The Winning Angle: Geometric Games

As someone who loves playing games, many games exist where I indirectly need to apply my understanding of geometric skills to come out victorious. We expect middle school students to use properties of shapes to create arguments and solve problems.  They also need to apply geometric ideas with 2D and 3D shapes to real life contexts (CCSS). In the “real world” someone is not going to come up to you and ask what shape something is but you may need to use spatial awareness and geometric understanding to solve problems. I wonder if time was devoted to playing with some of these concepts in the classroom if students would better develop their skills. 

Blockus Gameplay

We expect middle school students to “apply transformations and use symmetry to analyze mathematical situations” (CCSS p. 232). While playing games students need to replicate an image or manipulate shapes through reflections, rotations, and translations in order to achieve a goal. In order for students to be successful at this skill they need to be able to manipulate the appearance of a shape or image accurately. Games where students need to replicate an image using these properties include Qbitz, Uzzle, and Color Code. I wonder if starting a unit with these games to explore shapes would help build the foundation students need to manipulate the shapes. Not only can shapes be manipulated to create an image but in games such as Blockus or Patchwork students achieve a secondary goal. This combines logical thinking skills as well as geometry in order to take over and lay down as many pieces as possible. 

Zangle Gameplay

Another geometric focus in math is “analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” (CCSS p. 232). This standard involves a few sub-skills such as breaking down a shape into its parts (decomposing), identifying and connecting similarities of shapes (properties), and using these observations to justify their thinking. Set is a game that can be played both as a physical game or online where students need to identify similarities and differences amongst shapes. To practice composing and decomposing shapes Zangle can be used to help students see these patterns. For both of these games students not only need to recognize properties of shapes but defend and explain their moves to their opponents. I wonder if this low pressure way for constructing arguments would help students do the same in a more math-like setting. 

While fun and engaging for students, games could be one tool that is used in the classroom to help students extend their mathematical thinking and enjoy themselves at the same time. As a teacher students light up whenever a game is thrown into a class. My Knowledge of Content and Students (Hill & Ball, 2009) has shown me the more I learn about my students the more value I see in “sneaking” learning into fun activities. While I often throw games into the other mathematical strands I never thought to apply this to geometric reasoning. By digging into the standards and deepening my Knowledge of Curriculum (Hill & Ball, 2009) I have become aware of the importance of playing with shapes in order to help students deepen their spatial relationships. This in turn also assists their ability to apply the properties of shapes to deepen their thinking about geometry. 

While often in math the end goal of games seems to be student engagement and interest. In reality I find that by pushing their thinking and being intentional the value goes beyond engagement. In We’re in Math Class Playing Games McFeetors and Palfy (2017) discussed the benefit of students playing games in class is that students can improve their logical thinking skills and their ability to explain their strategies in a low pressure context. I feel this can not only help students develop mathematical practices but can tie in specific math standards and help students learn to make connections through enjoyable experiences while developing real world skills at the same time.

References

Common Core State Standards Initiative (CCSSI). (n.d.). Mathematics standards. Mathematics Standards | Common Core State Standards Initiative. http://www.corestandards.org/Math/ 

Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71.

McFeetors, P. J. & Palfy, K. (2017). We’re in math class playing games, not playing games in math class. Mathematics Teaching in the Middle School, 22(9), 534–544.