Effects of the Use of Dynamic Visualization on Inservice Teachers’ and Graduate Students’ Content Knowledge and Pedagogical Content Knowledge of Transformations of Functions

In this qualitative study, we investigate how the use the dynamic visualization in the teaching and learning of transformations of functions effects the basic content knowledge (CK) and pedagogical content knowledge (PDK) of three teachers of high school second-year algebra and three graduate students teaching or assisting in introductory-level college mathematics courses. In audio-taped interviews, participants answered content-based and pedagocially-based questions on transformations of functions, described their observations when viewing dynamic animations related to these questions, and then answered follow-up questions on content and pedagogy. Findings suggest that both the teachers' and graduate students' descriptions conveyed visual descriptions that contradict their mathematical meanings. We discuss the ways in which the technology enhanced CK or PDK and also characterize the ways in which the technology exposed weak CK or PDK as well as influenced erroneous or non-generalizable thinking about the mathematics.