Variables and Functions: Using Geometry to Explore Important Concepts in Algebra

Scott Steketee
Students find the concepts of variables and functions in algebra very challenging. Part of the challenge arises from the use of static media, and part arises from insufficient emphasis on how variables change and functions behave. A geometric approach provides students with experiences in which they manipulate variables directly and continuously, and in which they observe, directly and immediately, the behavior of functions as they vary the independent variables. Sketchpad ® dynamic mathematics
more » ... dynamic mathematics software makes it easy for students to create geometric variables and functions and to use them to study domain, range, composition, and inverses. Through these experiences, students can more easily progress from an atomic view of function (taking a single input variable to a single output variable) to a collective view (mapping an entire domain to an entire range).