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Developing Mathematical Proficiency for Elementary Instruction

Y. Li, R. E. Howe, W. J. Lewis, and J. J Madden, eds.
Publication Date: 
Number of Pages: 
Advances in STEM Education
[Reviewed by
Mary Beth Rollick
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The idea for this book came from two national workshops: One in 2017 which focused on mathematics training for preservice elementary teachers and one in 2018 which focused on professional development for in-service elementary teachers. The book includes research reports and extensions on the work shared at these two workshops. 
Two of the pivotal chapters address the questions of what pre-service elementary teachers need to learn in their college experience and how they should best learn the concepts. They describe programs that have been tested and are currently being refined. One such program is the Elementary Mathematics Project which began in 2009. The chapter includes an explanation of how the topics were chosen, the design principles, and how pre-service teachers interact with the material.  Interesting examples and transcript excerpts are included. The other chapter describes a course that focuses on structure and sensemaking that was developed from a conceptual core idea where the definition of multiplication acts as the central organizer. Examples of problems and student responses contribute to make enjoyable reading.
Several chapters focus on the development of thinking-oriented training and each of these chapters highlights a different aspect of what teachers need to learn. One approach is “doing” mathematics in a problem solving/discussion environment to develop “habits of mind” to help one solve unusual problems. Another approach focuses on justifying and explanations rather than just using an algorithm. 
Several other successful ventures described in the book include a “Math Semester” which involves a partnership between mathematicians and mathematics educators where students simultaneously take a mathematics course, a methods course, and a field experience. Another program features video-recorded interviews to battle “hindsight bias” and allow the pre-service teachers to reflect on what they knew at the beginning of the course so they can see how their knowledge expanded over the semester and realize that learning elementary mathematics is actually not elementary.
The last section of the book describes several approaches for professional development for in-service teachers. I was surprised to find that one of the chapters was targeted for pre-school teachers.  The TRIAD Model (Technology-enhanced Research-based Instruction, Assessment, and professional Development) is based on pre-school children’s thinking and learning trajectories. The tone of the final chapter is different. It advocates an alternative approach with long-term content-based professional development using precise mathematical definitions and reasoning. 
The book includes extensive bibliographies, a subject index, and an author index. Unfortunately these indices are only marginally useful because the page references for many names on the author index did not match the page where the author could be found and the same was true for the subject index. 
This book is an important contribution to the field of Mathematics Education particularly as it applies to preparing and supporting elementary teachers and their mathematical knowledge for teaching. I highly recommend the book as essential reading for all mathematicians and mathematics educators who teach pre-service elementary teachers. Graduate students in mathematics education will find it a very useful synopsis of the current research in the field.


Mary Beth Rollick is Professor Emerita at Kent State University, in Kent, Ohio. She continues to tutor undergraduate students and enjoys helping them to understand the “why” as well as the “how” of mathematics.