Computer technology may be a powerful support for teaching through guided inquiry, but this process still depends on teachers who often find it difficult to carry it out in classrooms. This article examines the efforts of a group of secondary school geometry teachers to shift their instruction toward guided inquiry with the use of a computer software program called the "Geometric Supposers." The study focuses on the evolution of the teachers' concerns, and the curricular and pedagogical dilemmas they faced during their work with this innovative approach. The paper analyzes several themes in these teachers' experiences which are likely to reappear whenever teachers try to shift from the predominant recitation mode of "teaching as telling" to the widely recommended, but difficult, process of joining students in a process of constructing and critiquing. The five teachers who participated in this study were from three different schools. (YP)