“Research has shown that visual learning theory is especially appropriate to the attainment of mathematics skills.” - Stuart Murphy

Lately I've been excited to learn more about the connections between visual literacy and learning particularly with respect to mathematics.

Again and again this year, I've read, heard and viewed discussions about the power of visual models when learning mathematics:

- I watched this Tedx video: "Teaching Without Words"
- Maureen Yoder explained the role of "hands-on observations . . . intuitions, conceptual thinking, and visual imagery" in Einstein's education as explained in Einstein: His Life and Universe by Walter Isaacson at the MassCue Conference.
- Steve Jobs relayed in his Stanford Commencement Speech how his experience studying calligraphy in college impacted his work at Apple.
- David Wees regularly questions, describes and blogs about the role of visual imagery in mathematics, and readily responds to educators' questions and needs.
- John Medina describes the role of visual imagery in his presentation, Brain Rules for Presenters noting that "vision trumps all other senses."
- At MassCUE, a research team from the University of Massachusetts presented 4Mality noting that children chose the visual coach most often when utilizing this web-based problem solving program.
- David Wedaman (@wedamen) sent me a link to another cognitive education site related to math which again emphasized visual literacy.

Yet the rainbow model misrepresents the relative distance between the factors. Is this important? What would a model look like that represents the relative distance.

As we discussed this with greater depth, we realized that the relative distance between factors for all composite numbers takes a similar shape? Is this important?

Over the weekend, I considered the models with greater depth, and wondered about the following questions.

- Does a number line that only demonstrates factor pairs misrepresent the notion of what a factor pair represents: a number shown as the sum of equal groups? Or is relative distance an important concept to convey?
- Should I give more time and attention in the Number Posters project to exploring visual models by allowing students to play around with the many, many ways a number can be visually represented?
- How will math instruction change and evolve given our current knowledge about the power of visual imagery?
- Will teachers at every level begin to employ more and more visual models to efficiently and comprehensively relay the meaning of math concepts?

I decided to add more time to the project for visual model making. I played around with it myself so that I could model this activity for students. This is what I came up with for 12.

I noted while making these models that this activity will strengthen students ability to grasp fractions, area and perimeter when we focus on those concepts.

Where will this exploration take us? What are your thoughts with respect to integrating visual models into your math lessons? How much time do you take to allow students to draw and explore math concepts with models? In what ways will we bolster this aspect of mathematical understanding?

As an elementary school teacher, I am continually evolving my approach to instruction based on the latest research. I look forward to your links, thoughts and ideas with respect to this investigation. Thanks for your consideration.

Additional Visual Resources for Math:

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