Keith Weber – författare

Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book.The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching.This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.

This book summarizes new directions in mathematics education research on proving at the university level, thereby providing contemporary extensions of the sub-fields of proof that Annie and John Selden introduced to the field. The chapters each describe an emerging new area of proof research, review the relevant findings in this area, present open research questions and the tools to address them. The book also discusses proof as a literary genre, and how students' feelings during the proof writing process can influence their behavior. The concluding chapter of the book reflects on new directions for research on proving. As such, this book provides mathematics educators, who have extensive experience researching proof, with an up-to-date review of the new methodologies and research questions with regard to proof, and young scholars, interested in proof, can use these chapters as primers on which they can build a research program.