Geometry, It's Fun for You and Me

              I consider myself both a geographer and an environmentalist, mostly because I majored in geography and environmental studies for my undergraduate degree. Everything about those two subjects appeals to me; I find it all so interesting. I can also confidently say that one reason why I grew do fond to those specific social sciences is that I am very spatially aware.

                In this past week’s math class, we focused on geometry, exploring the ins and outs of 2D and 3D shapes. One topic we also focused on was how geometry connect to spatial skills, specifically how the development of geometric thinking can have a profound effect on a child’s development in regards to spatial skills and awareness. The text, Making Math Meaningful to Canadian Students, K-8, summarizes the ideas behind Pierre van Hiele and Dina van Hiele-Geldof’s Taxonomy of Geometric Thinking, explain how students go through 5 stages on their way to developing geometric thinking.  Level 0 is what they explained as the “Visualization” stage where students begin to be able to identify shapes based on the fact that they a circle simply “looks like” a circle and a triangle is a triangle is because it “looks like” a triangle. Level 1 is the Analysis stage where students begin to conceive shaped in groups based on their similarities, followed by Level 2, the Informal Deduction stage where students develop the greater ability to develop their own simple logical arguments about shape properties. Level 3 and 4, Deduction and Rigor, apply to students learning at a high school level and beyond where students develop advanced understanding about shapes through traditional and non-traditional axiom structures. I found it very interesting how the stages the van Hiele’s developed, mirror many cognitive taxonomies in regards to students general development as well. This makes me believe that the fact that geometric thinking is s connected to one’s own spatial skills, the development of good understanding of geometric thought is crucial for both math students and math teachers.

                For the most part, I think some of my most favourite activities in math class during my time in elementary school revolved around the geometric strands. I recall making 3D shapes with straws and pipe cleaners. I think that exercise is used today often because it allows students to create the shapes they are learning about through the construction of their own manipulatives. Use of manipulatives while teaching geometric operations at any level is a great idea, but is also simple because there are so many different types of manipulatives teachers can use. Pipe cleaners and straws cam be used to make 3D shapes, students can also construct their own shapes with paper. The creation of shapes by students addresses the first three levels of the Taxonomy of Geometric Thinking, and most importantly, it does this in a fun and engaging way. There are many other activities students can complete with the use of manipulatives, in class we completed some “Tangram Duos”, which allowed us to use different shapes to create specific 2D shapes.

Tangram Fun!

                For me, I think my appreciation of my time studying geometry in my early years of education can be connected to my spatial awareness, but also my appreciation to geography because it is the study of space and how we interact with it. All strands of math are important , but the development of geometric reasoning and thought is somewhat more important because it can shape how individuals use and understand space. It also can be considered as one of the most important stands of math because it follows cognitive development so closely.

Thank you for reading!