seen as following natural paths of development through existing mathematical knowledge, to socio-cultural models predicated on students being initiated into the human world and understood through the reflective gazes this world has of itself, such as those found in comparisons of student learning in different countries. This book addresses the domain, purpose and functioning of contemporary research in mathematics education and is an original contribution to this theme. The book is aimed at a mathematics education research audience. It continues a dialogue with existing publications, seen widely as a cutting edge and will also be of interest to students and practitioners in the fields of qualitative research, social theory and psychology.

The purpose of this book is to collect, organize and disseminate collective wisdom with respect to designing, conducting, and publishing quality research in mathematics education. This wisdom will be gleaned from among those who, over the past several decades, have been instrumental in guiding the field in the pursuit of excellence in mathematics education research—insightful editors, educative reviewers, prolific writers, and caring mentors. Each chapter is written to the novice researcher with the intent of aiding them in avoiding common pitfalls, navigating difficult intellectual terrain, and understanding that they are not alone in experiencing rejection, frustration, confusion, and doubt. This book differs from existing literature in the sense that it is written about the enterprise of designing, conducting and publishing research in mathematics education as opposed to being reports of the results of such work. It also differs in the sense that it is written with the intent to mentor the rising generation as opposed to capture the state of the field (as would happen in a handbook, for example). It is written for the express purpose of helping the field work collectively to aid in the often isolated enterprise of mentoring new researchers. The primary audience is a potentially wide one: graduate students, novice researchers, graduate faculty, advisors, and mentors – or anyone seeking to improve their own abilities to design, conduct, and publish quality research in mathematics education.

While the importance of knowledge for effective instruction has long been acknowledged, and the concept and structure of mathematics knowledge for teaching are far from being new, the process of such knowledge acquisition and improvement remains underexplored empirically and theoretically. The difficulty can well associate with the fact that different education systems embody different values for what mathematics teachers need to learn and how they can be assisted to develop their knowledge. To improve this situation with needed consideration about a system context and policies, How Chinese Acquire and Improve Mathematics Knowledge for Teaching takes a unique approach to present new research that views knowledge acquisition and improvement as part of teachers’ life-long professional learning process in China. The book includes such chapters that can help readers to make possible connections of teachers’ mathematical knowledge for teaching in China with educational policies and program structures for mathematics teacher education in that system context. How Chinese Acquire and Improve Mathematics Knowledge for Teaching brings invaluable inspirations and insights to mathematics educators and teacher educators who wish to help teachers improve their knowledge, and to researchers who study this important topic beyond a static knowledge conception.

This book is about the role and potential of using digital technology in designing teaching and learning tasks in the mathematics classroom. Digital technology has opened up different new educational spaces for the mathematics classroom in the past few decades and, as technology is constantly evolving, novel ideas and approaches are brewing to enrich these spaces with diverse didactical flavors. A key issue is always how technology can, or cannot, play epistemic and pedagogic roles in the mathematics classroom. The main purpose of this book is to explore mathematics task design when digital technology is part of the teaching and learning environment. What features of the technology used can be capitalized upon to design tasks that transform learners’ experiential knowledge, gained from using the technology, into conceptual mathematical knowledge? When do digital environments actually bring an essential (educationally, speaking) new dimension to classroom activities? What are some pragmatic and semiotic values of the technology used? These are some of the concerns addressed in the book by expert scholars in this area of research in mathematics education. This volume is the first devoted entirely to issues on designing mathematical tasks in digital teaching and learning environments, outlining different current research scenarios.