Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice

The idea of ‘interpretative flexibility’ underpins new approaches to studying technological artefacts and curricular resources in use. This paper opens by reviewing – in this light – the evolving design of dynamic geometry, its pioneering use within classroom projects, and early sketches of its mainstream use in ordinary classrooms. After examining curricular context and its instrumental dimension, the paper then reports a study of teacher constructions of dynamic geometry in classroom practice, conducted in professionally well-regarded mathematics departments in English secondary schools. From departmental focus-group interviews, four teacher-nominated examples of successful practice were selected for study in depth through lesson observation and post-lesson interview. Iterative thematic analysis was employed, first to establish a narrative outline of each case, and then the ideas and issues salient across cases. The study illustrates the interpretative flexibility surrounding the emergent use of dynamic geometry. It found important differences in practical elaboration of the widespread idea of employing dynamic geometry to support guided discovery. The process of evaluating the costs and benefits of student software use was influenced by the extent to which such use was seen as providing experience of a mathematical reference model, and more fundamentally as promoting mathematically disciplined interaction. Approaches to handling apparent mathematical anomalies of software operation depended on whether these were seen as providing opportunities to develop students’ mathematical understanding, in line with a more fundamental pedagogical orientation towards supporting learning through analysis of mathematical discrepancies. Such variation was associated with differences in positioning dynamic geometry in relation to curricular norms and in privileging a mathematical register for framing figural properties. Across all cases, however, incorporating dynamic manipulation into mathematical discourse moved implicitly beyond established norms when dragging was used to focus attention on continuous dynamic variation, rather than being treated as an efficient means of generating multiple static figures.