I recently had the opportunity to try out a digital breakout with a Precalculus 12 math class. The classroom teacher and I wanted to create an opportunity for students to have some interleaved practice as a cumulative review for the course. We liked the idea of a breakout game but we wanted to make sure that all of the students got a chance to do a wide variety of problems. Our solution was to do a digital breakout in small groups of 2-3 students.
This was the first time that I had created a digital breakout game so I went hunting online for some examples that might spark some ideas. I found Tom Mullaney's (@TomEMullaney) Digital Breakout template page to be very helpful in figuring out what I was going to do. It gave me lots of ideas and inspiration. I also found I found a post from Meagan Kelly (@meagan_e_kelly) showing an example of a math digital breakout that I was just what I was looking to do. I learned how to create a google site and conquered a number of new technical challenges. While creating the site took some effort, the classroom setup was easy and there were no materials required.
I thought the breakout went well. The students were very engaged and they reviewed lots of different concepts from throughout the year. They liked working in groups and having a variety of different types of puzzles to solve. Many students were consulting their notes and examples from the textbook to find solution strategies. They were also using online tools like https://www.desmos.com/ to help them graph and visualize mathematical relationships. All the problems were self-checking. If the combination for a lock didn't work, they knew that they had made a mistake and had to work together to find and solve it. They also all got to work at their own pace. To add a bit of additional flair, we added a final physical lock and box for students to unlock with a small treat inside.
If you'd like to give this breakout a try, check it out. The link is: bit.ly/PC12Breakout.
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.