How students interpret and enact inquiry-oriented defining practices in undergraduate real analysis

• Investigation of student's frames for defining in inquiry-oriented college class.
• Identifies four categories of students’ conceptions of the defining situation.
• Students’ frames for defining influenced their sense of authority in the classroom.
• Students acting as mathematicians identified meta-mathematical values for defining.
• All students reported that the engaging in defining yielded benefits to learning.

This study investigates the influence of inquiry-oriented real analysis instruction on students’ conceptions of the situation of mathematical defining. I assess the claim that inquiry-oriented instruction helps acculturate students into advanced mathematical practice. The instruction observed was “inquiry-oriented” in the sense that they treated definitions as under construction. The professor invited students to create and assess mathematical definitions and students sometimes articulated key mathematical content before the instructor. I characterize students’ conceptions of the defining situation as their (1) frames for the classroom activity, (2) perceived role in that activity, and (3) values for classroom defining. I identify four archetypal categories of students’ conceptions. All participants in the study valued classroom defining because it helped them understand and recall definitions. However, students in only two categories showed strong acculturation to mathematical practice, which I measure by the students’ expression of meta-mathematical values for defining or by their bearing mathematical authority.