Visual Thinking in the Arts and Mathematics

Last summer I hosted an art and math class for middle school girls. I was inspired by the work of Jo Boaler, Lang Chen, Cathy Williams & Montserrat Cordero in their paper Seeing as Understanding the Importance of Visual Mathematics for our Brain and Learning. In the paper they present evidence from brain research to dispel the myth that “that visual mathematics is for lower level work, and for struggling or younger students, and that students should only work visually as a prelude to more advanced or abstract mathematics” (Boaler, et al., 2017).

Material for math and art lesson based on the art of Piet Mondrian.

Brain research has shown that math concepts are stored as both visual and sensory motor memories. Teacher who use visual mathematics tasks and use manipulatives (hand-on learning) in their lessons encourage higher achievement. In the integrated math and art class I hosted, we looked at the art of Piet Mondrian. I used the “Make a Fake” lesson from Mindset Mathematics: Visualizing and Investigating Big Ideas by Jo Boaler, Jen Munson, and Cathy Williams as guide for the class. We spent equal time discussing and looking at art as we did math. The girls were introduced to the modern art movement and we discussed Piet Mondrian’s life and works. We looked at his use of color and shapes. Then I presented the girls with the problem: Create a Good Piet Mondrian Fake.

Identifying the fractional amount of color to black and white.

In order to create a good fake, the girls had to identify the fractional amount of color to black and white space in his paintings. Then they had to identify the fractional amounts of yellow, red, and blue used in the paintings. Each girl chose an art note card with a Mondrian painting to identify the fractional amounts. The girls had access to blank note cards, rulers, graph paper, and colored paper to help them figure out the fractional amounts. As they finished, they each shared their method for finding the fractional amounts of each color and of color to black and white. We had a wonderful discussion about fractions, fraction equivalents and benchmark fractions.

Piet Mondrian art notecards

After the girls found the fractional amounts of each color to black and white they created their own Piet Mondrian inspired piece. They each worked very focused during the entire session and talked about how they were going about creating the fake. The atmosphere of the class was supportive and interactive. After the session ended, I asked the girls for written feedback about the class by answering the following questions:

  • What was the main idea you learned about today?
  • What good ideas did you have?
  • What did you enjoy about the class today?
  • What would you like to learn more about in the future?
  • Would you take another class?

They all enjoyed the art portion of class and were able to see the connection between math and the artwork of Mondrian and wrote that they would enjoy taking future classes. I think they enjoyed the class because they were able to work on an open-ended problem through a creative and visual process. Teaching math through art and with a focus on visual thinking is engaging. Jo Boaler writes that providing students with open-ended problems that encourage visual models and thinking is more engaging for students.

‘The math was open, creative and visual. Such activities not only offer deep engagement, new understandings, and visual brain activity, but they show students that mathematics can be an open and beautiful
subject, rather than a fixed, closed and impenetrable subject” (Boaler et al., 2017, p.6).

Visual SEEING AS UNDERSTANDING: The Importance of Visual Mathematics
for our Brain and Learning.

When learners use visual thinking to make sense of and to explain math concepts, it helps them both process and expand their ideas. When we provide them with opportunities to build models and create, we also engage them in a joyful learning process. I have plans for to offer more art and math integrated classes for elementary and middle school aged learners. It is important to provide children with an experience that helps them think of themselves as mathematical thinkers.

“Visual mathematics is important for everyone, at all levels of mathematics.”

(Jo Boaler et al., 2017, p.6)


Boaler, J., Chen, L., , Williams, C., & Cordero, M. (2017). SEEING AS UNDERSTANDING: The Importance of Visual Mathematics
for our Brain and Learning.

Published by

Maria Arana

Hi, I am Maria, a mom to three wonderful kiddos. My family and I live in Phoenix, Arizona. We love the beauty of the desert southwest. I am a former primary teacher and elementary math coach. I love to encourage my children to follow their interests and passions. At Guided Learning Studio, I offer private personalized lessons and enrichment classes. Tutoring services are best for families seeking long-term educational support over a semester or school-year.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s