is a text designed to give readers a highly conceptual understanding of mathematics topics essential for Common Core Standards-based elementary school teaching. In this book, the development of mathematical concepts, methods, and skills takes place through discussions and analyses of alternative solutions to engaging problems and activities with the use of manipulatives, visual models, and technology. Prospective teachers are expected to make sense of the problems and activities, communicate and articulate their ideas, critique the reasoning of others, and persevere solving problems using appropriate tools. Special features of the book include “Polya’s corners” for challenging problems with multiple access points, chapter reflection writing assignments, individual and group project descriptions, and extensive problem sets. The material in Exploring Mathematics is extensively classroom-tested, making this book an ideal, practical text for upper-division mathematics courses for pre-service elementary school teachers. The book not only shows ideas for implementing the eight standards of mathematical practices described in the common core standards into elementary teaching, but also allows the readers to actually experience those practices in their own learning process. received his Ph.D. in Mathematics Education from Indiana University. He is a professor in the Mathematics Department at California State University, Fresno. He directs professional development workshops for teachers locally and internationally. received his Ph.D. in Mathematics from Oregon State University. He is an assistant professor in the Mathematics Department at California State University, Fresno. His research interests are mathematics education and linear algebra, with a particular focus on how students transfer familiar knowledge when they solve problems in unfamiliar contexts. received her Ph.D. in Mathematics from the University of Rochester. She is an associate professor in the mathematics department at California State University, Fresno. received her Ph.D. in Mathematics Education from Ohio State University. She is a professor in the mathematics department at California State University, Fresno, where she teaches a variety of courses. In addition, she teaches courses and conducts workshops for prospective and in-service teachers and their students. She has collaborated on the use of GeoGebra in the international teaching community. received his Ph.D. in Mathematics from the University of Iowa. He is an assistant professor in the mathematics department at California State University, Fresno.