Preservice teachers do not feel prepared to teach mathematics using technology (Smith & Shotsberger, 2001). To address this issue, we have developed a tool-based categorization of mathematics software and used it to instruct preservice teachers. Changes in thinking that occurred as a result of the course are analyzed primarily using repertory grid techniques supported by heuristic questions, reflections and Internet communication group correspondence. (Contains 1 table and 2 figures.) [For complete proceedings, see ED489538.]