Deciding Optimal Experiences in Coordinate Geometry for Pre-Service Elementary School Teachers

Abstract: This study was undertaken to determine if more advanced coordinate geometry topics could be integrated into a mathematics course for prospective elementary school teachers. The topics were incorporated into a series of interactive computer activities that pre-service teachers completed as part of their mathematics coursework. Results showed that the introductory activities with dynamic graphs and concluding activities with iteratively defined functions were less challenging for the future teachers than were activities involving functional attributes and composite functions. Several recent research studies have demonstrated the usefulness of technology as a powerful tool that can enable students to: (1) make meaningful connections between symbolic and graphic representations of functions; (2) develop a greater understanding in generating and coordinating multiple representations of functions; and (3) exhibit greater evidence of a transition from an operational to a structural understanding of functions (Kordaki and Potari, 2002; Hollar and Norwood, 1999; O’Callaghan, 1998). Other studies (Chinnappan, 1998; Adams, 1997) have related the difficulties experienced by their subjects, many of whom were prospective teachers, on a multitude of tasks related to characteristics of functions. Implications in these studies have emphasized the need to devise learning environments that make functional relations more prominent. Abramovich and Brouwer (2003), Pandiscio (2002), an