"It's a square because it looks like one" suddenly became an unsatisfactory answer! How awesome! This is when we math teachers insert a tiny "not drawn to scale" under each diagram and thereby stretch our students' mathematical thinking and visual perception. In math class this week, I learned about the developmental stages of geometry learning. I find it intriguing how there is a correlation between these stages and the ability for us to perceive geometry by trusting our logic and creativity rather than our eyes.
I am still left wondering about the use of the paper folding to build a conceptual knowledge of proofs. In order to verbally express your reasoning, you need to have a certain vocabulary. For example, we used the terms "linear pair", "alternate interior angles", and "perpendicular bisector". So, would a lesson like the paper folding fall sequentially after learning terms and before formal proofs? Would this type of activity be an effective learning tool for understanding terminology? I'm curious about the different modifications for this paper folding activity so that I can use this hands-on, engaging activity to assist in the learning of different geometry concepts.
Now that I know there are distinct stages of developing geometric reasoning, it has become a lot clearer to me why some students seem to grasp geometry concepts quickly and can manipulate them while others are seemingly confined by the strict parameters of what they see. I will utilize this new knowledge to help my students sequentially build their understanding of geometry.
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