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Developing Mathematical Thinking A Guide to Rethinking the Mathematics Classroom

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

09.07.2014

Verlag

Rowman & Littlefield

Seitenzahl

144

Maße (L/B/H)

23,5/15,7/1,3 cm

Gewicht

370 g

Sprache

Englisch

ISBN

978-1-4758-1056-1

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

09.07.2014

Verlag

Rowman & Littlefield

Seitenzahl

144

Maße (L/B/H)

23,5/15,7/1,3 cm

Gewicht

370 g

Sprache

Englisch

ISBN

978-1-4758-1056-1

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Developing Mathematical Thinking
  • Produktbild: Developing Mathematical Thinking

  • Preface
    Introduction
    What Will You Find in This Book

    Chapter 1: An Explanation of the ISA Approach to Teaching and Learning Mathematics
    Introduction
    A Vision of Mathematics in an ISA Classroom
    Guide To Creating a Vision and Four-Year Plan
    ISA Mathematics Rubric
    Indicators of Teacher Instructional Practices That Elicit Student Mathematical Thinking
    Indicators of Student Demonstration of Mathematical Thinking

    Chapter 2: A Guide to Teaching and Learning Mathematics Using the Five Dimensions of the ISA Rubric
    Introduction
    Dimension 1: Problem Solving
    Problem Solving Definition and Overview
    Teaching Idea #1: Choosing the Appropriate Problem
    Teaching Idea #2A: Use Problems with Multiple Strategies
    Teaching Idea #2B: Selecting an Appropriate Strategy
    Teaching Idea #3: Value Process and Answer
    Teaching Idea #4: Answer Student Questions to Foster Understanding
    Teaching Idea #5: Error as a Tool for Inquiry
    Teaching Idea #6: Students Create Their Own Problems
    Dimension II: Reasoning and Proof
    Reasoning and Proof Definitions and Overview
    Teaching Idea #1: Conjecturing
    Teaching Idea #2: Evidence and Proof
    Teaching Idea #3: Metacognition
    Dimension III: Communication
    Communication Definition and Overview
    Teaching Idea #1: Writing in Journals
    Teaching Idea #2: Writing in Problems and Projects
    Teaching Idea #3: Oral Communication
    Dimension IV: Connections
    Connections Definition and OverviewX
    Teaching Idea #1: There Are Common Structures That Bind Together the Multiple Ideas of Mathematics
    Teaching Idea #2: The History of Mathematics Helps Students Make Sense of and Appreciate Mathematics
    Teaching Idea #3: Using Contextual Problems That Are Meaningful to Students
    Dimension V: Representation
    Representation Definition and Overview
    Teaching Idea #1A: Learning to Abstract - Moving from Arithmetic to Algebra
    Teaching Idea #1B: Learning to Abstract - Use Examples of Physical Structures
    Teaching Idea #2: Making Sense of Confusion to Solve Problems
    Teaching Idea #3: Interpreting and Explaining
    Teaching Idea #4A: Mathematical Modeling - Modeling Mathematical Ideas and Real World Situations
    Teaching Idea #4B: Mathematical Modeling - Projects of the World That Use Rich Mathematics

    Chapter 3: Problems, Investigations, Lessons, Projects, and Performance Tasks
    Introduction
    Example 1: Display Dilemma Problem - Using Multiple Strategies / Looking for Patterns
    Example 2: Shakira's Number - Valuing Process
    Example 3: Crossing the River - Valuing Process
    Example 4: Checker Board Problem - Simplifying the Problem
    Example 5: When Can I Divide? - Using Errors as a Tool of Inquiry
    Example 6: Creating a Mathematical Situation: Three Examples - Students Create Their Own Problems
    Example 7: The Game of 27 - Reasoning and Conjecturing
    Example 8: The String Problem - Conjecturing
    Example 9: Congruence and Similarity - Conjecturing and Proof
    Example 10: The Race - Metacognition on Multiple Strategies
    Example 11: Murder Mystery - Evidence and Proof
    Example 12: The Locker Problem - Metacognition
    Example 13: Gaming the Dice - Writing in Problems
    Example 14: Does Penelope Crash Into Mars? - Problems Are Meaningful to Students
    Example 15: Consecutive Sums Problem - Patterns and Conjecturing
    Example 16: Activity to Lead to Definition and Multiple Representations of a Function - Structures in Mathematics
    Example 17: The Pythagorean Triplets - The History of Mathematics
    Example 18: Laws of Exponents - Moving From Arithmetic to Algebra
    Example 19: Working with Variables - Learning to Abstract: Moving from Arithmetic to Algebra
    Example 20: Models of the Seagram Building - Use of Physical Structures
    Example 21: How Tall Is Your School Building? - Use of Physical Structures
    Example 22: Model Suspension Bridge Project - Modeling Real World Situations
    Example 23: Shoe Size Problem - Modeling Real World Situations
    Example 24: The Peg Game - Using Games to Understand Mathematics
    Example 25: Concentration of Medication in a Patient's Blood Over Time - Modeling Using Real World Data
    Example 26: Marcella's Bagels - Working Backwards
    Example 27: What is normal? - Modeling Mathematical Ideas and Real World Situations
    Example 28: Can You Build the Most Efficient Container? - Mathematical Modeling
    Example 29: Salary Choice - Mathematical Modeling
    Example 30: Border Problem - Learning to Abstract: Moving from Arithmetic to Algebra
    Example 31: The Magical Exterior Angles - Encouraging the Use of Evidence and Proof in Daily Problem Solving
    Example 32: Creating a Fair Game - Projects of the World That Use Rich Mathematics

    Chapter 4: Various Guides for Teachers
    Introduction
    School Mathematics: A Self-Assessment
    What Does An Inquiry Process Look Like In Mathematics?
    How to Write an Inquiry Lesson
    Questions to Think About When Planning an Inquiry-Based Common Core Aligned Unit
    List of Questions to Think About When Writing a Mathematical Performance Task
    Guide to Writing an Inquiry Lesson
    Inquiry-Based Lesson Planning Template
    Big Ideas in Algebra
    Big Ideas in Geometry
    Big Ideas in Probability and Statistics
    Questions for Students to Ask Themselves When Solving a Problem
    An Inquiry Approach to Look at Student Work
    An Inquiry Approach to Look at a Teacher-Created Task, Activity, or Lesson
    Teacher's Perceptions Continuum
    Student's Perceptions Continuum
    School Mathematics: A Self-Assessment
    References