How Long Is Its Projection?

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  • 1 Valdosta State University in Valdosta, Georgia
  • | 2 University of Oklahoma in Norman, Oklahoma

PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS (NCTM 2000) is designed around the idea of integrating content and process skills in teaching and learning mathematics. A curriculum is envisioned in which the content is taught through problem solving, communicating, and making connections. In the Grade 6–8 Standards, one key idea that connects much of the content is proportionality: “Proportionality connects many of the mathematics topics studied in grades 6–8” (NCTM 2000, p. 217). For example, in this digital age, numerous students have access to equipment for enhancing photographs, including stretching and shrinking. Proportional reasoning is an important idea in the manipulation of such objects and involves distinguishing between changes that occur in both one-dimensional, or linear (length), and two-dimensional space (area) as well as the development of the mathematics of similarity. Textbooks typically equate proportions with the cross-products rule, which states that the “product of the extremes equals the product of the means.” In other words, if a/b = c/d, then a × d = b × c.


SANDRA DAVIS TROWELL is interested in how students learn mathematics as well as in problem solving.

ANNE REYNOLDS interests include students' mathematical thinking and how imagery supports problem solving.

Mathematics Teaching in the Middle School
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