Taking Shape: Activities to Develop Geometric and Spatial Thinking : 9780134153490

Taking Shape: Activities to Develop Geometric and Spatial Thinking

Published by
Pearson Canada
Available on demand
Title type

Research shows that children with good spatial skills perform better in mathematics overall. This research-based resource is a unique blend of professional learning and classroom activities. It includes:

  • 32 field-tested and research-based activities designed to appeal to young children
  • Guided lesson plans, including 15 videos, that serve as models for best practice in instruction
  • Tips on observing, questioning, and assessing young children’s geometric and spatial thinking
  • Free access to website with videos, curriculum correlations, line masters, and observation guides 
Table of contents


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

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) 
Chapter D: Location, Orientation, and Mapping

What It Is
A Focus on Coding
Why We Engage Children in These Tasks
Chapter Overview
  • Guided Lesson: Introductory Barrier Game
  • Secret Shape Code
  • What Did You Make?
  • Exploring Coordinates
  • Pathway Moves
  • Paper Pathways
  • Secret Code Game
  • Pathway Coding Game
Chapter E: Perspective Taking

What It Is
Why Engage Children in These Tasks?
Overview of the Chapter
  • Guided Lesson: Mother Bird and Her Babies
  • Top-Front-Side
  • What Do You See?
  • The Shoebox Window
  • Build It, Photograph It, Make It
  • See It, Remember It, Build It!
  • Building Blueprints
  • Crazy Creatures
Author biography
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 the Numerical Cognition Laboratory at the University of Western Ontario. Prior to this, he completed his M.A. and teacher training at the University of Toronto’s Dr. Eric Jackman Institute of Child Study. Not wanting to leave the Institute, and having developed a keen interest in how children learn mathematics, Zack stayed on to work as a research officer for four years. His past and current research is broadly focused on understanding the development of mathematical thinking and ways in which to improve such learning. More recently, he is interested in studying the relationship between spatial and numerical cognition, with the ultimate goal of using this information to leverage classroom instruction. Other interests include painting, traveling, and playing basketball.