How secondary school mathematics teachers construct an understanding of 'appropriate use' of graphing calculators in the context of collegial inquiry

Mathematics reform documents urge "appropriate use" of graphing calculators in mathematics classrooms. This study examines how five secondary school teachers, working together with the researcher in four professional development study sessions, produced a shareable tool intended to help teachers make decisions about using calculators appropriately in the teaching and learning of mathematics. This AUGC (Appropriate Use of Graphing Calculators) tool was the focus of a design experiment in which iterative feedback guided both the design of the sessions and the development of the tool. The teachers' developing understanding of what was appropriate calculator use became observable in negotiation of the tool's structure and content.;Tool development was influenced by (1) teachers' perceptions of issues requiring negotiation, particularly those related to their teaching contexts, (2) teachers' prior learning experiences and exposure to new ideas, and (3) their beliefs about mathematics and about calculators. Negotiation of issues showed teachers struggling to reconcile their own understanding of mathematics in conjunction with graphing calculators with what they saw as prerequisite knowledge for student use of graphing calculators. Emergence of a very tentative communal understanding of appropriate use of graphing calculators was revealed by examining the stages of tool development. As they worked on the tool, teachers focused less on the deficiencies of their students and more on how calculator activities could be used to help students understand mathematics. Thus, their understanding of appropriate use of graphing calculators focused less on whether calculators should be used, and more on how their use can help student learning. Implications include a caution that new teachers with strong technology backgrounds do not necessarily make easy transitions to understanding the goals of calculator use in reform curricula.