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A geometric path to the concept of function. (English)
Math. Teach. Middle Sch. 17, No. 1, 48-55 (2011).
Summary: The concept of "function" spans elementary school through high school. When introducing the topic to elementary school and middle school students, the authors ask them to work with a variety of examples and representations of functions, since a formal definition of a function is rather abstract. They give the most accessible geometric functions completely different names: "transformations" and "loci". A transformation, or a locus, takes a geometric object as input and produces a related geometric object as its output. These mathematical operations fit the definition of a function in a way that is readily accessible to middle school students and provide an important opportunity to expand and deepen their ideas about functions. When students explore such functions in a dynamic environment, they encounter the behavior of functions through the continuous variability of the input and output. This article discusses and provides examples of how exploring transformations and loci using dynamic geometry software, in this case The Geometer’s Sketchpad[R], can expand students’ thinking about functions and encourage them to progress to a more sophisticated, abstract concept of these mathematical objects. (Contains 5 figures.) (ERIC)
Classification: I23 G53
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