Secondary Preservice Teachers' Mathematical Discourses on Geometric Transformations

To uncover their knowledge and evidence of learning on geometric transformations, this study examined the nature and the development of four preservice teachers’ mathematical discourses about geometric transformations from a commognitive perspective.The design of the study was guided by the following research question: What is the nature of secondary preservice teachers' mathematical discourses on geometrics transformations, and how does their discourses change over time? This study employed a descriptive case study approach with interviews and participant-observation to understand what preservice teachers have learned during a five-week instructional unit. The commognitive framework developed by Sfard (2008) was utilized to analyze preservice teachers’ mathematical discourses. Data analysis revealed that various types of keyword use (e.g., operational word use, structural word use), routines (e.g., identification routines, specification routines), and narratives (e.g., geometric transformations as reflection and rotation; geometric transformations as one-to-one and onto functions) emerged from preservice teachers’ discourses on geometric transformations, which illustrated the complex nature of their discourses. In addition, preservice teachers’ discourses on geometric transformations shifted toward an objectified and mathematically sophisticated direction at the end of the instructional unit. This analysis suggested that preservice teachers developed deeper knowledge about geometric transformations, and that studying preservice teachers’ learning from a discursive perspective can provide explicit indicators for observing learning.