This book leads readers from simple number work to the point where they can prove the classical results of elementary number theory for themselves.

This volume celebrates the 50th anniversary of the famous and influential work of Jean Piaget and Alina Szeminska, The Child's Conception of Number. It is a tribute to those two authors as well as to the entire Geneva school that pioneered the genetic study of cognitive structures in children. Dealing with the process of the child's construction of the notion of number -- a very important subject for the child as well as for the teacher, the researcher, and the practicing psychologist -- it summarizes the progress that has been made and outlines new research directions in this area. The book is a compilation of the work of the foremost international researchers in this area and includes a wide spectrum of viewpoints and schools of thought. It also introduces several new authors from Europe, including students of Piaget, to the American academic community.

Most parents and teachers know that reading to children is an important part of developing literacy, but unfortunately, when it comes to developing mathematical thinking, these same parents and teachers sometimes feel confused and inadequate about how best to jumpstart their young children's interest in and understanding of numbers. Pathway to Mathematical Understanding in Early Childhood contains easy to understand explanations of important number concepts, along with activities and resources to develop them. In other words, this book contains the pathway not only to mathematical excellence, but also a love of math!

Everyone can imagine their future self, even very young children, and this future self is usually positive and education-linked. To make progress toward an aspired future or away from a feared future requires people to plan and take action. Unfortunately, most people often start too late and commit minimal effort to ineffective strategies that lead their attention elsewhere. As a result, their high hopes and earnest resolutions often fall short. In Pathways to Success Through Identity-Based Motivation Daphna Oyserman focuses on situational constraints and affordances that trigger or impede taking action. Focusing on when the future-self matters and how to reduce the shortfall between the self that one aspires to become and the outcomes that one actually attains, Oyserman introduces the reader to the core theoretical framework of identity-based motivation (IBM) theory. IBM theory is the prediction that people prefer to act in identity-congruent ways but that the identity-to-behavior link is opaque for a number of reasons (the future feels far away, difficulty of working on goals is misinterpreted, and strategies for attaining goals do not feel identity-congruent). Oyserman's book goes on to also include the stakes and how the importance of education comes into play as it improves the lives of the individual, their family, and their society. The framework of IBM theory and how to achieve it is broken down into three parts: how to translate identity-based motivation into a practical intervention, an outline of the intervention, and empirical evidence that it works. In addition, the book also includes an implementation manual and fidelity measures for educators utilizing this book to intervene for the improvement of academic outcomes.

This volume of Math Pathways & PitfallsK-8 intervention curriculum helps students tackle stubborn pitfalls head-on and transform them into pathways for learning key standards for grades 2-3. The lessons in this book address place value and whole number operations interwoven with algebraic reasoning. In rigorous research studies, Math Pathways & Pitfallssignificantly increased student achievement for diverse students, including for English learners, in all grades tested. Math Pathways & Pitfallsintervention lessons and instructional strategies: Help students master key mathematical standards. Include concepts important for algebra readiness. Provide students with guided and independent practice. Support academic language development. Add value to any adopted curriculum. Prevent common pitfalls on homework and standardized assessments. This all-in-one book contains everything a teacher needs to teach Math Pathways & Pitfallswith ease and success: 21 complete lessons Teaching manual DVD video footage of Math Pathways & Pitfallsin action CD with black line masters of student handouts, classroom quizzes, answer keys, and resources Discussion Buildersclassroom poster Teacher professional development tasks, activities, and video footage