A student's construction of transformations of functions in a multiple representational environment

This paper reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multi-representational environment. The didactic approach to reflections, translations and stretches began with visualization exercises, and then was extended to investigate the implications of visual changes in data points, and subsequently, in algebraic symbolism. A detailed analysis of the student's work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism is presented. Two new semiotic forms are introduced as an alternative kind of algebraic symbolism and as a means to facilitate the transition to f(x) notation: covariational equations and the horseshoe display for transformations. The implications of this case for the redesign and modification of the software are discussed. © 1996 Kluwer Academic Publishers.