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The Development of Arithmetic Concepts and Skills
This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars,...
Hypothetical Learning Trajectories
The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. The issue begins by briefly introducing learning trajectories. The remaining articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to learning trajectories construct; they are not a set of verification studies.
Fostering Children's Mathematical Power
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics,...
A Guide to Teaching Mathematics in the Primary Grades
Grade level: 1, 2, 3, k, p, e, t.
Problem Solving, Reasoning, and Communicating, K-8
Examines in depth how teachers can help foster children's mathematical thinking. Provides practical suggestions, builds on the most recent research, uses case studies, encourages interactive learning, presents challenging problems, discusses the importanct of process-oriented math instruction, demonstrates "writing-to-learn" mathematics
Children's Mathematical Thinking
This book provides a framework for understanding children's mathematical development and the ways in which it can go wrong. The author first summarizes the major theoretical and practical research on the development of numeration, arithmetic, and problem solving, and then details strategies and activities for encouraging specific mathematical skills, concepts, and beliefs. Particular emphasis is placed on using the children's informal knowledge of mathematics as a basis for building up to a formal understanding.
Engaging Young Children in Mathematics
Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Confere...
Conceptual and Procedural Knowledge
First Published in 1986. This book is intended for those people who are interested in how mathematics is learned. It is intended especially for those who are interested in the mental processes involved in becoming mathematically competent and the mental processes that inhibit such competency from developing. The volume opens with an overview of the issue and then traces the relationships between conceptual and procedural knowledge in mathematics from preschool days through the years of formal schooling. Mathematics educators and cognitive psychologists from a variety of perspectives contribute theoretical arguments and empirical data to illuminate the nature of the relationships and, in tum, the nature of mathematics learning.
The Wiley Handbook of Early Childhood Care and Education
The essential resource to the issues surrounding childhood care and education with contributions from noted experts The Wiley Handbook of Early Childhood Care and Education is a comprehensive resource that offers a review of the historical aspects, best practices, and the future directions of the field. With contributions from noted experts in the field, the book contains 30 interdisciplinary essays that explore in-depth the central issues of early childhood care and education. The handbook presents a benchmark reference to the basic knowledge, effective approaches to use with young children, curriculum design, professional development, current policies, and other critical information. The e...
Mathematics in the Early Years
Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining children's mathematical thinking. The chapters are: (1) "Why Do We Teach Young Children So Little Mathematics? Some Historical Considerations" (Balfanz); (2) "Children's Ways of Knowing: Lessons from Cognitive Development Research" (Sophian); (3) "The Sociology of Day Care" (McDill and Natriello); (4) "Cultural Aspects of Young Children's Mathematics Knowle...
