Roza Leikin – författare

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristicsof challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristicsof challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.

This book represents a pioneering effort to establish mathematical curiosity as its own field of study within mathematics education. The authors take a multifaceted approach, examining curiosity through three key lenses: cognitive (how the mind processes and engages with mathematical concepts), affective (the emotional and motivational aspects of mathematical learning), and social (how curiosity develops through interaction with others).The historical and cultural perspectives offer valuable context by exploring how different societies and time periods have understood and cultivated mathematical wonder. This broader view helps educators understand that curiosity isn't just a modern pedagogical tool, but has deep roots in how humans have always engaged with mathematical thinking.The practical applications section likely provides concrete strategies and techniques that teachers can implement immediately. Rather than remaining purely theoretical, the book bridges the gap between research findings and classroom reality, offering evidence-based methods for nurturing student curiosity.By positioning mathematical curiosity as a distinct scholarly domain, the authors are essentially arguing that this area deserves dedicated research attention, theoretical development, and practical exploration. This could lead to new research methodologies, assessment approaches, and pedagogical frameworks specifically designed around curiosity-driven learning.The book's ultimate goal is transformative - not just to inform readers about curiosity, but to actively engage their own sense of mathematical wonder and potentially recruit them as contributors to this emerging field.

This book represents a pioneering effort to establish mathematical curiosity as its own field of study within mathematics education. The authors take a multifaceted approach, examining curiosity through three key lenses: cognitive (how the mind processes and engages with mathematical concepts), affective (the emotional and motivational aspects of mathematical learning), and social (how curiosity develops through interaction with others).The historical and cultural perspectives offer valuable context by exploring how different societies and time periods have understood and cultivated mathematical wonder. This broader view helps educators understand that curiosity isn't just a modern pedagogical tool, but has deep roots in how humans have always engaged with mathematical thinking.The practical applications section likely provides concrete strategies and techniques that teachers can implement immediately. Rather than remaining purely theoretical, the book bridges the gap between research findings and classroom reality, offering evidence-based methods for nurturing student curiosity.By positioning mathematical curiosity as a distinct scholarly domain, the authors are essentially arguing that this area deserves dedicated research attention, theoretical development, and practical exploration. This could lead to new research methodologies, assessment approaches, and pedagogical frameworks specifically designed around curiosity-driven learning.The book's ultimate goal is transformative - not just to inform readers about curiosity, but to actively engage their own sense of mathematical wonder and potentially recruit them as contributors to this emerging field.

This book explores mathematical problem posing in education, a topic of interest for at least 40 years. Over time, a research community has gradually formed around studying mathematical problem posing as a phenomenon of its own and as a component of mathematics instruction. This book is to provide advances on the impact of scholars (e.g., Polya, Kilpatrick, Brown, Walter, and Silver) and the role of problems in the development of mathematical ideas. It is the first book, which systematically explores the problem-posing processes, both cognitively and affectively. The book reports studies that employ problem posing as an instructional approach directed at deepening students’ understanding of learning mathematics, knowledge, skills, and cognitive and affective characteristics related to their learning of mathematics. In addition, this book examines issues related to teachers and their learning when they start to take on mathematical problem posing as an instructional practice. It describes not only changes in teachers’ beliefs and classroom instruction as a result of engaging in problem posing, but also teachers’ instructional expertise of teaching mathematics through problem posing.

This book explores mathematical problem posing in education, a topic of interest for at least 40 years. Over time, a research community has gradually formed around studying mathematical problem posing as a phenomenon of its own and as a component of mathematics instruction. This book is to provide advances on the impact of scholars (e.g., Polya, Kilpatrick, Brown, Walter, and Silver) and the role of problems in the development of mathematical ideas. It is the first book, which systematically explores the problem-posing processes, both cognitively and affectively. The book reports studies that employ problem posing as an instructional approach directed at deepening students’ understanding of learning mathematics, knowledge, skills, and cognitive and affective characteristics related to their learning of mathematics. In addition, this book examines issues related to teachers and their learning when they start to take on mathematical problem posing as an instructional practice. It describes not only changes in teachers’ beliefs and classroom instruction as a result of engaging in problem posing, but also teachers’ instructional expertise of teaching mathematics through problem posing.

This volume provides readers with a broad view on the variety of issues related to the educational research and practices in the field of Creativity in Mathematics and Mathematical Giftedness. The book explores (a) the relationship between creativity and giftedness;  (b) empirical work with high ability (or gifted) students in the classroom and its implications for teaching mathematics; (c) interdisciplinary work which views creativity as a complex phenomena that cannot be understood from within the borders of disciplines, i.e., to present research and theorists from disciplines such as neuroscience and complexity theory; and (d) findings from psychology that pertain the creatively gifted students. As a whole, this volume brings together perspectives from mathematics educators, psychologists, neuroscientists, and teachers to present a collection of empirical, theoretical and philosophical works that address the complexity of mathematical creativity and giftedness, its origins, nature, nurture and ways forward. In keeping with the spirit of the series, the anthology substantially builds on previous ZDM volumes on interdisciplinarity (2009), creativity and giftedness (2013).

This volume provides readers with a broad view on the variety of issues related to the educational research and practices in the field of Creativity in Mathematics and Mathematical Giftedness. The book explores (a) the relationship between creativity and giftedness;  (b) empirical work with high ability (or gifted) students in the classroom and its implications for teaching mathematics; (c) interdisciplinary work which views creativity as a complex phenomena that cannot be understood from within the borders of disciplines, i.e., to present research and theorists from disciplines such as neuroscience and complexity theory; and (d) findings from psychology that pertain the creatively gifted students. As a whole, this volume brings together perspectives from mathematics educators, psychologists, neuroscientists, and teachers to present a collection of empirical, theoretical and philosophical works that address the complexity of mathematical creativity and giftedness, its origins, nature, nurture and ways forward. In keeping with the spirit of the series, the anthology substantially builds on previous ZDM volumes on interdisciplinarity (2009), creativity and giftedness (2013).

This volume provides readers with a broad view on the variety of issues related to the educational research and practices in the field of Creativity in Mathematics and Mathematical Giftedness. The book explores (a) the relationship between creativity and giftedness;  (b) empirical work with high ability (or gifted) students in the classroom and its implications for teaching mathematics; (c) interdisciplinary work which views creativity as a complex phenomena that cannot be understood from within the borders of disciplines, i.e., to present research and theorists from disciplines such as neuroscience and complexity theory; and (d) findings from psychology that pertain the creatively gifted students. As a whole, this volume brings together perspectives from mathematics educators, psychologists, neuroscientists, and teachers to present a collection of empirical, theoretical and philosophical works that address the complexity of mathematical creativity and giftedness, its origins, nature, nurture and ways forward. In keeping with the spirit of the series, the anthology substantially builds on previous ZDM volumes on interdisciplinarity (2009), creativity and giftedness (2013).

The idea of teachers Learning through Teaching (LTT) – when presented to a naïve bystander – appears as an oxymoron. Are we not supposed to learn before we teach? After all, under the usual circumstances, learning is the task for those who are being taught, not of those who teach. However, this book is about the learning of teachers, not the learning of students. It is an ancient wisdom that the best way to “truly learn” something is to teach it to others. Nevertheless, once a teacher has taught a particular topic or concept and, consequently, “truly learned” it, what is left for this teacher to learn? As evident in this book, the experience of teaching presents teachers with an exciting opp- tunity for learning throughout their entire career. This means acquiring a “better” understanding of what is being taught, and, moreover, learning a variety of new things. What these new things may be and how they are learned is addressed in the collection of chapters in this volume. LTT is acknowledged by multiple researchers and mathematics educators. In the rst chapter, Leikin and Zazkis review literature that recognizes this phenomenon and stress that only a small number of studies attend systematically to LTT p- cesses. The authors in this volume purposefully analyze the teaching of mathematics as a source for teachers’ own learning.

The idea of teachers Learning through Teaching (LTT) – when presented to a naïve bystander – appears as an oxymoron. Are we not supposed to learn before we teach? After all, under the usual circumstances, learning is the task for those who are being taught, not of those who teach. However, this book is about the learning of teachers, not the learning of students. It is an ancient wisdom that the best way to “truly learn” something is to teach it to others. Nevertheless, once a teacher has taught a particular topic or concept and, consequently, “truly learned” it, what is left for this teacher to learn? As evident in this book, the experience of teaching presents teachers with an exciting opp- tunity for learning throughout their entire career. This means acquiring a “better” understanding of what is being taught, and, moreover, learning a variety of new things. What these new things may be and how they are learned is addressed in the collection of chapters in this volume. LTT is acknowledged by multiple researchers and mathematics educators. In the rst chapter, Leikin and Zazkis review literature that recognizes this phenomenon and stress that only a small number of studies attend systematically to LTT p- cesses. The authors in this volume purposefully analyze the teaching of mathematics as a source for teachers’ own learning.