THE GEOMETRY OF QUILTING
An example from research by Richard Lehrer, a researcher at WCER, illustrates how video analysis helps identify and promulgate best practices in K-12 teaching. Carman Curtis is a 2nd-grade teacher at Country View Elementary School in Verona, Wisconsin. Five years ago she began teaching her young pupils the concepts of symmetry using shapes the students would arrange into quilting patterns.
Curtis' "geometry of quilting" curriculum was deemed a best practice in K-12 math education, and Lehrer's team spent many days in her classroom filming her and her students. The film shows a typical classroom with 7- and 8-year-olds sprawled out over the floor, cutting pieces of colorful construction paper into squares, rectangles, and triangles. Curtis shows them a finished quilt, and they talk about how it's composed of matched sets of patterns arranged in squares. As the students put together their own sets, Curtis moves among them, asking them questions about how many shapes it will take to create a matched pattern.
She quizzes them--"Does anyone have a core-square that isn't symmetric? Could a core-square that isn't symmetric be used to make a two-by-two design?" The students' responses--often preceded by arranging the patterns in front of them to determine the correct answer--demonstrate that they're grasping the concept of symmetry. "They discover the transformations required to create symmetric patterns on their own," Curtis said.
In composing the individual patterns, her students are also learning about replication in 2-D space. "It's quite remarkable to watch them understand how a shape must be repositioned as it moves through the four quadrants of x-y defined geometric space," Curtis said. "To make a matched quilting pattern, for example, a triangle has to be flipped on its axis as it moves from quadrant to quadrant. It can't be just simply placed in the same orientation in each quilt square. The students absorb this principle in second grade, and when it resurfaces in high school math, it isn't so difficult to grasp."
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We're working to create virtual distributed communities for teacher preparation. Traditionally, it has been difficult to get scientists, teacher education faculty, and teachers in the field all involved in the production of new teachers, because it's difficult to get all these people physically together in the same room."
Greg Moses, University of Wisconsin
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