ABSTRACT
Recent efforts to improve students’ conceptualizations of functional relationships as described by graphs have emphasized the need to move beyond plotting and reading points to interpreting the global meaning of a graph and the functional relationship that it describes. Some instructional approaches show promise for improving students’ qualitative understanding of graphs that describe aspects of familiar physical phenomena. The availability of function-plotting software has raised the possibility of visual representations of algebraic functions playing a more important role in mathematical reasoning, but new instructional models are needed to encourage graphical reasoning. Educators should be aware of, and attempt to minimize, common misconceptions among students using function-plotting tools. Given that changing perceptions and evolving ideas are a normal part of learning, students also need to develop a capacity for recognizing and resolving apparent contradictions and refining mathematical reasoning through experience.
