The editors and contributors of these ten articles focus on the idea that communication includes both what is happening and being said among participants in a classroom and also the politics, values and ideologies that serve as the foundation of the practice. They describe how communication thereby involves register, representation and contexts through media-human interfaces in the classroom and in interpreting mathematics as a text, how communication in mathematics teaching becomes social interaction in cooperative settings and classroom activities, and how communication translates into practice, community, identity and policy.

This volume is a forward–looking intersection of Sociological perspectives on mathematics classrooms and socio-political perspectives on mathematics education. The first perspective has generated a substantial body of knowledge in the mathematics education. Interactionist research has deepened our understanding of interaction processes, socio-mathematical norms and the negotiation of meaning, generating a ‘micro-sociology’ or a ‘micro-ethnography’ of the mathematics classroom. More recently, socio-political perspectives on mathematics education interrelate educational practices in mathematics with macro-social issues of social equity, class, and race and with the policies that regulate institutionalized mathematics education. This book documents, strings together and juxtaposes research that uses ethnographical classroom data to explain, on the one hand, how socio-political issues play out in the mathematics class. On the other hand, it illuminates how class, race etc. affect the micro-sociology of the mathematics classroom. The volume advances the knowledge in the field by providing an empirical grounding of socio-political research on mathematics education, and it extends the frame in which mathematical classroom cultures are conceived.

Language can be simultaneously both a support and a hindrance to students’ learning of mathematics. When students have sufficient fluency in the mathematics register so that they can discuss their ideas, they become chiefs who are able to think mathematically. However, learning the mathematics register of an Indigenous language is not a simple exercise and involves many challenges not only for students, but also for their teachers and the wider community. Collaborating to Meet Language Challenges in Indigenous Mathematics Classrooms identifies some of the challenges—political, mathematical, community based, and pedagogical— to the mathematics register, faced by an Indigenous school, in this case a Mäori immersion school. It also details the solutions created by the collaboration of teachers, researchers and community members.

International mathematics education researchers give a differentiated overview of views and beliefs of both teachers and students. Beliefs about how to teach mathematics have a high impact on the instructional practice of teachers. In the same way, views and beliefs about mathematics are an essential factor to explain achievement and performance of students. The 19th MAVI conference added a variety of research perspectives to the international discussions of mathematics related beliefs. The authors of this volume have compiled a rich selection of research results, which may further enhance the discussion of MAVI topics in the future.

Mathematics education research as a discipline is situated at the confluence of an array of diffuse‚ seemingly incommensurable‚ and radically divergent discourses. Research claims that have grown out of mathematics education are wide-ranging and antagonistic rather than circumscribed by hidebound disciplinary frames. While there has never been a unified‚ totalising discipline of knowledge labelled ‘mathematics education research’‚ and while it has always been a contested terrain‚ it is fair to say that the master paradigm out of which this field has been generated has been that of cognitive psychology. Mainstream mathematics education knowledges refracting the master discourse of psychology —whereby cognition serves as the central privileged and defining concept— clearly delimits its possibilities for serving as a social tool of democratic transformation. The central point of departure of this new collection is that mathematics education research is insufficiently univocal to support the type of uncompromising interpretation that cognitive psychologists would bring to it. The hallmark contribution of this pathbreaking volume edited by Paola Valero and Robyn Zevenbergen is the paradigmatic shift the authors have effected in the field of mathematics education research‚ taking up a position at the faultline of socio-cultural analysis and critical pedagogy.

During the past 30 years, researchers have made exciting progress in the science of learning (i.e., how people learn) and the science of instruction (i.e., how to help people learn). This second edition of the Handbook of Research on Learning and Instruction is intended to provide an overview of these research advances. With chapters written by leading researchers from around the world, this volume examines learning and instruction in a variety of learning environments including in classrooms and out of classrooms, and with a variety of learners including K-16 students and adult learners. Contributors to this volume demonstrate how and why educational practice should be guided by research evidence concerning what works in instruction. The Handbook is written at a level that is appropriate for graduate students, researchers, and practitioners interested in an evidence-based approach to learning and instruction. The book is divided into two sections: learning and instruction. The learning section consists of chapters on how people learn in reading, writing, mathematics, science, history, second language, and physical education, as well as how people acquire the knowledge and processes required for critical thinking, studying, self-regulation, and motivation. The instruction section consists of chapters on effective instructional methods—feedback, examples, questioning, tutoring, visualizations, simulations, inquiry, discussion, collaboration, peer modeling, and adaptive instruction. Each chapter in this second edition of the Handbook has been thoroughly revised to integrate recent advances in the field of educational psychology. Two chapters have been added to reflect advances in both helping students develop learning strategies and using technology to individualize instruction. As with the first edition, this updated volume showcases the best research being done on learning and instruction by traversing a broad array of academic domains, learning constructs, and instructional methods.

Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the “boy problem,” with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which socio-cultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and proto-mathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.

Mathematics education research has blossomed into many different areas which we can see in the programmes of the ICME conferences as well as in the various survey articles in the Handbooks. However, all of these lines of research are trying to grapple with a common problem, the complexity of the process of learning mathematics. Although our knowledge of the process is more extensive and deeper despite the fragmented nature of research in this area, there is still a need to overcome this fragmentation and to see learning as one process with different aspects. To overcome this fragmentation, this book identifies six themes: (1) mathematics, culture and society, (2) the structure of mathematics and its influence on the learning process, (3) mathematics learning as a cognitive process, (4) mathematics learning as a social process, (5) affective conditions of the mathematics learning process, (6) new technologies and mathematics learning. This book is addressed to all researchers in mathematic education. It gives an orientation and overview by addressing some carefully chosen questions on what is going on and what are the main results and questions what are important books or papers if further information is needed.

The main idea of the book is to contribute to a broader understanding of learning, identity and diversity by presenting actual research findings that were retrieved from classroom settings and related social practices. Learning is to a large extent an ongoing social process as both students and their teachers learn by being part of shared social practices through social interactions that facilitate learning gains. Sociocultural research shows that the organization of schooling promotes or restricts learning, and is a crucial factor to understand how children from a diversity of backgrounds profit from instruction. This is a first urgent issue to be considered by teachers and teacher education in our socio and culturally diverse society. A second issue is the on-going debate about learning as a process that involves the construction of identities in schools and classrooms, and in the transitions between school and home practices. Last but not least, since school practices can be addressed from the perspective of diversity and special educational needs an on-going discussion about optimizing pedagogical approaches is of main importance to allow maximum educational effectiveness. Our potential audience for this book are researchers, post-graduate students in education and psychology, teachers, teacher education, other academics and policy makers.