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.

This volume explores how technology-supported learning environments can incorporate physical activity and interactive experiences in formal education. It presents cutting-edge research and design work on a new generation of "body-centric" technologies such as wearable body sensors, GPS tracking devices, interactive display surfaces, video game controller devices, and humanlike avatars. Contributors discuss how and why each of these technologies can be used in service of learning within K-12 classrooms and at home, in museums and online. Citing examples of empirical evidence and specific implementation, this timely and critical volume examines how body responsive technologies are being used within the educational community to advance the next generation of educational technology.

This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students’ broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors, which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy.

This book provides a common language for and makes connections between transfer research in mathematics education and transfer research in related fields. It generates renewed excitement for and increased visibility of transfer research, by showcasing and aggregating leading-edge research from the transfer research community. This book also helps to establish transfer as a sub-field of research within mathematics education and extends and refines alternate perspectives on the transfer of learning. The book provides an overview of current knowledge in the field as well as informs future transfer research.

Students do not experience math in a vacuum. The curriculum, the students' social and emotional well-being, and the teacher's expertise as a facilitator must all be attended to, and each interacts with the others. -Geoff Krall Math instruction in high school is often something of a grab bag, with schools jumping from curriculum to curriculum, lacking a guiding vision or continuity between years. No wonder so many students conclude, "I'm not a math person." Geoff Krall thinks that's a problem. And he's devoted his career to fixing it. Necessary Conditions posits for the first time a coherent approach to secondary math pedagogy. Krall identifies three essential elements that will open the door to math for all your students: academic safety, quality tasks, and effective facilitation. Krall takes readers into real middle- and high-school classrooms to see how teachers cultivate these three "necessary conditions." With extensive examples, practical techniques and resources, and insightful analysis, this guide equips teachers to do the following: Design classroom experiences that increase engagement and build all students' identities as mathematicians. Create dynamic, high-quality lessons that include meaningful, efficient assessment. Facilitate routines and discussions that increase all students' access to conceptual mathematics. The biggest drivers of students' math experiences are their teachers. With Krall's guidance, you can help every student come to recognize that they are indeed a "math person."

This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

For many children much of the time their experience in classrooms can be rather dull, and yet the world the school is supposed to initiate children into is full of wonder. This book offers a rich understanding of the nature and roles of wonder in general and provides multiple suggestions for to how to revive wonder in adults (teachers and curriculum makers) and how to keep it alive in children. Its aim is to show that adequate education needs to take seriously the task of evoking wonder about the content of the curriculum and to show how this can routinely be done in everyday classrooms. The authors do not wax flowery; they present strong arguments based on either research or precisely described experience, and demonstrate how this argument can be seen to work itself out in daily practice. The emphasis is not on ways of evoking wonder that might require virtuoso teaching, but rather on how wonder can be evoked about the everyday features of the math or science or social studies curriculum in regular classrooms.

This practical, engaging book explores the fundamentals of pedagogy and the unique challenges of teaching undergraduate mathematics not commonly addressed in most education literature. Professor and mathematician, Suzanne Kelton offers a straightforward framework for new faculty and graduate students to establish their individual preferences for course policy and content exposition, while alerting them to potential pitfalls. The book discusses the running of day-to-day class meetings and offers specific strategies to improve learning and retention, as well as concrete examples and effective tools for class discussion that draw from a variety of commonly taught undergraduate mathematics courses. Kelton also offers readers a structured approach to evaluating and honing their own teaching skills, as well as utilizing peer and student evaluations. Offering an engaging and clearly written approach designed specifically for mathematicians, A Beginner’s Guide to Teaching Mathematics in the Undergraduate Classroom offers an artful introduction to teaching undergraduate mathematics in universities and community colleges. This text will be useful for new instructors, faculty, and graduate teaching assistants alike.

An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.