This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

After a brief description of three Piagetian stages (pre-operational, transition to concrete operations, and concrete operations), the author identifies 12 key statements from Piaget's writings. These statements, together with related implications for teaching elementary school mathematics, methods of diagnosing stage acquisition, and examples are…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…

This yearbook is intended to be primarily a highlighting of the essential elements of those basic mathematical understandings which should be continually developed and extended throughout the entire mathematics curriculum. An attempt is also made to illustrate training in mathematical modes of thought, sometimes labeled problem solving or creative…

On the basis of studies reported elsewhere (SE 019 717 and 719) the author discusses the implications of research on cognitive development for teachers whose subjects involve an understanding of proportionality. Several common methods of teaching chemistry students to use proportionality in chemical problems are described. Research on the…

In the foreword to this book, Inhelder states that its essential contribution is that "it transposed to actual reality Piaget's central epistemological thesis according to which mathematical thought is, from its most elementary manifestations, the product of the subject's activity that he characterized by the term 'reflective…

This is volume 6 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This book contains both a theoretical examination of the connection between instruction and the development of children, and experimental data on a definite…

This booklet contains 43 "workjobs," (experiences in manipulating common objects) adapted from classroom activities, that are appropriate and easy for parents to make and use with children in the home. These manipulative activities are designed to help children develop language and number skills and hand-eye coordination, and give children…

This book is for teachers of children in preschool through grade 4. It is designed to help teachers make important decisions about the mathematics curriculum and give them some effective ways to help children attain the mathematical power needed for everyday use and for future careers. Relevant research in each chapter provides a framework and…