This book explores mathematical problem posing in education, a topic of interest for at least 40 years. Over time, a research community has gradually formed around studying mathematical problem posing as a phenomenon of its own and as a component of mathematics instruction. This book is to provide advances on the impact of scholars (e.g., Polya, Kilpatrick, Brown, Walter, and Silver) and the role of problems in the development of mathematical ideas. It is the first book, which systematically explores the problem-posing processes, both cognitively and affectively. The book reports studies that employ problem posing as an instructional approach directed at deepening students' understanding of learning mathematics, knowledge, skills, and cognitive and affective characteristics related to their learning of mathematics. In addition, this book examines issues related to teachers and their learning when they start to take on mathematical problem posing as an instructional practice. It describes not only changes in teachers' beliefs and classroom instruction as a result of engaging in problem posing, but also teachers' instructional expertise of teaching mathematics through problem posing.

Autorentext

Jinfa Cai is the Kathleen and David Hollowell Professor at the University of Delaware, an elected member of USA National Academy of Education (NAEd) and a Fellow of American Educational Research Association (AERA). Jinfa received his B.S. in mathematics from Hangzhou Normal University, M.Ed. in mathematics education from Beijing Normal University, and his Ph.D. in Cognitive Studies (in mathematics education) from the University of Pittsburgh. He served as the Editor-in-Chief for the Journal for Research in Mathematics Education (2017-2020). He also served as Program Director at the USA National Science Foundation. He is the Editor of the 2017 Compendium for Research in Mathematics Education, by NCTM. Currently, he is the vice-president of International Commission of Mathematical Instruction (ICMI). His research is well-funded from various funding agencies, such as the USA National Science Foundation, Department of Education, and Spencer Foundation. Currently, he is working on a 4-year longitudinal research project on problem posing.

Dr. Roza Leikin is a Professor of Mathematics Education and Gifted Education at the Faculty of Education, University of Haifa and since October 2020, she serves as the Faculty Dean. Dr. Leikin is the Establishing Director of the RANGE Center - the Interdisciplinary Center for the Research and Advancement of Giftedness and Excellence. Prof. Leikin's research focuses mathematical creativity and ability, task design, teachers' professional potential, and integration of neuro-cognitive research to the field of mathematics education. From 2012-2017 she served as the President of the International Group for Mathematical Creativity and Giftedness and was the Head of the National Advisory Board in Mathematics Education of the Israeli Ministry of Education. Since 2013 she is serving as a Senior Mathematics Education Editor of the International Journal of Science and Mathematics Education. She has edited 13 volumes related to research in mathematics and gifted education and has published more than 180 papers and chapters in peer reviewed research.