Part 1 Introduction -- Developing Mathematical Proficiency for Elementary Instruction: An Introduction -- Part 2 Mathematical Training for Pre Service Elementary School Teachers -- Towards a Thinking-Oriented Training in Mathematics for Elementary School Teachers -- The Missing Element for Teachers: Learning What Mathematics Is -- The Elementary Mathematics Project: Supporting Pre-Service Teachers’ Content Knowledge for Teaching Mathematics -- Mathematics and Mathematics Education at the University of Nebraska-Lincoln: Partnering to Implement Core Practices in Elementary Teacher Preparation -- Focusing on Mathematical Structure and Sense-Making in Courses for Future Teachers -- The Work of Coaching in Rehearsals to Enlist Mathematical Knowledge for Teaching -- How Do I Know I Learned Something? Reflecting on Learning by Using Video-Recorded Interviews to Battle Hindsight (“I-knew-it-all-along”) Bias -- Part 3 Professional Development in Mathematics for In-Service Elementary School Teachers -- Mathematics in the Yale Teachers Institute -- Sustainable, Scalable Professional Development in Early Mathematics: Strategies, Evaluation, and Tools -- Inservice Mathematics Professional Development: The Hard Work of Learning Mathematics.

The need to improve the mathematical proficiency of elementary teachers is well recognized, and it has long been of interest to educators and researchers in the U.S. and many other countries. But the specific proficiencies that elementary teachers need and the process of developing and improving them remain only partially conceptualized and not well validated empirically. To improve this situation, national workshops were organized at Texas A&M University to generate focused discussions about this important topic, with participation of mathematicians, mathematics educators and teachers. Developing Mathematical Proficiency for Elementary Instruction is a collection of articles that grew out of those exciting cross-disciplinary exchanges. Developing Mathematical Proficiency for Elementary Instruction is organized to probe the specifics of mathematical proficiency that are important to elementary teachers during two separate but inter-connected professional stages: as pre-service teachers in a preparation program, and as in-service teachers teaching mathematics in elementary classrooms. From this rich and inspiring collection, readers may better understand, and possibly rethink, their own practices and research in empowering elementary teachers mathematically and pedagogically, as educators or researchers. .