How two undergraduates used examples and an Euler diagram for making and proving conjectures

Abstract

Traditional approaches to undergraduate classrooms tend to present mathematical theorems and proofs as finished products, hiding the mathematical activity that went into their development. In this study, we crafted opportunities for two undergraduate students in a teaching experiment setting to engage in the activity of making and proving their own conjectures. We investigated how these students (with the guidance of a teacher-researcher) used an Euler diagram and examples to support their conjecturing and proving activity. The students’ evolving Euler diagram served as an organizer for their examples, allowing them to capture particular instances of the concepts and structural relationships between the concepts. By identifying different ways that the students leveraged this evolving Euler diagram with their examples, we provide insight about beneficial tools for students to engage in such mathematical activity.