Visualizing for Math Comprehension
“Just as proficient readers use visualization to make meaning as they read, proficient mathematicians employ visualization as they work to understand concepts and solve problems.” – Laney Sammons
In Building Mathematical Comprehension, Laney Sammons points out the important relationship between visualization and cognition. Our growing mathematicians need to be aware of the role that visualizing plays in helping them to build a deeper understanding of math concepts. Some of our students automatically form visual pictures in their minds to help them solve problems, but research shows that most do not. Teacher modeling is a critical tool for helping our students see how the process works and to see that there are multiple ways to represent ideas and solve problems.
Here are a few ways to promote the visualization of mathematical ideas:
Teacher think-alouds can demonstrate how to draw on prior knowledge (schema) to make connections and build understanding of new concepts. For example: “Sometimes I have trouble knowing if a number is even or odd. I know that 6 + 6 = 12, so 12 must be an even number. I can visualize a dozen donuts. (draw them on the board) If I give you half, you will have 6 and I will have 6. We will have equal shares, so 12 must be an even number.
Teachers can also demonstrate how to revise their thinking as they acquire new information. We need to show our students the importance of reflecting on our work and then being flexible enough to change directions when needed. Our growing mathematicians need to see how we make changes and learn from mistakes in our problems solving. Our mental images are not set in stone and will evolve with our learning.
Teachers can also create a climate where students feel comfortable in showing and sharing their thinking. “Learning is a social process.” Allowing our students the time to verbally share their mental images builds their math reasoning and communication skills. As students listen to each other, they gain new insights, tweak their ideas, and deepen their understanding of math concepts.
Encourage students to represent math concepts in ways that make sense to them. When exploring a math problem, demonstrate a variety of strategies and methods for solving the problem. Use words, numbers, and pictures to represent the processes. Laney tells us that “students may first visualize fractions as pieces of pizza or sections of a candy bar, as their understanding expands they are also able to represent fractions as parts of a group, fraction bars, ratios, division or as numbers.”
Building the ability to visualize is an important skill and it is one that needs thoughtful practice. Math standards call for our children to create multiple representations of mathematical concepts. Think about a concept that you teach and see how many mental representations you can make. You purposefully create mental images as you engage with the concept. Share these with your growing mathematicians to help them add to their problem solving tool boxes.
Want to discover more about visualization and math? Check out these links.
https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/
http://www.weareteachers.com/4-strategies-to-help-kids-understand-math-using-visualization/