James A. Middleton is Professor of Mechanical and Aerospace Engineering at Arizona State University. Prior to these appointments, Dr. Middleton served as Associate Dean for Research for the Mary Lou Fulton College of Education at Arizona State University and as Director of the Division of Curriculum and Instruction. He received his Ph.D. in Educational Psychology from the University of Wisconsin-Madison in 1992, where he also served in the National Center for Research on Mathematical Sciences Education as a postdoctoral scholar for 3 years. Jim’s research interests focus in the following areas where he has published extensively: Children’s mathematical thinking; Teacher and Student motivation in mathematics; and Teacher Change in mathematics. He has served as Senior co-Chair of the Special Interest Group for Mathematics Education of the American Educational Research Association, and as chair of the National Council of Teachers of Mathematics Research Committee. Jinfa Cai is a Professor of Mathematics and Education and the director of Secondary math education at the University of Delaware.  He is interested in how students learn mathematics and solve problems, and how teachers can provide and create learning environments so that students can make sense of mathematics.  He received a number of awards, including a National Academy of Education Spencer Fellowship, an American Council on Education Fellowship, an International Research Award, and a Teaching Excellence Award. He has been serving on the Editorial Boards for several international journals, such as the Journal for Research in Mathematics Education.  He was a visiting professor in various institutions, including Harvard University.  He has serves as a Program Director at the U.S. National Science Foundation (2010-2011) and a co-chair of American Educational Research Association’s Special Interest Group on Research in Mathematics Education (AERA’s SIG-RME)(2010-2012).  He will be chairing a plenary panel at the ICMI-12 in Germany in 2016. Stephen Hwang is currently a post-doctoral researcher working with Jinfa Cai in the Department of Mathematical Sciences at the University of Delaware. His research interests include the teaching and learning of mathematical justification and proof, the nature of practice in the discipline of mathematics, the development of mathematical habits of mind, and mathematics teacher preparation.