Chapter 5: The Importance of Visualizing Mathematical Ideas
In this chapter, Laney Sammons again connects what we are accustomed to talking about in reading class to needed skills for mathematicians: "proficient mathematicians employ visualization as they work to understand concepts and solve problems." The list of ideas students need to understand include:
- Mathematicians purposefully and spontaneously generate mental images to enhance their understanding as they explore mathematical ideas.
- Mathematicians draw upon their schema as they generate mental images of new mathematical ideas.
- Mathematicians are motivated and engaged as they visualize mathematical concepts and problems.
- Mathematicians continue to reviese their mental images as they work and discover new mathematical information.
- Mathematicians understand the value of sharing their mental images of mathematical ideas with others
How do we get our students to the point where they do visualize? I'm guessing that you, like me, run into students who can't seem to visualize. The chapter talks about how we tend to be passive viewers, taking in many images -- images that are provided for us. This may hamper students in actually creating their own visualizations.
There are some great ideas in the book for helping students develop this ability. I"ll tell you, though, I read this great stuff in books and have a hard time remembering it when I'm actually involved in the classroom. To help with this, I created a couple help sheets of key points from the chapter that I'm sharing with you.
These are hopefully going to help keep me focused as I work with my students in the small group setting. I they might be helpful for you, please click on the pictures to download them.
Next week: Making Inferences and Predictions