A model for professional development for graphics calculator use*

A key component of any kind of mathematics curriculum change is the development of professional expertise among teachers. This paper offers an outline model of the stages through which mathematics teachers seem to pass when learning to integrate a graphics calculator into their professional practice. The model describes four developmental stages of progression: (1) Where’s the ON button? (2) Black line mastery; (3) Routine use; and (4) Curriculum change. For each stage identified, the characteristics of teacher activity are described, together with an analysis of the professional development needs characteristic of the stage. The paper concludes with some consideration of ways in which the model might be used to guide professional support programs and to understand typical problems associated with the integration of technology into the regular mathematics curriculum. Few would doubt that technology is a major influence on the mathematics curriculum today and into the foreseeable future. For mathematics education, many modern technologies have been developed and considered for educational use. However, this paper concentrates attention on the particular technology of the graphics calculator, arguably the only form of technology developed particularly for school mathematics education. The significance of graphics calculators for mathematics education rests in no small part on their accessibility, a function of their physical size, price relative to other technologies and ready portability from one educational setting to another. (Kissane, 1995). These characteristics together make it much more likely that the personal technology of the graphics calculator will be available for mathematics teachers to use and hence much more likely that technology can be regarded as relevant to curriculum development in mathematics. Availability of technology is not by itself adequate, of course, to effect changes in the mathematics curriculum. A crucial mediating factor is the teacher, and curriculum developers ignore the real needs of teachers at their peril (Kissane, 2002). Mathematics teachers need professional development directly related to graphics calculators if they are to be the main agents of reform, and ultimately directly responsible for whatever happens in the classroom. It is already clear in those countries where this sort of technology has been available for some time that sound integration of the technology into the curriculum does not come about by chance alone. This paper offers a tentative theoretical model for thinking about the various stages through which mathematics teachers progress in order to incorporate the technology appropriately into their practice. The model describes four identifiable stages, based mostly on the author’s experiences of being involved in activity of this kind over the past decade. It is proposed that the key features of each stage are identifiably different, and that care is needed to recognise the stage of development in which teachers are located in order to plan professional development accordingly. Outcomes to be attained at the end of each of the first three stages are identified, and it is suggested that these provide a signal that movement has taken place from stage to stage. The model rests on the author’s belief that technology ought be integrated into the curriculum, rather than being regarded as an optional extra, so that it is a key element in the everyday practice of teachers and their pupils and is adequately taken into account when curricula are devised or developed. To date, empirical data have not been formally collected in order to validate the model, although it does rest in part on various professional conversations over at least the past decade about the needs of teachers in relation to graphics calculators. It seems important to explicate and develop a theory before it is tested empirically, however. Table 1 offers a brief summary of the model, which is described in a little more detail in the remainder of the paper, followed by some suggestion for its use and further development. Table 1: A summary of the model Stage Outcome Teacher activity Professional Development