| A secondary mathematics teacher's understanding of teaching with the graphing calculator was studied with respect to the relation between changes in her teaching and what happened in her classes when the graphing calculator was used as an everyday instructional tool. Classroom observations of two college preparatory courses and interviews with the teacher were the main data-collection methods.;The teacher's descriptions of changes in her teaching were analyzed into four components based on Goldsmith and Schifter's model for teacher transition: qualitative reorganization of understanding, orderly progression of changes, mechanisms and sociocultural contexts, and motivational and dispositional factors. From the findings of the study, another component, teacher understanding of students, was added to the model.;With the advent of the graphing calculator, the teacher repositioned herself as an orchestrator of mathematical activities in the classroom. The changes in her teaching showed not a unitary progression but a sequence of continual restructurings of her practice. The mechanisms for transition arose from the interplay of various forces such as ideas from Standards-based reform, collegial support, and her understanding of the changes in her students and society. The transition included the teacher's motivation and disposition, which helped her undertake change and kept her curious about other ways of teaching.;In each of the two courses, ten teaching techniques with the graphing calculator were identified. The techniques showed clearly how the use of the calculator was changing the ways in which mathematics was being taught. In the second-year algebra course, the teacher emphasized not only the graphing approach, but basic algebraic skills as well as connecting algebraic and graphing approaches. In the third-year algebra and trigonometry course, she did many mathematical experiments and tested the students' ideas with the help of the graphing calculator.;This study documented how the graphing calculator is changing both the content and pedagogy of secondary mathematics. It revealed that teachers may have unique interpretations of reform and may use technology differently in different courses. The study provides a framework that helps research move beyond conjectures about the capabilities of calculators into the actual use of calculators in the mathematics classroom. |
