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This study investigated novice mathematics teachers participating in an online teacher education course focused on covariational reasoning and understanding the behavior of functions. The analysis centered on documenting the emergence of participants’ sociomathematical norms for engaging in online asynchronous discussions. In this paper, we characterized participants’ initial mathematical discourse and documented two emergent sociomathematical norms, namely explaining why and emergent shape discourse. When participants explained why, they used specific quantities or symbolic representations of functions to justify why function graphs have particular visual features. When participants engaged in emergent shape discourse, they coordinated change between covarying quantities to justify why function graphs behave in certain ways. This study provides evidence that online settings can provide context for mathematics teachers engaging in legitimate collaborative mathematical activity and that activity can be enhanced by participation in discourse featuring specific sociomathematical norms. We discuss conjectures regarding the potential of reflective discussion activities paired with the Notice and Wonder Framework to support the emergence of generative sociomathematical norms. We also discuss potential relationships between characteristics of participants’ mathematical discourse and their membership with the core and periphery of a social network. 

Virtual professional development increases meaningful and diverse learning opportunities for in-service teachers (Darling-Hammond & McLaughlin, 2011). As part of virtual professional development the participants in this study engaged in doing math collaboratively and began thinking about mathematical and pedagogical decision making within their classrooms. Preliminary results suggest that participants valued the time to think flexibly about their own work and that of others and began to learn to recognize the hidden decisions they were making when solving a problem that it may benefit their students to know. 

This paper reports on a correlation analysis of two cohorts of mathematics teachers’ patterns of participation in online asynchronous discussions and their persistence in a sequence of professional development workshops. Findings indicate that increased access to colleagues’ knowledge resources and more frequent dispersion of these resources across the social network related to persistence. We discuss how variations in the design of our online workshops may have impacted teachers’ potential to persist in the professional development. The findings have implications for network-based instructional strategies that could increase mathematics teachers’ potential to persist in online professional developments. 

Understanding and utilizing the Five Practices for Orchestrating Productive Mathematics Discussions (Smith et al., 2009; Stein et al., 2008) has grown in importance as teachers continue to be challenged to engage their students in student-centered, discourse-based instruction. We argue that by engaging in rehearsals of the five practices and decomposing practice, the teachers are not only able to advance their understandings of each of the five practices, but also gain knowledge of its value in their classroom practice and its role in the supporting student development. Preliminary results from analysis of our online professional development suggest that participants learned more about utilizing the five practices within their classrooms and are able to share the role they believe it has in their classroom practice. 

Understanding how to design online professional development environments that support mathematics teachers in developing mathematical and pedagogical knowledge is more important than ever. We argue that productive social and sociomathematical (SM) norms have benefits for teachers learning mathematics in online asynchronous collaboration and that particular patterns in interactions can create context for the emergence of such norms. We employed social network analysis to compare the emerging social networks of two iterations of an online asynchronous professional development course focused on functions to understand whether particular scaffolds can support the emergence of specific patterns of interactions. Results suggest that evidence-based noticing and wondering can impact the “small world” properties of a social network and associated potential for the emergence of social and SM norms. 

The EnCoMPASS project (Emerging Communities for Mathematical Practices and Assessment) at Drexel University has produced a web-based software tool for the assessment of student work. This paper discusses research on the impact of this tool on teachers’ attitudes toward engaging with students in the software environment. The tool supports teachers adopting a more dialogic perspective towards learning and teaching through cycles of problem solving, discussion and mathematical development. It is suggested that the tool aids teachers’ transition toward this more interactive approach to teaching mathematics while also acknowledging and addressing concerns about the time it takes to engage in more detailed dialogue and thinking about mathematics with their students.