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.

This work reports the findings of the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students ́ Mathematical Literacy project (COACTIV). COACTIV applies a broad, innovative conceptualization of teacher competence to examine how mathematics teachers’ knowledge, beliefs, motivational orientations, and self-regulation skills influence their instructional practice and teaching outcomes In this project data was collected on various aspects of teacher competence and classroom instruction from the perspective of both the teachers themselves and their students. Moreover, it gauges the effects of these teacher characteristics on student learning, as indexed by the progress students in each class. Questions addressed in the study which are reported in this volume include: What are the characteristics of successful teaching? What distinguishes teachers who succeed in their profession? How can the quality of instruction be improved?

The book provides an overview of state-of-the-art research from Brazil and Germany in the field of inclusive mathematics education. Originated from a research cooperation between two countries where inclusive education in mathematics has been a major challenge, this volume seeks to make recent research findings available to the international community of mathematics teachers and researchers. In the book, the authors cover a wide variety of special needs that learners of mathematics may have in inclusive settings. They present theoretical frameworks and methodological approaches for research and practice.

This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.

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.

This open access book presents 8 novel approaches to measure and improve diagnostic competences with simulation. The book compares the effects of interventions on these diagnostic competences in both teacher and medical education. It includes analyses showing that important aspects of diagnostic competences and effects of instructional interventions aiming to facilitate them are comparable for teachers and doctors. Through closely analyzing projects from medical education, mathematics education, biology education, and psychology, the reader is presented with multiple options for interventions that may be used in each of the subject areas and the improvements in diagnostic skills that could be expected from each simulation. The book concludes with an outline of promising future research on the use of simulations to facilitate professional competences in higher education in general, and for the advancement of diagnostic competencies in particular. This is an open access book.

This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, 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.

The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.