Prototypes: Brakes or levers in learning the function concept? The role of computer tools

Prototypes are used as references to cope with new examples in concept learning. Prototypes can, however, be detrimental to concept learning, as shown in the use of linear functions for learning the function concept. This research characterizes students' function concept images that arise in an interactive environment based on multirepresentational software. We capitalize on a 20-year curricular program to contrast the concepts students develop in this environment with those developed in traditional environments. We show that students who are learning functions in the interactive environment (a) often use prototypic functions (linear and quadratic) but do not consider them as exclusive, (b) use prototypes as levers to handle a variety of other examples, (c) articulate justifications often accounting for context, and (d) understand functions' attributes.