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Our paper explores the differences between online and traditional, in-person teaching and learning modalities, looking specifically at courses preparing teachers to be mathematics teacher leaders. In the context of current research on the teaching and learning of mathematics in an online setting, we share our own experiences. We describe the preparation for and teaching of online mathematics, focusing on establishing norms and the use of technology. The changing teaching and learning opportunities of the 21st century require discussion of these vital issues. We include stories of interactions between candidates and teachers and among groups of candidates in mathematics courses, detailing not just the discursive and work-sharing tools but the nature and nuance of these interactions and how they mediate mathematics learning. We share our online teaching and learning experiences, drawing on research to frame our impressions. By identifying key similarities and differences between instructional modalities and by reflecting critically on our own successes and challenges, we present a vision of online teaching and learning for mathematics courses, in particular those for mathematics specialists, that can be effective, inclusive, and relational.





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