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November 2005, Volume 99, Issue 4


The Tellem Weavers Meet the Graphing Calculator
S. Gould
A hands-on activity that explores weaving patterns of the Tellem people. Students can look for patterns and discuss similarities and differences between their classmates' patterns. A graphing calculator program that simulates the weaving pattern is included.

Chinese Algebra: Using Historical Problems to Think About Current Curricula
Erik Tillema
Analyzing three problems from the Jiu Zhang Suanshu, a Chinese mathematics text from the first century BCE. Each problem examines how the Chinese generated equivalent expressions, an important concept in algebra today. Historical text is be adapted thereby algebraic thinking can be honed.

Math through the Mind's Eye
Sara Fisher, Christopher Hartmann
This paper considers recommendations from the Principles and Standards for School Mathematics (PSSM) in relation to pedagogy for the visually impaired. The authors present three examples of ways that mathematics instruction for blind learners can employ representations in ways that are consistent with PSSM. In reflecting on these examples, the authors identify lessons for all mathematics teachers. The nature of these accommodations provide a new perspective on the recommendations in the PSSM.

Making Quilts without Sewing: Investigating Planar Symmetries in Southern Quilts
Holly Anthony, Amy Hackenberg
An activity for "making quilts without sewing" that enables high school students to develop their understanding of planar symmetries and wallpaper patterns. This activity incorporates the culture and traditions of quilting into the study of geometry. From the same block, students can make quilts with different patterns by using various combinations of transformations, in addition to the possible combinations of transformations that might have been used to create a quilt or wallpaper pattern. Students may also reflect upon the cultural activity of quilt makers and the art of quilt making.

Multiple Solutions: More Paths to an End or More Opportunities to Learn Mathematics
Rose Zbiek, Jeanne Shimizu
Similarities and differences among multiple solutions to two different problems (How much skin covers the human body? and How many melon balls in a melon?) and how thinking about the differences among problems and their solutions can be used to extend students' understanding of mathematical concepts and skills. The article discusses the teachers' questioning skills as they focused on the conceptual and procedural aspects of the alternative solutions. The authors noted that when the solutions differ conceptually, the conceptual diversity of solutions helps students refine their understanding of definitions and nuances of underlying concepts.

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