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This paper reports a qualitative study of how small group problem solving was enacted differently across sections of a multi-section undergraduate introduction to proof course. Common course materials, common guidelines for instruction, and weekly instructor meetings led by a faculty course coordinator supported similar instruction across sections, including an emphasis on in-class group work. But within that shared structure, classroom observations revealed important differences in how group work was introduced, organized, and managed. Our results focus on differences in the time allotted to group work, the rationale for group work, the selection and organization of groups, and aspects of student activity and participation. We suggest that these differences shaped different opportunities to learn proof writing in small groups. These results have implications for the design and teaching of collegiate mathematics courses where group work is a regular element of classroom work. 

This study examined how eight students in an introduction to proof (ITP) course viewed a “cheating scandal” where their peers submitted homework containing solutions found on the web. Drawing on their weekly log entries, the analysis focuses on the students’ reasoning about the difference between acceptable and unacceptable use of internet resources in learning mathematics. One pattern was that students’ view of the relationship between beliefs about mathematics and the work of learning mathematics grounded their views of “cheating.” Specifically, some felt that an implicit didactical contract required that model solutions should be available when one learned new material. The case raises the general issue of the relationship between the process of learning mathematics and the appropriate use of external resources. It suggests that instructors may need to re-examine the role of homework, especially its assessment, in their courses, so that productive struggle is valued, not avoided.