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Merging of the theory with mathematical teaching and learning practices
Two chapters that illustrate ways to study mathematical thinking and learning over time
Specific modeling of major theoretical constructs via examples of mathematics content
Rhetorical Ways of Thinking focuses on how the co-construction of learning models the interpretation of a mathematical situation. It is a comprehensive examination of the role of sociocultural-historical theory developed by Vygotsky. This book puts forward the supposition that the major assumptions of sociocultural-historic theory are essential to understanding the theory’s application to mathematical pedagogy, which explores issues relevant to learning and teaching mathematics-in-context, thus providing a valuable practical tool for general mathematics education research. The most important goal, then, is to exemplify the merging of the theory with practice and the subsequent applications to mathematics teaching and learning. This monograph contains five chapters, including a primer to Vygotsky’s sociocultural historic theory, two comprehensive empirical studies examining: prospective teachers’ perception of mathematics teaching and learning and the practice of scaffolded instruction to assist practicing teachers in developing their understanding of pedagogical content knowledge. Finally, the book concludes with a contextualization of the theory, linking it to best practices in the classroom.
Content Level »Research
Keywords »Mathematics content knowledge - Mathematics teacher education - Scaffolding - Sociocultural historic theory - Vygotskian theory - Vygotsky
Preface.- Chapter 1 Introduction.- Why Rhetorical Thinking.- Overview of Chapters.- Chapter 2 Vygotsky’s Sociocultural Historic Theory, A Primer.- INTRODUCTION.- TOOLS OF HUMAN INTENSIFICATION.- Mediation through Signs.- THE DEVELOPMENT OF HIGHER PSYCHOLOGICAL FUNCTIONS.- Distinguishing Between Lower and Higher Functioning.- THE ROLE OF THE ZONE OF PROXIMAL DEVELOPMENT.- The Complex Nature of the Zone of Proximal Development.- Learning Potential, Performance, and Context.- Intersubjective Learning.- CONCEPT DEVELOPMENT IN THINKING.- Spontaneous and Scientific Concepts.- THE RELATIONSHIP BETWEEN THINKING AND LANGUAGE.- CONCLUSION. Chapter 3 Images and Drawings: A Study of Prospective Teachers' Perceptions of Teaching and Learning Mathematics.- INTRODUCTION.- AN EMERGING FRAMEWORK METHODOLOGY.- Coding Drawings.- Analysis of Focus Group Transcripts.- RESULTS.- The Changing Roles of Teachers.- Student Affect and Pedagogy.- Trends in Mathematical Representations and Content.- Changes in Room Structure.- DISCUSSION OF RESULTS.- CONCLUSION.- Chapter 4 Improving Teachers’ Mathematical Content Knowledge through Scaffolded Instruction.- INTRODUCTION.- THEORETICAL FRAMEWORK AND RELEVANT RESEARCH.- Explanation of the Framework.- METHODOLOGY.- Context and Participants.- Data Sources and Procedures.- Data Analysis.- FINDINGS.- Content Knowledge: Pretest and Posttest.- Presurvey and Postsurvey Results.- Talk and Scaffolded-Interactions.- Teacher-learner Talk and the More Knowledgeable Other.- DISCUSSION OF FINDINGS.- Connecting Learning to the Field of Social Interaction.- The Importance of Language and Action.- CONCLUDING COMMENTS.- Chapter 5 Closing Thoughts and Implications.- Teacher-generated Drawings as Tools of Human Development.- Achieving Intersubjectivity through Collaborative Learning.- Index.