Graphing formulas: Unraveling experts’ recognition processes

Abstract

An instantly graphable formula (IGF) is a formula that a person can instantly visualizeusing a graph. These IGFs are personal and serve as building blocks for graphing formulasby hand. The questions addressed in this paper are what experts’ repertoires of IGFs are andwhat experts attend to while recognizing these formulas. Three tasks were designed andadministered to five experts. The data analysis, which was based on Barsalou and Schwarzand Hershkowitz, showed that experts’ repertoires of IGFs could be described using functionfamilies that reflect the basic functions in secondary school curricula and revealed thatexperts’ recognition could be described in terms of prototype, attribute, and part-wholereasoning. We give suggestions for teaching graphing formulas to students.