Foreword: Another Decade of PME Research -- Introduction -- Reviewers of the Chapters in This Volume -- Presidents of the PME International Group -- Local Organizers of the PME International Conferences -- Editors of the Proceedings of the PME International Conferences -- PME International Group Conferences -- PME North American Chapter (PME-NA) Conferences -- Part 1: Cognitive Aspects of Learning and Teaching Content Areas -- Generalization, Covariation, Functions, and Calculus -- On Numbers: Concepts, Operations, and Structure -- Research on the Learning and Teaching of Algebra -- Research on the Teaching and Learning of Geometry -- Part 2: Cognitive Aspects of Learning and Teaching Transverse Areas -- Curriculum and Assessment -- Developmental, Sociocultural, Semiotic, and Affect Approaches to the Study of Concepts and Conceptual Development -- Digital Technology in Mathematics Teaching and Learning: A Decade Focused on Theorising and Teaching -- Language in Mathematics Education Research -- Proof and Argumentation in Mathematics Education Research -- Recent Advances in Research on Problem Solving and Problem Posing -- Reflections on Progress in Mathematical Modelling Research -- Part 3: Social Aspects of Learning and Teaching Mathematics -- Research on Mathematics-Related Affect: Examining the Structures of Affect and Taking the Social Turn -- Tracing the Socio-Cultural-Political Axis in Understanding Mathematics Education -- Part 4: Professional Aspects of Teaching Mathematics -- Pre-Service and In-Service Mathematics Teachers’ Knowledge and Professional Development -- Author Index -- Subject Index.Since its establishment in 1976, PME (The International Group for the Psychology of Mathematics Education) is serving as a much sought after venue for scientific debate among those at the cutting edge of the field, as well as an engine for the development of research in mathematics education. A wide range of research activities conducted over the last ten years by PME members and their colleagues are documented and critically reviewed in this handbook, released to celebrate the Group’s 40 year anniversary milestone. The book is divided into four main sections: Cognitive aspects of learning and teaching content areas; Cognitive aspects of learning and teaching transverse areas; Social aspects of learning and teaching mathematics; and Professional aspects of teaching mathematics. The selection for each chapter of a team of at least two authors, mostly located in different parts of the world, ensured effective coverage of each field. High quality was further enhanced by the scrupulous review of early chapter drafts by two leaders in the relevant field. The resulting volume with its compilation of the most relevant aspects of research in the field, and its emphasis on trends and future developments, will be a rich and welcome resource for both mature and emerging researchers in mathematics education.