Symbol sense with a symbolic-graphical system: a story in three rounds

The paper consists of a trilogy of high-school teachers solving an algebraic problem while learning to use a Computer Algebra System (CAS) in 1995, 1998, and 2001. The different approaches the teachers used and the ways the symbolic-graphical software influenced their solution process are discussed in terms of theoretical views on “symbol sense,” and regarding the notion of “instrumentation” developed among the CAS-in-education community. Two epistemological perspectives of symbol sense that were involved in the creation of instrumentation schemes were identified: (a) awareness of the special ways that the CAS software utilizes (makes sense of) symbols in algebraic manipulations and in implicit plotting, and (b) the need to make explicit the algebraic interpretations of sophisticated graphs in relation to the context of the problem. Consequently, the instrumentation schemes led to the development of advanced symbol sense.