Visualizing Math

By |2018-10-10T09:04:08-07:00April 19th, 2012|

As a kid, I always seemed to struggle with math.

It was beyond frustrating because I was consistently placed in the “gifted/talented” classes and I excelled in all subject areas easily… but I had to really work at math.  By the time I got to middle school, the gap was getting more and more apparent and I couldn’t hide my struggle with math much longer.  I truly came face-to-face with the evil that was Algebra in 8th grade and had to succumb to tutoring.  Which is normal, but isn’t talked about in the world of “gifted/talented”.  What I learned from those tutoring sessions, though, was that my struggle in math wasn’t really my fault.

You see, I was taught math like many students have been and still are – even today.  I was taught with “tricks”.  You do this and that to reduce a fraction, unless this happens.  Then you do this.  There was never any explanation of WHY or a break down of HOW it actually worked.  I didn’t understand the basic practices of math – all I knew were my bag of tricks.  And when I got to algebra, those tricks couldn’t help me because algebra is based in practices.

The other thing about math that is so clear to me now is that it is a visual form of communication.

Numbers are visual representations of logical practices.  Yet, we don’t teach math this way.  Why not?  80% of our students are visual learners.  Yet, we stubbornly refuse to teach math visually.  We use tricks and abstract ideas, but we never allow our students to visualize math concepts and practices.  How much easier would students grasp mathematical ideas and concepts if we taught them with visual means?

My theory about why this is so difficult is that we just don’t know how to teach math this way.  Most elementary teachers I run into will readily admit that they aren’t comfortable with math.  How can we expect our teachers to help students visualize math when our teachers aren’t comfortable with it themselves?

So here are a few ways that you can make visualizing math a little easier in the classroom, today:

1.) Math Journals – These journals allow students to use art techniques like collage, mosaics, drawing, watercolor and more to explore math concepts like angles, fractions, ratios, and algebraic functions.  By providing students with the opportunities to create their own visual representation of a concept and write about it forces the brain to develop personal understanding of a concept.

2.) Sculpture – Sculpture involves adding and cutting away from material to create something new.  This requires planning and a great deal of mathematical understanding to see how the pieces fit into the whole.

3.) Color theory – Providing students with an opportunity to experiment with colors and color theory gives them a concrete experience in ratios, fractions, and makes math a relevant part of a student’s life.

Do YOU have ways of making math visual for your students?  If so, please share them!  We could all use creative ways to see this uncharted territory!



  1. Hi Susan,
    Good post! Math is extremely visual (or at least it can and should be). This year I really took my time with multiplication concepts as I taught my students double digit multiplication. It was SO very much worth the time. We created models of easy mult expressions: 2 * 3 in an arrangement of 2 boxes by 3 boxes. And then more complex ones: 28 * 45 For these we disassembled the numbers into more manageable ones (20 + 8) * (40 + 5) so that we had (20 + 8) boxes by (40 + 5) boxes. In each rectangle created, we counted boxes and did the math. Later, we transfered this information to the more abstract algorithms connecting (with COLOR) how the numbers were present in both the model and the standard algorithm. It was a very hands on approach and really helped to solidify the concepts.

    • Susan Riley April 23, 2012 at 3:27 am - Reply

      What an amazing way to truly break down the math practices, Elizabeth! Thanks for sharing your wonderful work!

  2. Rosalind Flynn April 28, 2012 at 6:03 pm - Reply

    Hi Susan–
    If you haven’t looked into my colleague Marcia Daft’s “Moving Through Math” programs, I highly encourage you to do so. The arts integrated math activities she conducts with students are amazing and she is writing and publishing books to share what she has learned and created. An entire school system in Cedar Falls, Iowa has adopted her Moving Through Math program and they are seeing superb test results when kids learn math concepts in this way!

    Rosalind Flynn

    • Susan Riley April 29, 2012 at 6:00 am - Reply

      Hi Rosalind,
      I LOVE Marcia’s work! I’ve seen it used at the Lucy School in Frederick with fantastic results. Thanks for sharing her as a resource with our readers!

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