How mathematicians assign homework problems in abstract algebra courses

How mathematicians characterize and attempt to develop understanding of concepts and definitions in proof-based courses

“…To an extent, these activities and approaches might be viewed as good advice applicable across most learning contexts. However, while lists of activities included doing the homework, prior work (Rupnow et al, 2021) argued that mathematicians crafted homework with different learning goals, and different mathematicians believed that students would learn different things from doing the same problem. Thus, while instructors shared a common "activity," even if the assigned problems were the same, the participants would be unlikely to hold the same learning goals for the particular homework assignment.…”

“…Fundamentally, mathematicians engage in their daily instructional practice based on their experience as learners and teachers-they are teaching a specific audience in a specific subject and consider what they consider to be "normal" classroom activity for the course in designing their lessons. For example, there is a "convergence" around the "right" number of homework problems to assign in a proof-based class (c.f., Rupnow et al, 2021), that balances the desire to promote student understanding with their willingness and ability to complete the work. Similarly, the genre of chalk-talk is remarkably similar across cultures and countries, and within the United States lectures are generally very similar in terms of structure, pacing, and the types of content and pedagogical practices engaged (c.f., Artemeva and Fox, 2011;Fukawa-Connelly et al, 2017;Johnson et al, 2018).…”