So if I’m being honest, I don’t like geometry. I mean…I like it the least of the major math sub-topics. I did not like it when I took it in school, and I did not find it as interesting in my college courses as my other math classes. Sure there is beauty in the theorems that give us rules by which to consider various shapes and shape interactions, but at the end of the day… it’s still shapes. It just does not capture my curiosity like other math subjects.
That said, teaching geometry is fun, because geometry is always linked to something tangible for students. They know what a square and a triangle are. They can see how our buildings and cities are constructed along the lines of known shapes. They can apply geometry with an immediacy that they do not always see with algebra or higher math subjects. When you teach geometry, you can really let students explore the pieces, and construct their understanding.
There are easily 3-4 times as many labs and explorations in the geometry class at my school than there are for algebra. Students can be equipped with geometry tools like compasses and protractors and construct all kinds of geometry shapes. They can use patty paper and miras and experiment with translations, or other geometry concepts. They can use shape-cutouts to construct and deconstruct in a variety of ways that will enhance their understanding. The only major downside is that these activities and experiences can be hard to replicate for absent students. With the advent of 1 to 1 technology they can use digital tools to explore, which somewhat mitigates that issue. The points of entry for understanding are numerous and varied.
When I teach students about the triangle sum theorem, they can get hands-on. I give them a piece of colored paper and tell them to make any kind of triangle they like. Students enjoy trying to make something different than what their neighbor has, which is excellent for this activity. Then I have students rip the corners off of their triangle, and see if they can match them up along a line. Then we discuss what this tells us about the angles of any triangle. Most students have heard of the triangle sum theorem coming into high school, but seeing it makes it real.
All students have familiarity with geometry, even if they have not been particularly great with math. This low entry point allows students to participate in a way they may be nervous about for other math classes. It is a great time to use Number Talks (Boucher, 2017) like WODB or Guided Discussion (Bransford, et al., 2000). All students will be able to talk about familiar shapes and what they know about them, or patterns they notice as we explore. Students can notice things about shapes in unique ways that enable participation across ability levels. A comment that “obtuse triangles are extra pointy” can lead to a better understanding of the triangle sum theorem. A comment that “the triangle is the same if you flip it over” can lead to discussions on symmetry. The low threshold for participation and understanding means all students can learn and be successful. That is why I like teaching geometry.
References:
Boucher, D. (2017). Interview with Sherry Parrish, author of Number Talks. Math Coach’s Corner. https://www.mathcoachscorner.com/2017/04/6501/
Bransford, J. L., Brown, A. L., & Cocking, R. R. (2000). How people learn: Brain, mind, experience, and school (Expanded Edition). National Academy Press. pp 164 – 172.