Case Study: Learning Geometry with a Spatial Disability
Tuesday, November 3rd, 2009One of my favorite success stories was a star hockey player who was failing geometry because he had a spatial disability. For many people, geometry is very intuitive because of the diagrams, but for this student, reading diagrams was extra difficult.
One of the first things I tried with this student was using erasable colored pencils to label different parts of the diagram in different colors. I hoped the different colors would help him distinguish different parts of the diagram, un-jumble them, and process the information better. But he didn’t seem to be into the colored pencils, so we stopped using them after a while.
However, I knew he must have excellent kinesthetic-spatial intelligence in order to be such an awesome hockey player. I mean, he specialized in creating and responding to vectors on ice, right? So I tried to talk with him about visualizing things in motion. I would tear up pieces of notebook paper and create animated versions of the diagrams by moving the pieces of paper around.
In the end, I think the teaching strategy that helped him the most was just really breaking down the geometry diagrams. I realized that he was missing a lot of crucial information about how to interpret diagrams that most teachers probably never explain, most likely because it seems so “obvious.”
For example, someone without a spatial disability would look at a diagram of a triangle and just infer that if a number is tucked inside an angle, then it is the measure of that angle. Similarly, it would be easy for them to intuit that if a number is next to a line, then it’s the measure of that line.
But because of his disability, these things weren’t obvious to my student, and no one had ever explained them to him before. So we filled in the missing pieces. We broke down the different parts of those diagrams so he’d know exactly what to look for and which numbers affected which part.
The awesome part is that after a couple months, he went from failing to getting As and Bs!
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The reflexive property in mathematics holds that every element is equal to itself. For any element \( a \), the equality \( a = a \) is always true. This principle is a key foundation in many mathematical proofs and principles.