Understanding Connections between Equations and Graphs

General consensus holds within the mathematicseducation research community that functions are among the most important unifying ideas in mathematics (Romberg, Carpenter, and Fennema 1993). In fact, “it can be argued that functions form the single most important idea in all of mathematics, at least in terms of understanding the subject as well as for using it” (Dubinsky 1993, 527). Further, the introduction of algebraic and graphical representations of functions can be seen as a crucial moment in mathematics learning and represents “one of the earliest points in mathematics at which a student uses one symbolic system to expand and understand another” (Leinhardt, Zaslavsky, and Stein 1990, 2).