Waubonsee Community College

Making the Connection, Research and Teaching in Undergraduate Mathematics Education, edited by Marilyn P. Carlson, Chris Rasmussen

eng

index present

non fiction

Making the Connection

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775429058

edited by Marilyn P. Carlson, Chris Rasmussen

Notes, v. 73

Research and Teaching in Undergraduate Mathematics Education

""Cover ""; ""copyright page ""; ""Title page ""; ""Preface""; ""Contents""; ""Part I Student Thinking""; ""a. Foundations for Beginning Calculus""; ""1 On Developing a Rich Conception of Variable""; ""Introduction""; ""Analysis of Problem 1""; ""Analysis of Problem 2""; ""Analysis of Problem 3""; ""Research Literature About Students� Conceptions of Variable""; ""Superficial Conceptions""; ""Varying Uses of Variable""; ""Parameters""; ""Changing Quantity, Dynamic versus Static Imagery, and Joint Variation""; ""Possible Explanations""; ""Historical Development: Shifts Over The Ages""""Calculational Attitude""""Lack of Rich Curricular Material""; ""Interventions and Promising Results""; ""A Call To Action""; ""Practical Suggestions""; ""Concluding Remarks""; ""References""; ""2 Rethinking Change""; ""Perspectives on Models""; ""Rates of Change in Realistic Contexts""; ""Making Sense of Realistic Data""; ""Making Realistic Sense of Graphs""; ""Connecting Teaching and Research""; ""References""; ""3 Foundational Reasoning Abilities that Promote Coherence in Students� Function Understanding""; ""Why Is The Function Concept So Important?""""Why is the Function Concept So Difficult for Students to Understand?""""Dynamic Conceptualizations Needed for Understanding and Using Functions""; ""The Action and Process Views of Functions � A More Formal Examination""; ""Fostering a Process View of Functions""; ""Building on the Process View of Function: Applying Covariational Reasoning""; ""The Covariation Framework""; ""Engaging Covariational Reasoning Through Analysis Of Function Situations""; ""Extending Ideas of Covariation To Higher Dimensions""; ""Concluding Remarks""; ""References""""4 The Concept of Accumulation in Calculus""""Composition of a Well-Structured Understanding of Accumulation Functions""; ""Accumulation Functions""; ""Riemann Sums""; ""Students� Difficulties in Understanding Accumulation Mathematically""; ""Promising Approaches In Helping Students Conceptualize Accumulation Functions""; ""Students� Understandings of Accumulation Functions within the Calculus as a Whole""; ""Connections with Other Ideas""; ""Conclusion""; ""References""; ""b. Infinity, Limit, and Divisibility""; ""5 Developing Notions of Infinity""; ""Comparing Infinite Sets""""Limits of Sequences""""Infinite Iterative Processes""; ""Conclusion""; ""References""; ""6 Layers of Abstraction: Theory and Design for theInstruction of Limit Concepts""; ""The Nature and Process of Abstraction""; ""Goals for Teaching Limits""; ""A Design Approach to Limit Instruction""; ""Summary""; ""References""; ""7 Divisibility and Transparency of Number Representations""; ""Snapshots from Research""; ""Example 1""; ""Example 2""; ""Example 3""; ""Example 4""; ""Example 5""; ""Reflecting On Examples""; ""Formalization of “Seeing�""; ""More Examples from Research""; ""Example 6""