Approaches to Algebra : Perspectives for Research and Teaching.

APPROACHES TO ALGEBRA -- Editor's page -- Copyright -- ACKNOWLEDGMENTS -- INTRODUCTION -- CHAPTER 1 APPROACHES TO ALGEBRA: PERSPECTIVES FOR RESEARCH AND TEACHING -- PART I HISTORICAL PERSPECTIVES IN THE DEVELOPMENT OF ALGEBRA -- CHAPTER 2 FROM EUCLID TO DESCARTES: ALGEBRA AND ITS RELATION TO GEOMETRY -- CHAP1ER 3 THE ROLES OF GEOMETRY AND ARITHMETIC IN THE DEVELOPMENT OF ALGEBRA: HISTORICAL REMARKS FROM A DIDACTIC PERSPECTIVE -- CHAPTER 4 THE ROLE OF PROBLEMS AND PROBLEM SOLVING IN THE DEVELOPMENT OF ALGEBRA -- PART II A GENERALIZATION PERSPECTIVE ON THE INTRODUCTION OF ALGEBRA -- CHAPTER 5 EXPRESSING GENERALITY AND ROOTS OF ALGEBRA -- CHAPTER 6 AN INITIATION INTO ALGEBRAIC CULTURE THROUGH GENERALIZATION ACTIVITIES -- CHAPTER 7 SOME REFLECTIONS ON TEACHING ALGEBRA THROUGH GENERALIZATION -- PART III A PROBLEM-SOLVING PERSPECTIVE ON THE INTRODUCTION OF ALGEBRA -- CHAPTER 8 EMERGENCE AND DEVELOPMENT OF ALGEBRA AS A PROBLEM-SOLVING TOOL: CONTINUITIES AND DISCONTINUITIES WITH ARITHMETIC -- CHAPTER 9 DEVELOPING ALGEBRAIC ASPECTS OF PROBLEM SOLVING WITHIN A SPREADSHEET ENVIRONMENT -- CHAPTER 10 ROUGH OR SMOOTH? THE TRANSITION FROM ARITHMETIC TO ALGEBRA IN PROBLEM SOLVING -- CHAPTER 11 ALGEBRAIC THOUGHT AND THE ROLE OF A MANIPULABLE SYMBOLIC LANGUAGE -- CHAPTER 12 PLACEMENT AND FUNCTION OF PROBLEMS IN ALGEBRAIC TREATISES FROM DIOPHANTUS TO VIÈTE -- CHAPTER 13 PROBLEM-SOLVING APPROACHES TO ALGEBRA: TWO ASPECTS -- CHAPTER 14 "WHEN IS A PROBLEM?": QUESTIONS FROM HISTORY AND CLASSROOM PRACTICE IN ALGEBRA -- PART IV A MODELING PERSPECTIVE ON THE INTRODUCTION OF ALGEBRA -- CHAPTER 15 MATHEMATICAL NARRATIVES, MODELING, AND ALGEBRA 1 -- CHAPTER 16 REFLECTIONS ON MATHEMATICAL MODELING AND THE REDEFINITION OF ALGEBRAIC THINKING -- CHAPTER 17 MODELING AND TIIE INITIATION INTO ALGEBRA -- PART V A FUNCTIONAL PERSPECTIVE ON THE INTRODUCTION OF ALGEBRA.

CHAPTER 18 A TECHNOLOGY-INTENSIVE FUNCTIONAL APPROACH TO THE EMERGENCE OF ALGEBRAIC THINKING -- CHAPTER 19 INIRODUCING ALGEBRA BY MEANS OF A TECHNOLOGY-SUPPORTED, FUNCTIONAL APPROACH -- CHAPTER 20 A FUNCTIONAL APPROACH TO ALGEBRA: TWO ISSUES THAT EMERGE -- PART VI SYNTHESIS AND DIRECTIONS FOR FUTURE RESEARCH -- CHAPTER 21 BACKWARDS AND FORWARDS: REFLECTIONS ON DIFFERENT APPROACHES TO ALGEBRA -- REFERENCES -- AUTHOR AFFILIATIONS.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.