id: 05957930
dt: j
an: 2012a.00571
au: Steketee, Scott; Scher, Daniel
ti: A geometric path to the concept of function.
so: Math. Teach. Middle Sch. 17, No. 1, 48-55 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I23 G53
ut: functions; geometric transformations; concept formation; computer software;
educational technology; computer uses in education; misconceptions;
algebra
ci:
li: http://www.nctm.org/publications/article.aspx?id=30479
ab: 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 Geometerâ€™s Sketchpad[R], can expand
studentsâ€™ thinking about functions and encourage them to progress to
a more sophisticated, abstract concept of these mathematical objects.
(Contains 5 figures.) (ERIC)
rv: