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Considering the relevance of teachers‘ diagnostic competence for understanding students'thinking and providing effective learning opportunities, Macarena Larrain investigates the development of future primary school teachers'diagnostic competence in error situations already during initial teacher education. Using video vignettes of classroom situations and samples of students'work, the author focuses on fostering future teachers'competence to identify students'errors, elaborate hypotheses about the causes of those errors and to design appropriate strategies for supporting students in overcoming their misconceptions. She also describes aspects of teachers'knowledge, beliefs and experience that are relevant for the competence and its development.

The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.

If we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane and Mark McCourt a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture. This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice. This is also a book for those who are interested in the theory behind tasks. Chris and his interviewees examine the key role tasks play in shaping learning, teaching, curriculum and assessment. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.

The issue of mathematics teaching and its impact on learners'attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers'world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers'education and teachers'knowledge, Teaching and Teachers'personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.

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 examines the various areas of mathematics education and neighboring disciplines that have recently contributed to a better understanding of the still vague construct of diagnostic competence. The work addresses the nature, development and effect of diagnostic competence in mathematics instruction, with a focus on the professional development of teachers.

Carola Bernack-Schüler geht der Frage der Veränderung von mathematikbezogenen Beliefs Studierender durch ein qualitatives Vorgehen in Form von Prä-Post-Interviews nach. Dabei wird die Änderung von Mathematikbildern durch ein Problemlöseseminar für Lehramtsstudierende aus unterschiedlichen Perspektiven und auf verschiedenen Ebenen in Einzelfallanalysen und fallübergreifend herausgearbeitet. Die Autorin identifiziert verschiedene Typen der Beliefänderung und zeigt die Kontextbezogenheit von Beliefs und die teilweise schwach ausfallende Argumentation bei deren Verbalisierung auf. Die Arbeit liefert Erkenntnisse zur Ausbildung eines reflektierten Beliefsystems zukünftiger Mathematiklehrerinnen und -lehrer sowie erste Anhaltspunkte zu Ursachen der Beliefänderung durch ein Problemlöseseminar.

Angela Schmitz analysiert die Überzeugungen und Ziele von Mathematiklehrkräften der Sekundarstufen I und II zum Visualisieren, einem wesentlichen Element des Betreibens von Mathematik. Sie untersucht die Sichtweisen der Lehrkräfte auf Visualisierung im Unterricht und inwiefern sich diese zwischen verschiedenen mathematischen Themengebieten unterscheiden. Dabei betrachtet die Autorin die Bruchrechnung, Algebra, Funktionen und Analysis und zeigt potenzielle Zusammenhänge zwischen den Beliefs von Lehrerinnen und Lehrern, verschiedenen Themengebieten und unterschiedlichen Überzeugungsfeldern auf.

What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers'mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers'lives in classrooms.

This volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts.In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity. This is followed by three main sections:An overview of current practices in teachers'use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiner's zone theory).A set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues.Meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements

This book consists of interviews with the most important mathematics educators of our time. These interviews were originally published in the International Journal for the History of Mathematics Education and are now being offered to a wider readership for the first time, collected in a single volume. Among the individuals interviewed are scholars from Brazil, France, Germany, Russia, the United Kingdom, and the United States who have made a significant impact on the development of mathematics education in their countries and internationally. The interviews cover their biographies, including their memories of their own studies in mathematics and their intellectual formation, their experience as researchers and teachers, and their visions of the history and future development of mathematics education.The book will be of interest to anyone involved in research in mathematics education, and anyone interested in the history of mathematics education.