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Paul Laumakis

Students bring the real world into the classroom by studying speeding data collected on two Pennsylvania highways.

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Marlena Herman and Paul Laumakis

Instructional standards promoted by the National Council of Teachers of Mathematics (NCTM) include the ideas that students at all levels should understand patterns, relations, and functions; represent and analyze situations with mathematical models; and analyze change in various contexts (NCTM 2000). Incorporated in these general standards are more specific expectations for the various grade levels that involve the use of words, tables, graphs, and equations for expressing mathematical relationships, with a focus on linear relationships at the middle school level and other classes of functions at the high school level. Past research shows that students' ability in these areas tends to be more procedural than conceptual. With respect to graphing abilities, for example, students have been able to produce graphs from ordered pairs but have insufficient ability to interpret graphs, even at the college level (Mokros and Tinker 1987). In a review of more recent studies, Skalsky and Pastel (2004) claim that many students enter college without an adequate grasp of how relationships are depicted by graphs; they have difficulties interpreting graphs and connecting graphs to real-world phenomena.