Argumentative Knowledge Construction in an Online Graduate Mathematics Course: A Case Study

The authors report on three students' argumentative knowledge construction in an asynchronous online graduate level geometry course designed for in-service secondary mathematics (ISM) teachers. Using Weinberger and Fischer's framework, they analyzed the ISM teachers' a) geometry autobiography and b) discussion board posts (both comments and attached work including solutions to assigned problems and Geometric Sketchpad explorations) throughout an 8-week summer course. The goal was to better understand the key similarities and differences in the nature of their interaction with each other and the course content that may have contributed to the differences in their knowledge construction. Findings led researchers to re-conceptualize a rubric to (1) assist instructors in facilitating productive interaction among students, (2) prepare students to better utilize the discussion board with a critical eye, and (3) provide specific guidelines for a more productive engagement among students, using the framework as a guide.