Teaching About the Graphs of Functions with Hand-held Technology

Abstract

Students have difficulties in understanding graphs of functions. We have observed that our night school students frequently have no idea what the graphs are representations for. What are the relationships between the graphs and (analytically defined) functions? Do the functions have anything to do with the real life situations? Do their graphs? In this paper we present the results of a test designed to see if students were making these conceptual connections. We present their answers, and categorize their answers according to a certain framework intended to roughly measure their mathematical sophistication. Some discussion is given. We then discuss some calculator-aided activities which we hope will increase interest in learning to draw the graphs of functions and in turn will improve students' performance as measured by this type of test.