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Approaches to algebra : perspectives for research and teaching / / edited by N. Bednarz, C. Kieran, L. Lee
| Approaches to algebra : perspectives for research and teaching / / edited by N. Bednarz, C. Kieran, L. Lee |
| Edizione | [1st ed. 1996.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (xv, 348 pages) |
| Disciplina | 370 |
| Collana | Mathematics Education Library |
| Soggetto topico | Mathematics - Study and teaching |
| ISBN | 94-009-1732-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910789204003321 |
| Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Approaches to algebra : perspectives for research and teaching / / edited by N. Bednarz, C. Kieran, L. Lee
| Approaches to algebra : perspectives for research and teaching / / edited by N. Bednarz, C. Kieran, L. Lee |
| Edizione | [1st ed. 1996.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (xv, 348 pages) |
| Disciplina | 370 |
| Collana | Mathematics Education Library |
| Soggetto topico | Mathematics - Study and teaching |
| ISBN | 94-009-1732-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910828274503321 |
| Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds : The Global Evolution of an Emerging Field of Research and Practice / / edited by Carolyn Kieran
| Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds : The Global Evolution of an Emerging Field of Research and Practice / / edited by Carolyn Kieran |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XIII, 443 p. 139 illus., 9 illus. in color.) |
| Disciplina | 370 |
| Collana | ICME-13 Monographs |
| Soggetto topico |
Mathematics - Study and teaching
Learning, Psychology of Teachers - Training of Mathematics Education Instructional Psychology Teaching and Teacher Education |
| ISBN | 3-319-68351-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Part I Theoretical Perspectives for Developing Early Algebraic Thinking -- The Emergence of Symbolic Algebraic Thinking in Primary School -- 2 Implementing a Framework for Early Algebra -- 3 New Words and Concepts for Early Algebra Teaching: Sharing with Teachers Epistemological Issues in Early Algebra to Develop Students’ Early Algebraic Thinking -- 4 Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking -- 5 Cultivating Early Algebraic Thinking -- Part II Learning to Think Algebraically in Primary and Lower Middle School -- 6 Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective -- 7 Function Tasks, Input, Output, and The Predictive Rule: How some Singapore Primary Children Construct the Rule -- 8 Algebraic Understanding of Equalities in Primary Classes -- 9 Observations of Structure within Shape Patterns -- 10 Generalizing Fractional Structures: A Critical Precursor To Algebraic Thinking -- 11 First Encounter with Variables by First and Third Grade Spanish Students -- Part III Teaching for the Development of Early Algebraic Thinking -- 12 Making Implicit Algebraic Thinking Explicit: Exploiting National Characteristics of German Approaches -- 13 Early Algebra as Analysis of Structure: A Focus on Operations -- 14 How Early Is too Early for Thinking Algebraically? -- 15 Cycles of Generalizing Activities in the Classroom -- 16 Scaffolding Teacher Practice to Develop Early Algebraic Reasoning -- 17 Preservice Teachers’ Knowledge to Teach Functional Thinking -- Conclusions and Looking Ahead. |
| Record Nr. | UNINA-9910299506303321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||