Building Mathematical Comprehension Chapter 5

The Importance of Visualizing Mathematical Ideas

I have used the visualization strategy for so long and not considered it while teaching math? In such simple, but profound ways Sammons's book is helping me rethink the way I teach math. Sammons shares that cognitively, if deeper learning and understanding is to be made students, they  must be able to process information in two ways. One being linguistically and the other nonlingustically. Combining the two when I teach will increase my student's comprehension. I have to say, when I think about my lessons that went very well I was naturally (intuitively) doing both.

Now, in order to help my students use visualization as a true strategy I need to be systematic and explicit in my teaching they use of the strategy. Sammons suggestions of what mathematicians do with this strategy is beneficial. Mathematicians...

• use their schema to create a mental image- remind students that we all have different schemas and that it is okay if they are unsure. That is common in learning something new.
• are motivated and engaged as they visualize- tell students that combining prior knowledge and new learning is essential to create images.
• revise their mental images as they discover new information- as students receive new information students need to learn how to incorporate that information into their mental images. I love this one! 
• understand the value of sharing their mental images- this not only helps build verbal skills, but it helps students process their own thinking. It will also help them with the revision of their mental images.

Pretty powerful stuff! Another amazing section was how to concretely help students who struggle with visualization. I can definitely visualize myself using this 7-step sequence in a small group. Is everyone as excited as I am?!

 This chapter also reiterates the power of modeling and Think- Alouds. I know that I cannot assume my students will naturally understand visualization on one try. My think-alouds need to go beyond the introduction to my lesson. I need to embed them throughout the lesson; in large group, small groups, with students help, in writing, one-to-one conferences etc.

I cannot do this chapter justice. I created an organizer that I hope will help me be more direct and explicit in teaching students to draw upon what they know and create a mental image. Just click on the pic to download. Let me know what you think.