Preface
PART 1
I. Why Teach Math in the Early Years?
- The Predictive Power of Early Mathematics
- Socioeconomic Factors and Equity
- Recent Research on Mathematics Readiness of Young Children
- The What and Why of Spatial Reasoning
- Spatial Reasoning in Our Daily Lives
II. What Makes This Resource Different from Others?
- A Different Approach to Geometry
- Reflection Symmetry
- Composition and Decomposition of 2D and 3D Figures
- Perspective Taking
- An Emphasis on Playful Pedagogy
- Opportunities and Limitations of Play-Based Learning
- Most Effective Pedagogy: Blending of Play and Instruction Approaches
- Story of a Research Study: Comparing Free Play, Direct Instruction and Guided Play
- The Math for Young Children Research Program
- What Does Playful Pedagogy Look Like in M4YC?
- M4YC Case Studies #1, #2
III. A Closer Look at Spatial Reasoning Concepts and Processes
- Visualization in Early Years Mathematics
- Mental Rotation in Early Years Mathematics
- Visual-Spatial Working Memory
- Information Processing in Early Years Mathematics
- Spatial Language in Early Years Mathematics
- Gestures in Early Years Mathematics
IV. How to Use this Resource
- How Is the Book Set Up?
- Math and Spatial Reasoning Connections
- Math Language in Focus
- Lesson Structure
- Key Questions
- What to Look For, What to Listen For: Ongoing Assessment of Student Learning
- Supporting Learners
- Assessing for Reporting
- Extensions/Variations
- From Our Research Classrooms - Implementation
- Where to Begin?
- Ways to Use the Resource Throughout the Year
- Connecting to Other Math Strands and Curriculum Areas
- Observing Student Thinking: JK–Grade 2 Assessment Suggestions
- Assessment Components in the Guided Lessons, Quick Challenge, and Exploratory Tasks
- One-to-One Interview Assessment Task
PART II
Chapter A: Reflection Symmetry
What It Is
Why We Engage Children in These Tasks
Chapter Overview
- Guided Lesson: Let’s Learn About Symmetry
- Symmetry Pattern Block Centre
- Double Pentomino Symmetry Games
- Symmetry on Grids: Integrating Location and Number
- Grid Symmetry Pair Game
- Finding the Symmetry of Pentomino Figures
- Symmetry of the Alphabet Letters
- Mental Symmetry Folding with the Hole Punch
- Symmetry Card Games
Chapter B: Composing, Decomposing, and Transforming 2D Shapes
What It Is
Why We Engage Children in These Tasks
Chapter Overview
- Guided Lesson: Finding the Magic (Pentomino) Keys
- See It, Build It, Check It (Pattern Blocks)
- Make a Hexagon Card Game
- The Shape Composer
- Can You Draw This?
- See It, Build It, Check It (Tangrams)
- Can You Cover It?
- The Square Mover
- Triangle Creations!
Chapter C: Composing, Decomposing, and Transforming 3D Shapes
What It Is
Why We Engage Children in These Tasks
Chapter Overview
- Guided Lesson: The Cube Challenge—Discovering 3D Congruence
- See It, Build It, Check It! (Cubes)
- Build It in Your Mind
- 2D–3D Building
- Box or Not?
- Cross-Section Challenge (or 3D Puzzle Challenge)
- Building Rules! (3-Layer Version)
- Building Rules! (Extension Version)
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