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We report on an effort to vet a list of 10 student learning objectives (SLOs) for geometry courses taken by prospective geometry teachers. Members of a faculty online learning community, including mathematicians and mathematics educators who teach college geometry courses taken by prospective secondary teachers developed this list in an effort to reach a consensus that might satisfy various stakeholders. To provide feedback on the final list of 10 SLOs, we constructed and collected responses to a survey in which 121 college geometry instructors ranked a set of potential SLOs, including the 10 proposed SLOs as well as 11 distractors. The 10 SLOs were, for the most part, among the highest ranked by the sample. 

an assemblage of argumentation analytic methods that can support research about faculty learning communities interacting across substantive differences. Drawing on our research with a cross-institutional faculty online learning community, we use data to show how theories from discourse analysis, systemic functional linguistics, and argumentation modeling can be operationalized to support researchers in brooking methodological tensions, including framing argumentation as the topic of or a resource for investigation and considerations of collaborative discourse as both process and content. Our methodological findings illustrate an example of this operationalization, highlighting analysis of transdisciplinary, collaborative discourse in a community composed of instructors of college geometry courses required for pre-service teachers. We share possible uses for this methodological approach vis-a-vis research about the professional work of undergraduate mathematics education and pre-service teacher preparation.