Research in Mathematical Problem Posing: New Advances and Directions

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.