Visualization and Modeling
Why we need to Visualize
Teachers, if you are hear you already know that visualization is important. But lets explore why this is important and how we use it.
The first idea is to realize the importance of motion in perception.
Causality from Motion
In addition to structure, our brains are designed to perceive interactions and causality from motion. In one of the first perception experiments of motion Michotte showed that people perceive causality if the motion fits certain parameters.
Controlling motion increases student engagement
Motion is helpful in perception, but a key factors is attention. Are students paying attention to the motion? One way to encourage attention/engagement is to require students to manipulate the objects as in the following applet.
Dynamic Geometry and Mathematical Inquiry
The term Dynamic Geometry was coined by Nick Jackiw the creator if Geometer's Sketchpad. He wanted to create a way for people to explore geometric objects. He created a microworld where everything behaves according to the rules of Euclidean Geometry. A point on a line can move, but only on that line. Parallel lines are always parallel, but their position can change. This tool (and others like GeoGebra that followed) provide a way to embody the rules into objects and explore how they work.
This allows students to go beyond proofs and problem solving to engage in inquiry - the systematic exploration of complex phenomena - in mathematics. You can ask questions like 'What is the area of intersection for two overlapping circles with the same radius?'.
A few good Dynamic Geometry links: