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Common Core Mathematics Standards and Implementing Digital Technologies

Book Description

Standards in the American education system are traditionally handled on a state-by-state basis, which can differ significantly from one region of the country to the next. Recently, initiatives proposed at the federal level have attempted to bridge this gap. Common Core Mathematics Standards and Implementing Digital Technologies provides a critical discussion of educational standards in mathematics and how communication technologies can support the implementation of common practices across state lines. Leaders in the fields of mathematics education and educational technology will find an examination of the Common Core State Standards in Mathematics through concrete examples, current research, and best practices for teaching all students regardless of grade level or regional location. This book is part of the Advances in Educational Technologies and Instructional Design series collection.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Book Series
  5. Editorial Advisory Board and List of Reviewers
    1. Editorial Advisory Board
  6. Foreword
    1. EDUCATIONAL TECHNOLOGY AND THE COMMON CORE MATHEMATICS STANDARDS
  7. Preface
    1. SECTION 1
    2. SECTION 2
    3. SECTION 3
    4. SECTION 4
  8. Section 1: Frameworks and Conceptual Orientations
    1. Chapter 1: Core Math Tools
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. AFFORDANCES OF FOR CURRICULUM MATERIALS DESIGN AND ENACTMENT
      5. CMT SUPPORTING SPECIFIC CONTENT STANDARDS
      6. CMT WEB PORTAL AND RESOURCES
      7. CHALLENGES AND IMPLICATIONS
      8. CONCLUSION
    2. Chapter 2: Supporting Mathematical Communication through Technology
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. ROLE OF DYNAMIC REPRESENTATIONS IN CLASSROOMS
      5. DISCUSSION AND CONCLUSION
      6. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      7. CONCLUSION
    3. Chapter 3: Implementing Common Core State Standards using Digital Curriculum
      1. ABSTRACT
      2. INTRODUCTION
      3. THE CHALLENGE OF TEACHING IN TODAY’S CLASSROOM
      4. NEW STANDARDS, NEW CURRICULUM, DIFFERENT INSTRUCTIONAL METHOD
      5. TEACHING AND LEARNING COMMON CORE WITH DIGITAL CURRICULUM
      6. COMMON CORE STATE STANDARDS FOR MATHEMATICS EMBEDDED IN DIGITAL CURRICULUM
      7. CONCLUSION
    4. Chapter 4: A Framework for TPACK Action Research
      1. ABSTRACT
      2. INTRODUCTION
      3. THE NEED FOR TEACHERS TO LEARN: THE ROLE OF TECHNOLOGY IN THE COMMON CORE
      4. A MEANS OF LEARNING: CYCLE OF TPACK ACTION RESEARCH
      5. A COLLEAGUE WITH WHOM TO LEARN IT: TEACHER EDUCATORS AS CATALYSTS
      6. TPACK ACTION RESEARCH QUESTIONS
  9. Section 2: Content and Context
    1. Chapter 5: Fostering Mathematical Competence through Technology-Enhanced Interactive Environments
      1. ABSTRACT
      2. INTRODUCTION
      3. GENERATIVE TASKS
      4. CONTEXT
      5. CURRICULUM
      6. TECHNOLOGY
      7. BEHAVIORAL INDICATORS: MATHEMATICAL PRACTICES
      8. PROCEDURE
      9. FINDINGS
      10. GROUP PERFORMANCE: AFTER THREE YEARS OF EXPOSURE
      11. INDIVIDUAL ANALYSIS
      12. DOES THREE YEARS MATTER?
      13. DISCUSSION
      14. APPENDIX
    2. Chapter 6: Using Technology to Engage Students with the Standards for Mathematical Practice
      1. ABSTRACT
      2. INTRODUCTION
      3. THEORETICAL BACKGROUND
      4. USING TOOLS STRATEGICALLY IN A DGS ENVIRONMENT
      5. CHOOSING APPROPRIATE TOOLS
      6. THE ROLE OF INSTRUMENTAL GENESIS
      7. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      8. CONCLUSION
    3. Chapter 7: The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND AND LITERATURE REVIEW
      4. STUDY
      5. DISCUSSIONS, IMPLICATIONS, AND RECOMMENDATIONS
      6. CONCLUSION
    4. Chapter 8: Integrating Digital Technologies for Spatial Reasoning
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. GOOGLE SKETCHUP MODELING PROJECT
      5. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      6. CONCLUSION
    5. Chapter 9: Design and Implementation of Computational Modeling for Learning Mathematical Concepts
      1. ABSTRACT
      2. BACKGROUND
      3. MAIN FOCUS OF THE CHAPTER
      4. IMPLICATIONS FOR PRACTICE AND RESEARCH
      5. CONCLUSION
    6. Chapter 10: PhET Interactive Simulations
      1. ABSTRACT
      2. INTRODUCTION
      3. PROJECT BACKGROUND
      4. PHET SIMULATIONS FOR MATHEMATICS EDUCATION
      5. IMPLEMENTING PHET SIMULATIONS IN CLASS
      6. CONCLUSION
    7. Chapter 11: Do Technologies Support the Implementation of the Common Core State Standards in Mathematics of High School Probability and Statistics?
      1. ABSTRACT
      2. INTRODUCTION
      3. IMPLICATIONS OF THE CCSSM-PS
      4. SURVEY OF TECHNOLOGY FOR STATISTICS AND PROBABILITY INSTRUCTION
      5. BENEFITS OF USING TECHNOLOGY IN CLASSROOM IN WAYS THAT SUPPORT THE CCSSM-PS
      6. CONCLUSION
    8. Chapter 12: Sketchpad®, TinkerPlots®, and Fathom®
      1. ABSTRACT
      2. INTRODUCTION
      3. CCSSM ELEMENTARY CONTENT APPLICATIONS
      4. CCSSM MIDDLE SCHOOL CONTENT APPLICATIONS
      5. CCSSM HIGH SCHOOL CONTENT APPLICATIONS
      6. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      7. CONCLUSION
  10. Section 3: Vignettes and Cases
    1. Chapter 13: Solving Equations is All about Balance
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. USING VIRTUAL MANIPULATIVES TO SOLVE ONE-VARIABLE EQUATIONS
      5. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      6. CONCLUSION
    2. Chapter 14: Two Classroom Portraits Demonstrating the Interplay of Secondary Mathematics Teachers’ TPACK on their Integration of the Mathematical Practices
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. TWO CLASSROOM PORTRAITS
      5. CONNECTIONS AND FUTURE DIRECTIONS
      6. IMPLICATIONS AND CONCLUDING REMARKS
    3. Chapter 15: Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets
      1. ABSTRACT
      2. INTRODUCTION
      3. USING PATTERNS TO EXPLORE ARITHMETIC SEQUENCES
      4. USING PATTERNS TO DEVELOP GEOMETRIC SEQUENCES AND SERIES
      5. STANDARDS FOR MATHEMATICAL PRACTICE
      6. CONCLUSION
    4. Chapter 16: Common Core Standards for Mathematical Practice and TPACK
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. TPACK AND THE COMMON CORE STATE STANDARDS FOR MATHEMATICS
      5. IMPLICATIONS
      6. CONCLUSION
    5. Chapter 17: Supporting the Common Core State Standards in Mathematics through Mathematics Journals
      1. ABSTRACT
      2. INTRODUCTION
      3. PURPOSE OF THE STUDY
      4. THEORETICAL FRAMEWORK AND LITERATURE REVIEW
      5. METHODS
      6. QUALITY CONTROL STRATEGIES
      7. FINDINGS
      8. DISCUSSION
      9. FUTURE DIRECTIONS AND CHALLENGES
      10. APPENDIX 1
    6. Chapter 18: The Impact of Investigations and the Interactive Whiteboard on Students’ Mathematical Practice in Investigations Classrooms
      1. ABSTRACT
      2. INTRODUCTION
      3. INVESTIGATIONS IN NUMBER, DATA, AND SPACE CURRICULUM
      4. INVESTIGATIONS FOR THE INTERACTIVE WHITEBOARD
      5. TEACHERS TRYING OUT THE SOFTWARE
      6. ILLUSTRATIVE MODELING: COMMON CORE MATHEMATICAL PRACTICE
      7. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      8. CONCLUSION
  11. Section 4: Innovative Approaches to Teacher Education and Professional Development
    1. Chapter 19: LessonSketch
      1. ABSTRACT
      2. INTRODUCTION AND BACKGROUND
      3. REPRESENTATIONS OF MATHEMATICAL PRACTICE IN INSTRUCTION
      4. THE LESSONSKETCH ENVIRONMENT AND ITS COMPONENTS
      5. CONCLUSION
    2. Chapter 20: Supporting Teachers’ Instrumental Genesis with Dynamic Mathematical Software
      1. ABSTRACT
      2. INTRODUCTION
      3. PRODUCTIVE DESIGN ELEMENTS FOR INSTRUCTIONAL SPACES
      4. AN EXTENDED DESIGN EXPERIMENT: DESCRIPTION, TRAJECTORY, AND SAMPLE TASKS
      5. IMPLICATIONS, CHALLENGES, FUTURE DIRECTIONS
      6. CONCLUSION
    3. Chapter 21: A Framework for Developing Robust Online Professional Development Materials to Support Teacher Practice under the Common Core
      1. ABSTRACT
      2. PROBLEM STATEMENT
      3. DESIGN FRAMEWORK
      4. APPLYING THE FRAMEWORK
      5. EXTENDING THE FRAMEWORK
      6. CONCLUSION
    4. Chapter 22: The Use of Digital Resources to Support Elementary School Teachers’ Implementation of the Common Core State Standards
      1. ABSTRACT
      2. INTRODUCTION
      3. THEORETICAL FRAMEWORK
      4. MODES OF SUPPORT
      5. IMPLICATIONS AND CHALLENGES
    5. Chapter 23: Digitizing Students’ Voices
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. IMPLEMENTING ASSESSMENT FOR LEARNING PRACTICES USING DIGITAL TECHNOLOGIES
      5. IMPLICATIONS, CHALLENGES, AND FUTURE DIRECTIONS
      6. CONCLUSION
    6. Chapter 24: TPACK Pathways that Facilitate CCSS Implementation for Secondary Mathematics Teacher Candidates
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. MOVING TEACHER CANDIDATES ALONG TPACK PATHWAYS TO SUPPORT CCSS-M IMPLEMENTATION
      5. IMPLICATIONS, CHALLENGES, AND FUTURE DIRECTIONS
      6. CONCLUSION
    7. Chapter 25: Using the iPad to Develop Preservice Teachers’ Understanding of the Common Core State Standards for Mathematical Practice
      1. ABSTRACT
      2. INTRODUCTION
      3. EXAMINING DISCOURSE PRACTICES
      4. USING TECHNOLOGY TO SUPPORT TEACHER DEVELOPMENT
      5. FROM THEORY TO PRACTICE
      6. USING THE IPAD AS AN OBSERVATIONAL TOOL
      7. USE OF THE IPAD IN METHODS COURSES
      8. SUPPORTING MATHEMATICS UNDERSTANDING
      9. USING THE IPAD TO STIMULATE PRODUCTIVE DISCUSSIONS
      10. IMPLICATIONS, CHALLENGES, AND FUTURE PLANS
      11. CONCLUSION
  12. Compilation of References
  13. About the Contributors