In this exercise, students are asked to verbally describe three-dimensional shapes. A typical instruction to the student is:
Pretend you are talking to your friend on the phone and are trying to describe what this shape looks like. What would you say?
The objective of this activity is to see if there are any patterns of change in students' verbal shape descriptions as a result of work with JavaGami.
Key points of observation:
Do students' descriptions become richer in terms of mathematical relationships? Some examples of this may be: describing orientation of polygons in relation to one another; observations of repeating patterns of polygons; observations about the general symmetery of the shape; incorporating edges, vertices, and faces into the description of the shape.
Do students describe shapes purely in terms of visual characteristics, or do they describe them procedurally? A design philosophy implicit in JavaGami is the idea of "closure" within an "algebra of shapes": an operation on a shape creates a new shape, which in turn may have operations applied to it. It would be interesting to observe whether students begin to describe shapes in terms of operations applied to other shapes.
Do students describe shapes in terms of what may be built with them/how they appear in the world around them?
Do students' descriptions of shapes become more personalized?