We Reason & We Prove for All Mathematics: Building Students' Critical Thinking, Grades 6-12

• Solving and discussing high-level mathematical tasks
• Analyzing narrative cases that make the relationship between teaching and learning salient
• Examining and interpreting student work
• Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove

Dr. Fran Arbaugh is an associate professor of mathematics education at Penn State University, having begun her career as a university mathematics teacher educator at the University of Missouri. She is a former high school mathematics teacher, received a M.Ed. in Secondary Mathematics Education from Virginia Commonwealth University and a PhD in Curriculum & Instruction (Mathematics Education) from Indiana University – Bloomington. Fran’s scholarship is in the area of professional learning opportunities for mathematics teachers and mathematics teacher educators, and her work is widely published for both research and practitioner audiences. She is a Past-President of the Association of Mathematics Teacher Educators (ATME) and served as a Co-Editor of the Journal of Teacher Education.

Margaret (Peg) Smith is a Professor Emerita at University of Pittsburgh. Over the past two decades she has been developing research-based materials for use in the professional development of mathematics teachers. She has authored or coauthored over 90 books, edited books or monographs, book chapters, and peer-reviewed articles including the best seller Five Practices for Orchestrating Productive Discussions (co-authored with Mary Kay Stein). She was a member of the writing team for Principles to Actions: Ensuring Mathematical Success for All and she is a co-author of two new books (Taking Action: Implementation Effective Mathematics Teaching Practices Grades 6-8 & 9-12) that provide further explication of the teaching practices first describe in Principles to Actions. She was a member of the Board of Directors of the Association of Mathematics Teacher Educators (2001-2003; 2003 – 2005), of the National Council of Teachers of Mathematics (2006-2009), and of Teachers Development Group (2009 – 2017).

Justin Boyle is an assistant professor at the University of Alabama. He is interested in learning how best to develop secondary mathematics teachers, so that they are prepared to engage their future students in becoming intellectually curious about mathematics. In particular, he uses reasoning-and-proving as a way to investigate and discuss the truth of mathematical statements, concepts and objects.

Gabriel J. Stylianides is Professor of Mathematics Education at the University of Oxford (UK) and Fellow of Oxford’s Worcester College. A Fulbright scholar, he received MSc degrees in mathematics and mathematics education, and then his PhD in mathematics education, at the University of Michigan. He has conducted extensive research in the area of reasoning-and-proving at all levels of education, including teacher education and professional development. He was an Editor of Research in Mathematics Education and is currently an Editorial Board member of the Elementary School Journal and the International Journal of Educational Research. He received an American Educational Research Association Publication Award for his 2009 article "Reasoning-and-proving in Mathematics Textbooks."

Michael D. Steele is a Professor of Mathematics Education and Chair of the Department of Curriculum and Instruction in the School of Education at the University of Wisconsin-Milwaukee. He is currently the President-Elect of the Association of Mathematics Teacher Educators. A former middle and high school mathematics and science teacher, Dr. Steele has worked with preservice secondary mathematics teachers, practicing teachers, administrators, and doctoral students across the country for the past two decades. He has published several books and journal articles focused on supporting mathematics teachers in enacting research-based effective mathematics teaching practices. He is the co-author of NCTM’s Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8 and Mathematics Discourse in Secondary Classrooms, two research-based professional development resources for secondary mathematics teachers. He is also the author of A Quiet Revolution: One District’s Story of Radical Curricular Change in Mathematics, a resource focused on reforming high school mathematics teaching and learning.