This study analyzes the pedagogical ideas underpinning teachers' accounts of the successful use of computer-based tools and resources to support the teaching and learning of mathematics. These accounts were elicited through group interviews with the mathematics departments in seven secondary schools in England, conducted in the first half of 2000. The central themes are organized to form a pedagogical model, capable of informing use of such technologies in classroom teaching, and of generating theoretical conjectures for future research. The thematic components of the model are summarized and related to prior research into computer use in mainstream schooling. Four themes depend most directly on exploiting affordances of information and communications technology (ICT): ambience enhanced in changing the general form and feel of a classroom activity; tinkering assisted in helping to correct errors and experiment with possibilities in carrying out tasks; routine facilitated in enabling subordinate tasks to be carried out easily, rapidly, and reliably; and features accentuated in providing vivid images and striking effects which highlight properties and relations. Three further themes depend in turn on these processes: restraints alleviated in mitigating factors inhibiting student participation; motivation improved in generating student enjoyment and interest, and building student confidence; and attention raised in creating the conditions for students to focus on overarching issues. Three final themes depend again on preceding processes: engagement intensified in securing the commitment, persistence, and initiative of students in classroom activity; activity effected in maintaining the pace and productivity of students within classroom activity; and ideas established in supporting the development of student understanding and capability through classroom activity. (Contains 24 references.) (AEF)