Visualization and Word Problems in Math

Visualization is an important skill in mathematics because it helps people see problems more clearly.  Although we teach students to draw pictures or diagrams but we don't always stress the diagrams can clarify the situation so much better than using only words.

In addition, visualization helps students turn mathematical language into something they can understand and apply.  It turns situations into understanding and students can process their learning.

Perhaps when we introduce word problems we might ask students how we'd represent the situation visually.  The problem with concentrating on key words is that some words such as per can mean multiplication or division depending on the context.  If students look at word problems as if they do when reading a book, they might do better.  In reading, they are told to picture the scene in their minds, why don't we ask them to produce a drawing of it on paper, on their iPads, or even create something in VR/AR or in animation.

Rather than working through umpteen word problems, why don't assign each student or group of students one or two word problems to do.  Before they start, ask them how they could represent the word problem visually, where have they run across this type of situation in real life, and how could they present the problem and its solution through video, Desmos, Geogebra, or a sequence of images or pictures.

Recent research indicates that it is important for the brain to use both symbols such as numbers, and visualizations because mathematical learning is optimized.  When students use symbols, they access one part of the brain and when they create visualizations, they are using a different part of the brain, so when they use both, the two parts of the brain communicate and their learning improves.

Furthermore, creating visualizations also makes math more exciting and improved student performance.  In addition, creating visualizations involves the brain using higher level thinking skills, and shows people there is creativity in math and math is not just numbers.

So back to word problems.  It is important for the student to create a visualization of the problem first so they understand the problem and the context of the mathematics.  The visualization can be as simple as drawing a picture or it could be more complex using stop motion animation, creating a cartoon, a comic strip, or a video.  Just some way for students to "see" the problem.

Once students are comfortable with creating visualizations for word problems, they can take the next step of creating their own word problems with associated visualization to show others the problem.  Visualization is the key to learning to do word problems.  Let me know what you think, I'd love to hear.  Have a great day.