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Young Mathematicians at Work : Constructing Algebra.

By: Contributor(s): Material type: TextPublisher: Portsmouth : Heinemann, 2010Copyright date: ©2010Edition: 1st edDescription: 1 online resource (220 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780325030623
Subject(s): Genre/Form: DDC classification:
  • 372.7
Online resources:
Contents:
Intro -- Table of Contents -- Acknowledgments -- Preface -- About This Book -- Chapter 1: Algebra: Structures or Structuring? -- Teaching and Learning in the Algebra Classroom -- What Is Revealed -- Back to the Workshop -- Visiting a Fifth-Grade Classroom -- What Is Revealed -- Summing Up -- Chapter 2: The Landscape of Learning -- Comparing Curriculum Frameworks -- The Algebra Landscape: Describing the Journey -- Dense and Sparse Structures -- Developing Dense Structures -- Landmarks on the Landscape -- Strategies -- Big Ideas -- Models as Tools for Thought -- Walking the Edge -- Summing Up -- Chapter 3: Early Structuring of the Number System -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- Emerging Multiplicative Structuring -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Further Structuring: Evens, "Threevens," and Place Value -- Summing Up -- Chapter 4: Continuing the Journey: The Role of Contexts and Models -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- The Role of Context -- Back to the Classroom -- What Is Revealed -- The Role of Context -- The Importance of Models -- Back to the Classroom -- What Is Revealed -- What Models Are Important for Multiplicative Thinking? -- More Examples: Linear Combinations -- Summing Up -- Chapter 5: Equivalence on the Horizon -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Back to the Classroom -- Summing Up -- Chapter 6: Variation versus Variables -- A Brief History of the Development of Algebra -- In the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- The Importance of Representation -- The Importance of Redrawing -- Back to the Classroom -- What Is Revealed -- Summing Up.
Chapter 7: Further Horizons: Integers and Equivalence -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Teaching and Learning in a Professional Development Seminar -- What Is Revealed -- Back to the Professional Development Seminar -- What Is Revealed -- Summing Up -- Chapter 8: Comparing Quantities and Relations -- Teaching and Learning in the Classroom: Midpoint Problems -- What Is Revealed -- Back to the Classroom: Benches and Fences -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Back to the Classroom: The Combination Chart -- What Is Revealed -- Back to the Classroom: Comparing Quantities and Systems of Equations -- Special Note on Symbolizing -- The Combination Chart and Systems of Equations -- Summing Up -- Chapter 9: Developing Algebraic Strategies with Minilessons -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Journeying the Landscape -- Choosing the Numbers -- Journeying the Landscape -- Choosing the Model -- Choosing a Context -- Teaching and Learning in Another Classroom -- Operating on Expressions -- Summing Up -- Chapter 10: Proof -- A Bit of History -- Children and Proof: Writing in Mathematics versus Development of Proof -- Teaching and Learning in the Classroom -- What Is Revealed -- Developing a System of Shared Principles and Rules of Deduction -- Gallery Walks, Asking Questions, and Revisiting Thinking -- Back to the Classroom -- What Is Revealed -- Generalizing from Specific Cases to All Cases -- Back to the Classroom -- What Is Revealed -- Summing Up -- References -- Index.
Summary: In Constructing Algebra, Catherine Twomey Fosnot and Bill Jacob help teachers recognize, support, and celebrate their students{u0092} capacity to structure their worlds algebraically. They identify for teachers the models, contexts, and landmarks that facilitate algebraic thinking in young students, supporting children as they construct mathematical strategies and big ideas, creating realistic contexts and representational models that develop children{u0092}s capacity to mathematize their world, and building a collaborative community of mathematical thinkers engaged in inquiry.
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Intro -- Table of Contents -- Acknowledgments -- Preface -- About This Book -- Chapter 1: Algebra: Structures or Structuring? -- Teaching and Learning in the Algebra Classroom -- What Is Revealed -- Back to the Workshop -- Visiting a Fifth-Grade Classroom -- What Is Revealed -- Summing Up -- Chapter 2: The Landscape of Learning -- Comparing Curriculum Frameworks -- The Algebra Landscape: Describing the Journey -- Dense and Sparse Structures -- Developing Dense Structures -- Landmarks on the Landscape -- Strategies -- Big Ideas -- Models as Tools for Thought -- Walking the Edge -- Summing Up -- Chapter 3: Early Structuring of the Number System -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- Emerging Multiplicative Structuring -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Further Structuring: Evens, "Threevens," and Place Value -- Summing Up -- Chapter 4: Continuing the Journey: The Role of Contexts and Models -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- The Role of Context -- Back to the Classroom -- What Is Revealed -- The Role of Context -- The Importance of Models -- Back to the Classroom -- What Is Revealed -- What Models Are Important for Multiplicative Thinking? -- More Examples: Linear Combinations -- Summing Up -- Chapter 5: Equivalence on the Horizon -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Back to the Classroom -- Summing Up -- Chapter 6: Variation versus Variables -- A Brief History of the Development of Algebra -- In the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- The Importance of Representation -- The Importance of Redrawing -- Back to the Classroom -- What Is Revealed -- Summing Up.

Chapter 7: Further Horizons: Integers and Equivalence -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Teaching and Learning in a Professional Development Seminar -- What Is Revealed -- Back to the Professional Development Seminar -- What Is Revealed -- Summing Up -- Chapter 8: Comparing Quantities and Relations -- Teaching and Learning in the Classroom: Midpoint Problems -- What Is Revealed -- Back to the Classroom: Benches and Fences -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Back to the Classroom: The Combination Chart -- What Is Revealed -- Back to the Classroom: Comparing Quantities and Systems of Equations -- Special Note on Symbolizing -- The Combination Chart and Systems of Equations -- Summing Up -- Chapter 9: Developing Algebraic Strategies with Minilessons -- Teaching and Learning in the Classroom -- What Is Revealed -- Back to the Classroom -- What Is Revealed -- Journeying the Landscape -- Choosing the Numbers -- Journeying the Landscape -- Choosing the Model -- Choosing a Context -- Teaching and Learning in Another Classroom -- Operating on Expressions -- Summing Up -- Chapter 10: Proof -- A Bit of History -- Children and Proof: Writing in Mathematics versus Development of Proof -- Teaching and Learning in the Classroom -- What Is Revealed -- Developing a System of Shared Principles and Rules of Deduction -- Gallery Walks, Asking Questions, and Revisiting Thinking -- Back to the Classroom -- What Is Revealed -- Generalizing from Specific Cases to All Cases -- Back to the Classroom -- What Is Revealed -- Summing Up -- References -- Index.

In Constructing Algebra, Catherine Twomey Fosnot and Bill Jacob help teachers recognize, support, and celebrate their students{u0092} capacity to structure their worlds algebraically. They identify for teachers the models, contexts, and landmarks that facilitate algebraic thinking in young students, supporting children as they construct mathematical strategies and big ideas, creating realistic contexts and representational models that develop children{u0092}s capacity to mathematize their world, and building a collaborative community of mathematical thinkers engaged in inquiry.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2025. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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