This important book makes a powerful contribution to our understanding of howchildren can learn fractions. The authors argue in this study that a broadly held assumption—that children’s prior whole number understanding tends to interfere with later fraction learning—is at best simplistic if not fundamentally mistaken. The research described in this book shows instead that children’s prior whole number understandings, suitably reshaped, provides essential groundwork for successful fraction learning. Each task and interaction of this study,builds from concurrent, evolving conceptual analyses of what the children didand said before, and tests that conceptual analysis through direct practice. In this way the researchers’ constructs, models, and interpretations can be seen to deepen and evolve in step with the emerging understanding of the children. “Children’s Fractional Knowledge presents a major, indeed innovating contribution to mathematics education. Original work on children's construction of fractional knowledge Provides new research on how the teaching of fractions canbe dramatically improved Written by pioneers in mathematics education INDICE: A New Hypothesis Concerning Children’s Fractional Knowledge.- Perspectives on Children’s Fractional Knowledge.- Operations that Produce Numerical Counting Schemes.- Articulation of the Reorganization Hypothesis.- Construction of Multiplying and Dividing Schemes: Rebecca and Tanya.- Construction of Multiplying and Dividing Schemes: Jason and Patricia.- Construction of Multiplying and Dividing Schemes: Joe and Laura.- The Partitive and Part-Whole Fractional Schemes: Jason and Laura—4th Grade.- The Fractional Composition, Commensurate Fractional, and Common Partitioning Schemes: Jason and Laura—5th Grade.- The Iterative Fractional, Fractional Composition, and Commensurate Fractional Schemes: Jason and Patricia--4th Grade.- The Iterative Fractional, Fractional Composition, and Commensurate Fractional Schemes: Joe and Melissa—5th Grade.- The Construction of the Rational Numbers of Arithmetic: Nathan and Arthur.- Perspectives on the Reorganization Hypothesis.
- ISBN: 978-1-4419-0590-1
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 550
- Fecha Publicación: 01/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés