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Enhancing Mathematics Understanding through Visualization

Book Description

Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a student’s understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Editorial Advisory Board and List of Reviewers
    1. Editorial Advisory Board
  5. Foreword
  6. Preface
    1. INTRODUCTION
    2. OBJECTIVE OF THE BOOK AND ITS CONTENTS
  7. Acknowledgment
  8. Section 1: The Theory
    1. Chapter 1: Technology and Differential Equations
      1. ABSTRACT
      2. THE STANDARD CURRICULUM
      3. A MORE APPROPRIATE APPROACH
      4. THE FORCED DAMPED PENDULUM
    2. Chapter 2: Sometimes Less is More
      1. ABSTRACT
      2. INTRODUCTION
      3. SUPPORTING AND DEFINING LITERATURE
      4. CLASSROOM TEBOS: EXAMPLES OF THE “LESS IS MORE” TECHNOLOGY
      5. CONCLUSION
    3. Chapter 3: “Click, Drag, Think!”
      1. ABSTRACT
      2. OVERVIEW
      3. THEORETICAL BACKGROUND
      4. ONGOING RESEARCH ON HEURISTIC LITERACY
      5. THE CONCEPT OF HEURISTIC RECONSTRUCTION
      6. AN ADVANCED CASE STUDY
      7. CONCLUSION
  9. Section 2: The Practice
    1. Chapter 4: Dynamical Mathematical Software
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. GRAPHING POLAR FUNCTIONS
      5. PHASE PORTRAITS FOR LINEAR SYSTEMS
      6. BEYOND THE TRADITIONAL CURRICULUM: LINEAR ITERATIVE SYSTEMS
      7. CONCLUSION
    2. Chapter 5: Nonlinear is Essential, Linearization is Not Enough, Visualization is Absolutely Necessary
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. NONLINEARITY
      5. CHAOTIC BEHAVIORS
      6. HIGHER DIMENSIONAL SYSTEMS
      7. SOLUTIONS AND RECOMMENDATIONS
      8. FINAL REMARKS
    3. Chapter 6: Vectors and Differential Equations
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. CONCLUSION
    4. Chapter 7: Interactive Applets in Calculus and Engineering Courses
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. CALCULUS MATHLETS FOR SELF-LEARNERS
      5. AEROSPACE ENGINEERING MATHLETS
      6. FUTURE WORK
      7. CONCLUSION
    5. Chapter 8: Applets for Mathematical Learning
      1. ABSTRACT
      2. INTRODUCTION
      3. CONCLUSION
    6. Chapter 9: Dynamical Software and the Derivative Concept
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE DERIVATIVE CONCEPT
      5. CONCLUSION
    7. Chapter 10: Supporting the Development of College-Level Students’ Conceptions of Statistical Inference
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. CASE DESCRIPTION
      5. FUTURE RESEARCH DIRECTIONS
      6. CONCLUSION
  10. Section 3: Outside the Norm
    1. Chapter 11: Coping with Infinity
      1. ABSTRACT
      2. INTRODUCTION
      3. CONCLUSION
      4. FUTURE RESEARCH DIRECTIONS
    2. Chapter 12: String Art and Linear Iterative Systems
      1. ABSTRACT
      2. INTRODUCTION
      3. LINEAR SYSTEMS OF ITERATIVE EQUATIONS AND STRING ART
      4. FURTHER EXAMPLES OF STRING ART DESIGNS
  11. Related References
  12. Compilation of References
  13. About the Contributors