The FUNd Stuff at PNA!

A New Understanding of Math

by Brenna McCormick | PNA Kindergarten Teacher

Think back to math instruction in your school years. I'm sure it was much like mine, filled with algorithms and abstract idea, ideas that I memorized and used to calculate answers, but did not understand. In grade school, I was not a fan of math. It wasn't until I was training to be a teacher and was introduced to math concepts visually and creatively that I started to enjoy--and truly understand-- math. Suddenly, when I could represent and explain them visually, those algorithms and abstract ideas made sense.

A paper from youcubed, a Stanford center designed to provide research-based mathematics resources to teacher and parents, explains my experience, which I share with many educators: "In our extensive work with school districts, teachers have also been inspired by visual and open mathematics. When we give teachers visual experiences of ideas that they have only previously encountered numerically and abstractly, such as multiplication facts or algebra, they gain insights into mathematical concepts and ideas they had never before experienced, and start to understand more deeply. They also feel empowered (Boaler et al., pg 10)."

The researchers go on to say, "Inviting people to think visually about mathematics is liberating for teachers and students alike. Mathematics is a multi-dimensional subject, and problems can be solved with numeric, abstract or visual mathematical pathways - we now know that our brain networks are correspondingly multi-dimensional and need to be developed and used. It is our belief that learners would develop stronger mathematical understanding if we helped them develop the visual networks in their brains, increasing their ability to work mathematically with a fully developed brain network (Boaler et al., pg. 10)."

If you've ever wondered why your child's math learning seems so different than the learning you most likely experienced as a child, it is because our our math curriculum stresses mathematical thinking, approaching problems in many different ways, and visual representations. Students explore patterns and relationships within mathematical concepts, usually through visual representations.

Brain research in recent years has revealed the importance of visual learning and representation in math. Traditionally, educators have taught math visually only as a bridge to more abstract thinking. Now, however, research has shown the importance of visual mathematics in all areas of math, even those traditionally labeled as abstract or higher-level. Brain research now shows that "everyone uses visual pathways when we work on mathematics and we all need to develop the visual areas of our brains. The problem of mathematics in schools is it has been presented, for decades, as a subject of numbers and symbols, ignoring the potential of visual mathematics for transforming students' mathematical experiences and developing important brain pathways (Boaler et al., pg 7)." Math learning is an inherently and highly visual process and visualizing math concepts deepens engagement, understanding, and enjoyment of math.

The paper concluded with three take-aways for educators and parents (Boaler et al., pg. 11):

  1. "Encourage and celebrate students' visual approaches and replace the idea that strong mathematical learners are those who memorize and calculate well."

  2. "Focus on finger discrimination and encourage finger use. Successful mathematics users have well developed finger representations in their brains that they use into adulthood. Finger discrimination even predicts mathematics success."

  3. "Importantly, mathematics teaching and learning needs to become more visual - there is not a single idea or concept that cannot be illustrated or thought about visually."

I encourage you to read the unit overviews for each math unit and delve into the visual representations of math. "The brain science supports this - work on mathematics draws from different areas of the brain and we want students to be strong with visuals, numbers, symbols and words. (Boaler et al., pg. 12)" You and your student together can think more creatively about math and develop new understandings and representations together.

Jo Boaler, Lang Chen, Cathey Williams, and Montserrat Cordero. "Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning." youcubed at Stanford University.

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The FUNd Stuff is a bi-monthly (or so) publication from the staff, students, parents, and teachers of PNA. Want to know more about anything we've highlighted here? Get in touch! (907) 333-1080 or


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Thank You! 

As always, our continued success is shared with the people and companies that support us.


Many thanks to... 

John Hardwick and Ral West


Skiva Investments LLC



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