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Anna Hermann's regular tessellation features fish and quadrilaterals.

The Weave of the World:
What's Dance Got To Do With Math?   Just About Everything.

Symmetry is part of the weave of the world. It's in the inkblot patterns of butterfly wings and in crystals of snow. It underlies the beauty and function of suspension bridges and the flying buttresses of cathedrals. It is apparent in computer programming and DNA sequences. From artists and musicians to architects and mathematicians, people devise patterns and symmetries to express human experience and to reshape environments. The language of mathematics governs these enterprises, and mastering this language can powerfully affirm one's place in the society of human beings.

For teachers like Ken Reiner, 50, and Michael Lang, 43, empowering young people to take their place in society is a potent motivation. They teach eighth-grade mathematics to students of varying academic abilities. Both men are highly effective teachers. They keep abreast of mathematics standards and best practices. They design active and challenging lessons, and question with skill and enthusiasm. And yet, they worry that they aren't reaching every student.

An opportunity to try something new arose when Jackson Middle School received a Bernstein Education Through the Arts (BETA) grant from the Leonard Bernstein Center. The center awarded the school $30,000 a year for three years to integrate arts into its core curriculum. Lang and Reiner subsequently designed a geometry unit on tessellations involving mathematics, visual art, and dance. Neither had done this kind of thing before, and planning the new unit took a considerable amount of their time-about 20 hours stolen from the school day, afternoons, and weekends. Nevertheless, they shared an emerging conviction that art could be a key to mathematical understanding for many students.

For Reiner, watching his students work with a choreographer on their movement tessellations was a memorable moment in his career as a mathematics teacher.

"Keith [Goodman] asked the kids to come up with some movement pattern using certain mathematical concepts, and every one of those 16 groups of students immediately began working," Reiner says. "I was amazed. I never thought eighth-grade students would be so uninhibited and would come up with such concise and amazing movement patterns.

The teachers' primary goals for the project were that students would understand the geometry of polygons-angle measurements, regular and semiregular polygons, and how polygons tessellate-and that students would make a connection between these mathematical concepts and the real world.     more...