Connecting Arithmetic to Algebra ─ Strategies for Building Algebraic Thinking in the Elementary Grades

The techniques described here are based on a classroom project conducted between 2006 and 2009; the book includes many real-life classroom dialogues and discussions between teachers and students from the project. The project and the book are based on the idea that students will be better prepared for algebra if they are taught to investigate the behavior of operations, notice commonalities across problems, make generalizations, and prove or disprove these generalizations. The book begins with two chapters introducing generalization in the context of arithmetic. Later chapters give ideas for lessons, differentiating instruction, and suggestions for using arithmetic and algebraic notation and proofs in elementary grades. The book is designed to be a text for a year-long course conducted face to face or online; guidelines for conducting an online course available online. The book can also be used in study groups for in-service teachers. Russell is a principal scientist at the Education Research Collaborative at TERC. Annotation c2012 Book News, Inc., Portland, OR (booknews.com)

Susan Jo Russell is a principal scientist at the Education Research Collaborative at TERC. Following ten years of classroom teaching and coaching in elementary schools, Dr. Russell directed projects focused on mathematics professional development, research on students' and teachers' understanding of mathematics, and mathematics curriculum. She co-directed the development of the NSF-funded elementary curriculum, Investigations in Number, Data, and Space and the professional development materials, Developing Mathematical Ideas. Her recent work is on supporting teachers to integrate a focus on generalizing about the operations into their core arithmetic instruction.Deborah Schifter is Principal Research Scientist at the Education Development Center (EDC) where she leads a range of projects concerning professional development in mathematics and research into student learning. Working with a variety of colleagues, she is coauthor of Reconstructing Mathematics Education, Developing Mathematical Ideas, The Mathematical Education of Teachers, and the Second Edition of Investigations in Number, Data, and Space. She also edited What's Happening in Math Class? (an anthology of teacher writing) and is co-editor of A Research Companion to the NCTM Standards. Deborah loves learning from the teachers with whom she works.Virginia Bastable has been the Director of the SummerMath for Teachers Program at Mount Holyoke College since 1993. She taught middle school and high school mathematics for more than twenty years. She is coauthor of the Developing Mathematical Ideas professional development curriculum and the Second Edition of Investigations in Number, Data, and Space. Dr. Bastable particularly enjoys helping others to discover their interest and abilities in mathematics, even if those interests and abilities have been blunted by past negative experiences with the subject.