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 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.

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. About the author Macarena Larrain Jory has been educating pre- and in-service Chilean primary school teachers for the last 10 years and completed her PhD as an external doctoral student in the field of mathematics education with Prof. Dr. Gabriele Kaiser at the University of Hamburg.

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.

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

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?

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.