(The Alberta 10-12 Mathematics Program of Studies with Achievement Indicators 2008, Alberta Education)
"Visualization is fostered through the use of concrete materials, technology and a variety of visual representations." (pg. 10)
"It is through visualization that abstract concepts can be understood concretely by the student." (pg. 10)
Thoughts on Visualization
The following are examples where manipulatives may assist in visualizing abstract concepts.
- M10C Polynomial Algebra Tiles - Algebra tiles are a life-saver for students who struggle with abstract concepts.
- M10C Nets for Surface Area - Allowing students to derive the surface area formulas from nets assists in their understanding of the formulas and how to use them.
- Volume of Pyramids vs. Prisms Investigation - Use giant geo-solids and water or sand to show how many pyramids will fit into the corresponding prism with the same base and height. Get students to guess first!
- M30-3 Transformations in Art - Students loved this lesson where we identified as many transformations that we could find in various pieces of geometric art. They then created their own pieces!
The use of images, animations and video can assist students in their visualization of concepts. See the Technology Process Page for some possible uses of technology.
Variety of Visual Representations
Graphic organizers are a great way to assist students in visualization as well as making connections.
Below is an example of a graphic organizer for slope of a line (Click on image to download a blank template):