Identifying a framework for graphing formulas from expert strategies

Abstract

It is still largely unknown what are effective and efficient strategies for graphing for-mulas with paper and pencil without the help of graphing tools. We here propose atwo-dimensional framework to describe the various strategies for graphing formulas withrecognition and heuristics as dimensions. Five experts and three secondary-school mathteachers were asked to solve two complex graphing tasks. The results show that theframework can be used to describe formula graphing strategies, and allows for differenti-ation between individuals. Experts used various strategies when graphing formulas: somefocused on their repertoire of formulas they can instantly visualize by graphs; others reliedon str..