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Boole, Bézier,

and Beauty

Carly Ziniuk ~ linktr.ee/CarlyZiniuk

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L: Elias Not Afraid, Warrior Women Cuff (2018)

R: Margaret Nazon, The Light Echo (2012)

National Gallery of Canada

Creative, curious explorations of math

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“I was just doodling.

She had to bring slope into it.”

“Somehow everything has become math now. “

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“When I have finished, if the solution is not beautiful, I know that it is wrong.”

~ Buckminster Fuller

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Mary Everest Boole

As is unfortunately typical for a woman of the late 1800s, Mary Everest Boole is often situated academically by her relationships with men, in this case she worked extensively with her husband George Boole, of Boolean Algebra, and yes, her uncle George Everest is the British surveyor whose name was given to the mountain.

In 1904, she wrote that mathematical thinking arises from interaction with the beauty of the natural world, and deeply reflects much of her self-taught understanding of mathematics. Her work in 1905, “Logic taught by Love” led to her Sewing Cards, here shown from 1906. This playful approach to math centred her writing as a mother. She writes of teaching her children even when they were small to “create mathematics” and especially noting their affinity for geometry.

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Springgay and Rotas (2014)

“How do you make a classroom

operate like a work of art?”

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What makes a good math task?

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What makes a good math task?

(Lappan & Phillips, 2009)

Builds connections
Requires higher-level thinking
Encourages discourse
Creates opportunity to assess (own) learning

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What makes a good math task?

(Lappan & Phillips, 2009)

Embedded, important
Develop concepts
Promotes skillful uses
Various solutions, allows different positions

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Lines segments approximate curves

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Embedded, Useful Math

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Conceptual Development

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Multiple perspectives

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“How is it different?”

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“How does it work?”

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“You can put the axis in different places”

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“Same, but

different”

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“It’s beautiful,

so I think it’s right.”

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“What is a variable?”

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A creative communication legacy

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Connections

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Higher-level Thinking

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Multiple perspectives

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Encourage

Discourse

In 2019, a student stumbled upon the research of Mathieu Patrel’s github which they did not understand, since it uses partial derivatives in the justification. This is the flattening of the hierarchy of mathematical discourse that has come with the internet. The technology makes it “work”, but students admit that they don’t really understand what is happening. Creativity OR just frustration or use of a tool to make something beautiful?

Some students just wanted the curve to match, others couldn’t understand why the curve was so much more complicated than what they had expected given their previous experiences. Since 2019, I have had students wrestle to connect a square root to a parabola, rotating quadratics upon a diagonal axis in learning-appropriate ways. On their own. Frustratedly adapting and arguing with each other and yet, creating.

https://www.desmos.com/calculator/n6cghqjswi

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Bézier’s beautiful extension

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Various Solutions

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Carly Ziniuk linktr.ee/CarlyZiniuk