The influences of social, cognitive, and teaching presence on pre-service teachers' online engagement in productive mathematical discourse

The increase in online education has implications for mathematics teacher educators who are tasked with teaching mathematics content and pedagogy to pre-service teachers (PSTs) who do not attend on-campus. Concerns about PSTs' content knowledge continues to be an ongoing issue, and ways to address this, especially in an online environment, require further investigation. While online courses offer accessibility and flexibility, it can be challenging to translate synchronous on campus teaching and experiences into the online environment. The importance of productive mathematical discourse has been identified as an appropriate pedagogy, yet the opportunity to engage in such discourse can be limited in the online environment. This paper provides the results from a case study of an online forum, which highlights how pre-service teachers can be engaged in productive online mathematical discussions, particularly when facilitated by the instructor's and other learners' interactions and presence. The findings indicated that social, cognitive, and teaching presence influenced the nature and frequency of online mathematical discourse. The study contributes to existing research through conceptualizing how productive mathematical conversations can occur outside of the classroom setting, with implications for mathematics teacher educators who are tasked with teaching content, pedagogy and practices to PSTs.