This study examined the structure of two preservice teachers' understandings of educational software in mathematics using repertory grid techniques. Specifically, the study focused on how teacher educators can enable preservice teachers to discern the features of mathematics software, and develop pedagogical goals that reflect the affordances and constraints of available tools. Results showed a deepening of knowledge and a differentiation of knowledge following experiences of exploration, evaluation, and comparison of different types of software. Results imply that directing preservice teachers' attention to utilizing the functional characteristics of software for developing plans and for the design of instruction may be fruitful for more effective integration of software in their future teaching. However, participants' preexisting content knowledge and their pedagogical worldview tempered this effect. (Contains 8 figures and 2 tables.)