Dynamic Attributes of Functions in Content Courses for Future Teachers

Abstract

Teaching experiments assessed the efficacy of using a sequence of dynamic computer activities to enhance prospective elementary school teachers' knowledge of functions. Based on earlier findings that activities involving characteristics of functions were more challenging for these students, a follow-up implementation of the sequence focused on enabling students to characterize and compose functions more effectively. Results indicated that students' performance on activities involving domain and range, functional parity, and composition of functions improved from earlier to later implementations of the instructional sequence. Students' performance on activities involving functions of distance and descriptions of variables in dynamic graphs showed comparable improvements, but there was no evident change between initial and subsequent groups on activities concerned with functions of length and iterations on Cartesian coordinates of points. The results confirmed reports that technology can enable students to exhibit greater evidence of a transition from an operational to a structural understanding of functions. There was also support for earlier findings that prospective teachers explored problems more deeply with dynamic technology and that these type of activities helped future teachers understand functional attributes embedded in a coordinate geometry context. Conclusions indicated that the sequence of activities (1) constituted a learning environment that made functional relations more salient, (2) connected students' prior work in geometry with alternative representations, characteristics, and compositions of functions, and (3) used computer-generated dynamic representations to deepen and extend students' expertise with functions.