Taking Shape

Joan Moss is an Associate Professor in the Department of Applied Psychology and Human Development at the Institute of Child Study at OISE/UT. A former elementary school teacher, her research has focused on the design of developmentally based curricula highlighting areas of mathematics that are traditionally challenging for students. Her research on early algebra has appeared in numerous international publications. Since 2011, Joan has been a co-Principal Investigator of the Math for Young Children (M4YC) project, which supports the teaching and learning of spatial reasoning in Early Years classrooms. Most recently, she collaborated with the Robertson Program for Inquiry-Based Teaching in Math and Science to expand the M4YC initiative to include collaborations in four First Nations communities and with the Rainy River District School Board. Joan has won many honours and awards, including the award for Distinguished Contributions to Teaching.  Catherine D. Bruce is an Associate Professor at the Trent University School of Education and Professional Learning. Catherine is a co-Principal Investigator of the Math for Young Children (M4YC) project. She won a SSHRC Award in 2013 to continue this research into early mathematics and young children’s spatial reasoning. A former teacher, Catherine has been studying teaching and learning for 25 years. She teaches mathematics methods courses at Trent where she brings her passion for mathematics teaching and learning to teacher candidates. In 2012—2013, Catherine was honoured to receive the prestigious Ontario Confederation of University Faculty Associations (OCUFA) teaching award. Additionally, she received the 2015 International Eduardo Flores Leadership Award for her contributions to action research locally, nationally, and internationally. Key areas of research include teacher and student efficacy, the effectiveness of alternative models of professional learning for teachers, the use of technology in the mathematics classroom, as well as teaching and learning in the difficult-to-learn areas of fractions and algebra. Her awesome family of boys keeps her on her toes. Bev Caswell is the Director of the Robertson Program for Inquiry-Based Teaching in Mathematics and Science at the Dr. Eric Jackman Institute of Child Study (Ontario Institute for Studies in Education at the University of Toronto). She works collaboratively with educators to design participatory learning environments that invite students to engage with ideas and develop a deeper understanding of mathematics concepts. Bev completed her doctoral research focusing on equity in mathematics. She is dedicated to working with students typically underserved by the educational system. Bev has ten years’ experience as an elementary school classroom teacher and fifteen years’ experience in pre-service and in-service teacher education. She is married and is the mother of four dynamic individuals. Tara Flynn is an educator, author, and editor who has worked with Dr. Cathy Bruce in the fascinating world of mathematics education research since 2007. As Project Manager and Research Officer, Tara has worked with countless dedicated and innovative educators, and has been an integral member of the Math for Young Children (M4YC) team since the project’s inception. She has co-authored several publications on young children’s spatial reasoning and has presented widely on this topic. As an editor, Tara cut her teeth at Alternatives Journal, and more recently has edited numerous teacher resources in mathematics education. She is the awestruck mother of a 20-year-old son. Tara has spent the past nine years trying to explain to her family what she does for a living, and is really hoping that this book will help to answer that question. Zachary Hawes is a Ph.D. candidate in th

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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