I recently read the book Taking Shape: Activities to Develop Geometric and Spatial Thinking (2016). This book is focused on developing spatial reasoning for P-2 students and was written by Joan Moss, Cathy Bruce, Beverly Caswell, Tara Flynn and Zachary Hawes. The book comes as the result of the ongoing Ontario-based Math for Young Children (M4YC) research program. I worked through some of the ideas and activities from Taking Shape with elementary educators and I would highly recommend it. The activities in the book are grounded in research and honed in elementary classrooms. I especially like the emphasis on playful pedagogy, "a method of playing with mathematical ideas that is intriguing, engaging, challenging, and joyful."
A number of studies have recently been published which focus on the benefits of spatial reasoning for elementary students and how spatial reasoning and mathematical thinking are linked. Mark Chubb (@MarkChubb3) wrote about one-hole punch puzzles on his blog based one such study (Tom Lowrie, Danielle Harris, Tracy Logan & Mary Hegarty (2019): The Impact of a Spatial Intervention Program on Students’ Spatial Reasoning and Mathematics Performance, The Journal of Experimental Education, DOI: 10.1080/00220973.2019.1684869). Check out his blog for a description of the study and activity.
I was disappointed after reviewing this research is that it didn't discuss how they determined which spatial reasoning tasks were used in the study interventions. I was hoping that there would be a discussion of the characteristics of an effective spatial reasoning task. How do you evaluate spatial activities in order to determine which activities might give the most benefit? I was listening to the Numberphile podcast with Grant Sanderson (of 3blue1brown) recently and he stated, "being forced to articulate something clarifies thought." In that spirit, I'm going to try to articulate the characteristics I use when analyzing spatial tasks.
Characteristics of an Effective Spatial Task
Here are a few games and tasks that satisfy my characteristics above:
Do you have a favourite spatial reasoning task or activity? Please share with a comment.