Undergraduates’ use of examples in online discussions

• Students used examples to communicate and share ideas.
• Students used examples to express disagreements.
• Students used examples to satisfy nested there-exist quantifiers.

Recent literature has examined undergraduate example use and production in response to researcher-generated generalizations, which did not include nested there-exist quantifiers. This article explores undergraduate students’ example use or production in response to a task in which students must develop their own claims, which at times involved nested quantifiers. The study uses on-line conversations of undergraduates in pursuit of a shared goal to identify constructive uses not necessarily directly linked to proof production. Findings include that undergraduates voluntarily used examples constructively to develop shared understandings of tasks and definitions, communicate approaches, express disagreements, and satisfy there-exist quantifiers nested in definitions and generalizations.