Responding to their recent research on how children learn mathematics, the authors have revised this bestselling textbook to provide practical advice on what works and what should be avoided when teaching second graders. This volume features important revisions to their groundbreaking program based on Piaget’s theory that children learn arithmetic by constructing it from the inside, through their own natural ability to think. New for the Second Edition! The harmful effects of teaching “carrying” and “borrowing”—compared with the results of encouraging children to invent their own ways of dealing with multidigit numbers. The addition of new games that respond to what has been discovered in recent research. A shift in strategy for doing subtraction with second graders—computational fluency de-emphasized in favor of word problems. The difference between repeated addition and multiplication for this age group and how teachers can respond appropriately. The harmful effects of “testmania” and quick fixes versus teaching based on the most recent scientific explanation of how children learn mathematics. Critical Acclaim for the First Edition! “The book is useful for practicing educators, administrators, and curriculum directors, as well as students of early childhood, cognitive development and mathematics methods.” —Childhood Education “The clear narrative writing style and frequent illustrations make the book easy to read and understand…a useful resource for any primary grade teacher and curriculum specialist.” —Arithmetic Teacher “An encouraging foray into the future of educational research and practice. Although written for teachers, administrators, curriculum developers, and evaluators, Young Children Continue to Reinvent Arithmetic would also be of interest to researchers and psychologists.” —Harvard Educational Review