Resumen de The role of examples in teaching
Margaret Kinzel, Laurie O. Cavey, Dana C. Cox (ed. lit.), Ann M. Schlemper (ed. lit.)
Students examined a set of nine functions to determine which functions had inverses; the functions were chosen to challenge assumptions about functions and their properties. Students determined whether the functions were injective, surjective, or both (bijective). Data from students provided insight that only the functions with inverses were bijective. This type of mathematical activity served to review function concepts and provide opportunities for making significant mathematical observations, which can then be explored further or proven. Through our examination of mathematicians' uses of examples in their own mathematical work and their teaching, we expanded Rissland's example classification framework to develop a framework for the purposeful use of examples in teaching.
