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.

Autorentext

Keith Weber is a distinguished professor of mathematics education at Rutgers University. Since earning his Ph.D in 2001, he has published 100 articles in on mathematics education topics, 25 of which have appeared in JRME and ESM, the two top journals in mathematics education. He has also published in other outlets, including journals in educational psychology (Cognition and Instruction, Educational Psychologist), philosophy (Philosophia Mathematica, Synthese), and psychology (Topics in Cognitive Science, JEP:HPP), as well as expository outlets for mathematicians (Notices of the AMS, Mathematics Intelligencer).

Dr. Weber's research on proof has received awards from the Mathematical Association of America, the American Education Research Association, the National Science Foundation, and the British Society for Research into Learning Mathematics. This includes the MAA's Annie and John Selden Prize for outstanding research in undergraduate mathematics education (the prize was named after whom this volume will honor). At the annual Conference for Research in Undergraduate Mathematics Education, he received the Best Paper Award on four occasions, and the Runner-Up for Best Paper three other times.

Milos Savic is an associate professor of mathematics education at the University of Oklahoma. Since earning his Ph.D in mathematics education from New Mexico State University in 2012, Dr. Savic has published 15 articles, mostly focusing on the teaching of proof. Particularly novel about Dr. Savic's research is his innovative focus on creativity in the proving process. Dr. Savic is a member and co-founder of the Creativity Research Group, which is supported by the National Science Foundation to develop and analyze methods for teaching creativity in the mathematics classroom. Dr. Savic was advised by John and Annie Selden, for whom this volume is honoring.