Approaches to Algebra : Perspectives for Research and Teaching /

This book aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. Four different perspectives, each related to a corresponding conception of...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bernarz, Nadine
Otros Autores: Kieran, Carolyn, Lee, Lesley
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Dordrecht : Springer Netherlands, 1996.
Colección:Mathematics education library ; 18.
Temas:
Education.
Mathematics.
Mathématiques.
mathematics.
applied mathematics.
Education
Mathematics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Approaches to Algebra: Perspectives for Research and Teaching
  • I. Historical Perspectives in the Development of Algebra
  • 2. From Euclid to Descartes: Algebra and its Relation to Geometry
  • 3. The Roles of Geometry and Arithmetic in the Development of Algebra: Historical Remarks from a Didactic Perspective
  • 4. The Role of Problems and Problem Solving in the Development of Algebra
  • II. A Generalization Perspective on the Introduction of Algebra
  • 5. Expressing Generality and Roots of Algebra
  • 6. An Initiation into Algebraic Culture through Generalization Activities
  • 7. Some Reflections on Teaching Algebra through Generalization
  • III. A Problem-Solving Perspective on the Introduction of Algebra
  • 8. Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic
  • 9. Developing Algebraic Aspects of Problem Solving within a Spreadsheet Environment
  • 10. Rough or Smooth? The Transition from Arithmetic to Algebra in Problem Solving
  • 11. Algebraic thought and the Role of a Manipulable Symbolic Language
  • 12. Placement and Function of Problems in Algebraic Treatises from Diophantus to Viète
  • 13. Problem-Solving Approaches to Algebra: Two Aspects
  • 14. 'When is a Problem?': Questions from History and Classroom Practice in Algebra
  • IV. A Modeling Perspective on the Introduction of Algebra
  • 15. Mathematical Narratives, Modeling, and Algebra
  • 16. Reflections on Mathematical Modeling and the Redefinition of Algebraic Thinking
  • 17. Modeling and the Initiation into Algebra
  • V.A Functional Perspective on the Introduction of Algebra
  • 18. A Technology-Intensive Functional Approach to the Emergence of Algebraic Thinking
  • 19. Introducing Algebra by Means of a Technology-Supported, Functional Approach
  • 20. A Functional Approach to Algebra: Two Issues that Emerge
  • VI. Synthesis and Directions for Future Research
  • 21. Backwards and Forwards: Reflections on Different Approaches to Algebra
  • References
  • Author Affiliations.

Ejemplares similares