This chapter describes how the authors structured effective online mathematics content courses for pre-service teachers (PSTs) using the promoting higher student mathematics achievement in online settings (PHiSMAOS) conceptual framework. This framework focuses on the mathematics teacher educator (MTE) view from which they are using their technological content knowledge (TCK) to develop their PSTs' own technological knowledge (TK), content knowledge (CK), and TCK when in an online mathematics classroom setting. The PHiSMAOS conceptual framework then wraps this reality in the concepts of growth mindset and productive struggle, providing a pragmatic way for MTEs to productively promote growth mindset in PSTs' mathematics content classrooms in online settings. This framework was developed using grounded theory research techniques from data consisting of exit cards, video-recorded discussions, assignments, and test scores across seven semesters of the authors' courses. Implications for MTEs, use in K-12 settings, and further research are also discussed.
The Effects of Problem Based Approach on Student's Conceptual Understanding in a University Mathematics Classroom
