This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school. It does this by reporting on major results and implications of the Problem@Web project that investigated youngsters’ mathematical problem solving and, in particular, their use of digital technologies in tackling, and communicating the results of their problem solving, in environments beyond school. The book has two focuses: Mathematical problem solving skills and strategies, forms of representing and expressing mathematical thinking, technological-based solutions; and students ́ and teachers ́ perspectives on mathematics learning, especially school compared to beyond-school mathematics.

This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment. Mathematical problem solving has long been recognized as an important aspect of mathematics, teaching mathematics, and learning mathematics. It has influenced mathematics curricula around the world, with calls for the teaching of problem solving as well as the teaching of mathematics through problem solving. And as such, it has been of interest to mathematics education researchers for as long as the field has existed. Research in this area has generally aimed at understanding and relating the processes involved in solving problems to students’ development of mathematical knowledge and problem solving skills. The accumulated knowledge and field developments have included conceptual frameworks for characterizing learners’ success in problem solving activities, cognitive, metacognitive, social and affective analysis, curriculum proposals, and ways to promote problem solving approaches.

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume’s three major themes—technology, creativity, and affect—represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book’s new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. Broadening the Scope of Research on Mathematical Problem Solving will prove to be a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

This book explores the topic of using technology, both physical and digital, to motivate creative mathematical thinking among students who are not considered ‘mathematically advanced.’ The book reflects the authors’ experience of teaching mathematics to Canadian and American teacher candidates and supervising several field-based activities by the candidates. It consists of eight chapters and an Appendix which includes details of constructing computational learning environments. Specifically, the book demonstrates how the appropriate use of technology in the teaching of mathematics can create conditions for the emergence of what may be called ‘collateral creativity,’ a notion similar to Dewey’s notion of collateral learning. Just as collateral learning does not result from the immediate goal of the traditional curriculum, collateral creativity does not result from the immediate goal of traditional problem solving. Rather, mathematical creativity emerges as a collateral outcome of thinking afforded by the use of technology. Furthermore, collateral creativity is an educative outcome of one’s learning experience with pedagogy that motivates students to ask questions about computer-generated or tactile-derived information and assists them in finding answers to their own or the teacher’s questions. This book intends to provide guidance to teachers for fostering collateral creativity in their classrooms.

This new and updated second edition of Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. By engaging with established and contemporary debates, this volume promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Divided into five accessible sections, this book investigates and offers fresh insight into topics of central importance in mathematics education, with this second edition including new discussions and chapters on: Classic and contemporary issues of pedagogy, politics, philosophy and sociology of mathematics education International comparisons of achievement Digital technologies for teaching Mastery in mathematics Pop culture and mathematics Whether mathematics can be harmful Designed to stimulate discussion and support you in your own research, writing and practice through suggested questions and activities throughout, Debates in Mathematics Education will be a valuable resource for any student or practising teacher, and those engaged in initial teacher education, continuing professional development or Master's level study. This book also has much to offer to those leading mathematics departments in schools and initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.

"Efforts to improve mathematics teaching and learning globally have led to the ever-increasing interest in searching for alternative and effective instructional approaches from others. Students from East Asia, such as China and Japan, have consistently outperformed their counterparts in the West. Yet, Bianshi Teaching (teaching with variation) practice, which has been commonly used in practice in China, has been hardly shared in the mathematics education community internationally. This book is devoted to theorizing the Chinese mathematical teaching practice, Bianshi teaching, that has demonstrated its effectiveness over half a century; examining its systematic use in classroom instruction, textbooks, and teacher professional development in China; and showcasing of the adaptation of the variation pedagogy in selected education systems including Israel, Japan, Sweden and the US. This book has made significant contributions to not only developing the theories on teaching and learning mathematics through variation, but also providing pathways to putting the variation theory into action in an international context.“This book paints a richly detailed and elaborated picture of both teaching mathematics and learning to teach mathematics with variation. Teaching with variation and variation as a theory of learning are brought together to be theorized and exemplified through analysis of teaching in a wide variety of classrooms and targeting both the content and processes of mathematical thinking. Highly recommended.” – Kaye Stacey, Emeritus Professor of Mathematics Education, University of Melbourne, Australia “Many teachers in England are excited by the concept of teaching with variation and devising variation exercises to support their pupils’ mastery of mathematics. However, fully understanding and becoming proficient in its use takes time. This book provides a valuable resource to deepen understanding through the experiences of other teachers shared within the book and the insightful reflections of those who have researched this important area. – Debbie Morgan, Director for Primary Mathematics, National Centre for Excellence in the Teaching of Mathematics, United Kingdom"

Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.