Approaches to algebra : perspectives for research and teaching
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory.
Print Book, English, 1996
Kluwer, Dordrecht, 1996
Aufsatzsammlung
XV, 345 Seiten : Illustrationen, Diagramme.
9780792341680, 9780792341451, 0792341686, 0792341457
263636944
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. AFunctional 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.