Chapter 5: The Importance of Visualizing Mathematical Ideas (BMC Book Study)

Visualization is essential to understanding, so how can we get our math students to visualize mathematical concepts and problems? How can we get our students to visualize multiple representations and then be able to evaluate which one is the most appropriate for a given purpose?

We probably have heard of picture walks in reading. Laney Sammons recommends doing "picture walks" to build the capacity to visualize (161). Mathematical picture walks can be used with textbooks, online screen shots, or even children's literature. Asking students why a particular image was chosen to represent a mathematical concept in a text can help them to build their own capacity of options to use when visualizing. Two questions that I feel can really lead to a deeper understanding the purpose behind visualizing are:
  • How effectively does this representation promote greater understanding of the concept?
  • Are there other ways that this concept or idea can be represented? What are they?
Another strategy recommended by Sammons was "Visualize, Draw, and Share (162)." This activity can help students to create mental images from verbal statements. The teacher gives a statement about a mathematical idea.
  • I'm adding ten plus five.
  • A rectangle with an area of 18 square units.
  • Two thirds
  • What do you visualize when you think about _____? (multiplication, decimals, a foot)
The students then are asked to create a mental image and then transfer it to a pictorial representation. Students then share their pictorial representations with classmates where they can discuss each representation and its effectiveness at improving mathematical comprehension.

You also can flip this idea and start with a representation and have students explain what the representation might be trying to explain. The example Sammons uses is an array with X's in a two rows by three columns representation (165). Answers may include:
  • 2 x 3 = 6
  • Two children have three cookies each. How many cookies do they have altogether?
  • Repeated addition
Sammons recommends using children's literature to bring in real-life examples to help students visualize (166). One recommendation was Basketball Angles: Understanding Angles (Wall 2009). Has anyone ever used this book before? It looks like an interesting book that certainly shows the importance of angles in the real world. Using nonfiction literature that explores real world math concepts can help create visual anchors for students. Poetry is another recommendation made by Sammons to help students visualize math concepts. One poem that I have used in the past is Smart by Shel Silverstein. A short little poem that teaches an important lesson about money. Students can be asked to "visualize" the trades to better understand why the poem title is quite ironic. Click the image to read the poem.

One key take-away is that visualization in math does not necessarily need to be a drawing. It is being able to represent a math concept in multiple ways: mathematical symbols, real-life examples, model/diagram, and/or explain with words (163). Click on the image to grab the freebie.
MyCuteGraphics, Creative Clips, Hello Fonts

What are some activities you use to help your students visualize in math? The next chapter is on making inferences and predictions. 

Chapter 2: Math Vocabulary
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