A picture is worth a thousand calculations

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BREANNA is a quiet student who patiently sits in my math class waiting for the ordeal to end. She is too polite to complain or cause a fuss or disturb any of her peers with disruptive behavior.

She does take some notes, and with encouragement will attempt some of my questions. But, to be frank, Breanna gets almost nothing from my math class, apart from sitting through a course she needs on her transcript to walk the walk.

Breanna’s passion is drawing, mainly caricatures heavily influenced by animé. She is good, very good. Tucked under the notebook for my class is her pad. As token gestures go into her math notebook, a detailed and dramatic picture builds unseen on her pad.

When we did our Pascal’s triangle and binomial theorem investigation and poster

Blaise Pascal by Breanna

project, Breanna got the basics, but was happier coloring the triangle. Draw me a picture of Blaise Pascal I suggested (result, left). Last year I had tried an art and geometry project with my geometry class. The task was to find an artist who uses math or geometry in their work and become an expert. For various reasons it was less than a success. But would it work for Breanna? Her eyes lit up, yes she said, it sounded interesting. She would research artworks, choose an artist or an art movement or the art of a culture (I secretly hoped she’d opt for Islamic art), become an expert on both the art and the mathematics and give a presentation to the class.

Dutifully she showed me her growing list of artists and I eagerly awaited which one she would choose… Vasarely, Riley, Mondrian… hopefully not Escher.

Is it OK to look at pyramids? she asked. The proportions are interesting she explained.

Since her math notebook — not her art pad — has added calculations about the angles and proportions of the Gizza Great Pyramid and neighbors. Was it OK to look at less famous pyramids asked Breanna.

Her self-selected extension was to find some more obscure pyramids and compare the proportions.

Then came the poster, with a giant yellow pyramid, drawn to the correct proportions.

❏ For me, the value of this project was that Breanna did some mathematical thinking, where before she was doing none, other than sitting through a curriculum that had little interest, meaning or use for her.

It was also interesting to see that simply giving Breanna the freedom to pursue some mathematics of her own choice based on her own interests did indeed lead to some mathematical work.

What was surprising was that Breanna didn’t choose an overtly artistic piece of mathematics, such as a painting influenced by geometrical shapes. Though, in Breanna’s eyes a Pyramid is a piece of art.

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