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This open access book provides an overview of Felix Klein's ideas, highlighting developments in university teaching and school mathematics related to Klein's thoughts, stemming from the last century.

This open access book, inspired by the ICME 13 Thematic Afternoon on ΓÇ£European Didactic TraditionsΓÇ¥, consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education.Written by mathematics teachers, mathematics teacher educators, school advisors, and developers and researchers in the field of instructional material, textbooks, and examinations, the book offers a multitude of perspectives on important issues in Dutch mathematics education, both at primary and secondary school levels. Topics addressed include the theoretical underpinnings of the Dutch approach, the subject of mathematics in the Dutch educational system, teacher education and testing, the history of mathematics education and the use of history in teaching of mathematics, changes over time in subject matter domains and in the use of technology, and the process of innovation and how the Dutch and in particular one Dutch institute have worked on the reform. 

This book examines new trends and developments in research related to the mathematical education of pre-service elementary teachers, and explores the implications of these research advances for theory and practice in teacher education.

This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24-31, 2016.

The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: * Theme 1: Epistemological issues related to proof and proving;

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness.

This open access book, inspired by the ICME 13 topic study group "Affect, beliefs and identity in mathematics education", presents the latest trends in research in the area.

This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems.

This book documents and expands on the diverse social and political dimensions of mathematics education issues, concerns, perspectives, contexts, and approaches presented in Topic Study Group 34 of the 13th International Congress on Mathematical Education (ICME-13).

The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education.

This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13).

This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community?These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research. Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country.

This open access book is the first major publication on the topic of "Interdisciplinary Mathematics Education" and arose from the work of the first International Topic Study Group of the same name at the ICME-13 conference in Hamburg in 2016.

This book presents innovative approaches and state-of-the-art empirical studies on mathematics teacher learning. The book details how representations of practice encourage and afford professional development, and describes how these tools help to investigate aspects of teacher expertise, beliefs, and conceptions.

This book discusses a significant area of mathematics education research in the last two decades and presents the types of semiotic theories that are employed in mathematics education.

This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states.

The third section presents four new innovations in mathematics learning and/or mathematics teacher education that involve the development of novel interfaces' for communicating mathematical ideas and analyzing student thinking and student work.

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers' decision making.

This book consists of 13 papers developed by participants in the ICME 13 Topic Study Group 40 on Classroom Assessment. The individual papers discuss various aspects of classroom assessment, focusing particularly on formative assessment as assessment for learning, and are grouped into four main sections: Examples of Classroom Assessment in Action, Technology as a Tool for Classroom Assessment, Statistical Models for Formative Assessment, and Engaging Teachers in Formative Assessment. The book opens with a brief discussion of the use of formative assessment as a critical component of the teaching¿learning process and concludes with an overview of lessons learned and ideas for future research. It is of interest to classroom teachers, university teacher educators, professional development providers and school supervisors.

The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education.

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources.

This book highlights innovative approaches to preparing secondary mathematics teachers. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for preparing secondary mathematics teachers, and discusses issues related to their professional and personal growth, such as identity, content knowledge, and pedagogical content knowledge which also includes knowledge of integrating technology into teaching and learning mathematics. Divided into four parts, the book focuses on field experiences, technologies, tools and resources, teacher knowledge, and teacher professional identities. Some of the main threads running through the book are: the importance of university and school partners working together to ensure preservice secondary mathematics teacher' success in developing pedagogical strategies that lead toward students' mathematical engagement and achievement; the critical need for preservice secondary mathematics teachers to develop strong content knowledge and pedagogical content knowledge; and the importance of providing opportunities, during pre-service education, for developing prospective teachers ¿professional identities.

The third section presents four new innovations in mathematics learning and/or mathematics teacher education that involve the development of novel interfaces' for communicating mathematical ideas and analyzing student thinking and student work.

This book highlights innovative approaches to preparing secondary mathematics teachers. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for preparing secondary mathematics teachers, and discusses issues related to their professional and personal growth, such as identity, content knowledge, and pedagogical content knowledge which also includes knowledge of integrating technology into teaching and learning mathematics. Divided into four parts, the book focuses on field experiences, technologies, tools and resources, teacher knowledge, and teacher professional identities. Some of the main threads running through the book are: the importance of university and school partners working together to ensure preservice secondary mathematics teacher' success in developing pedagogical strategies that lead toward students' mathematical engagement and achievement; the critical need for preservice secondary mathematics teachers to develop strong content knowledge and pedagogical content knowledge; and the importance of providing opportunities, during pre-service education, for developing prospective teachers ¿professional identities.

This book, inspired by the ICME 13 Thematic Afternoon on ΓÇ£European Didactic TraditionsΓÇ¥, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education.

This book discusses a significant area of mathematics education research in the last two decades and presents the types of semiotic theories that are employed in mathematics education.

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources.

The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: * Theme 1: Epistemological issues related to proof and proving;