All through high school and college, my favorite type of mathematics was Geometry. Whether it was writing proofs, figuring out missing measurements, or classifying something, I was always eager and excited to do so. When I became a teacher and saw that the majority of my classes were Geometry, you can understand how excited I was. Not that I don’t enjoy teaching Algebra or Calculus, but there’s that special connection I have with Geometry.
I figured that I would teach Geometry the same way I was taught. I figured good old lectures and lots of note taking would be sufficient. I found out real quick that I was wrong. My students were not able to grasp the material in the same way I did when I went through school. What was I going to do?
Well after calming down first and collecting my thoughts, I looked through my textbook, Discovering Geometry, and found tons of activities to do with the kids. Instead of lecturing, we were now going to learn by discovery and inquiry. Students will complete an activity, take note of what they see, and then complete a conjecture or theorem from their observations.
My favorite activities include what is known as patty paper. It’s a 6 inch by 6 inch piece of thin transparent paper. Students can fold to find midpoints, trace polygons and segments, and perform transformations with it. There are books out there with specific patty paper activities to explain further what you can do with it. But, what the best part about using patty paper is that the students are learning in a tactile fashion. They are holding onto concrete things and being able to see what they are learning. I use my SMART board simply to model what they are supposed to be doing. But once the students are able to make observations, I stop teaching and they start learning. We collect all our thoughts and put them into concisely written conjectures and theorems.
Everyone says, including the research, that we learn best by doing. You learn how to drive by going for driving lessons, you learn how to play sports by practicing, and you learn how to play an instrument by playing it over and over again. So why do we learn in school by being told? The one place where learning is the biggest priority seems to steer away from the “learning by doing” philosophy. As educators, let’s step back a little bit. Be a facilitator as opposed to an instructor. Have students come up with their own ideas and thoughts from observation. Let them learn it by doing.