for the learning of mathematics

an international journal of mathematics education

Kathleen Melhuish ,  Cody L. Patterson ,  Paul C. Dawkins - Vol. 45 Num. 3 (2025)
 Can consuming mathematics be compatible with inquiry?

9-13
 ABSTRACT:

Inquiry-based instruction in undergraduate mathematics is commonly characterized by students producing mathematical content (e.g., definitions, theorems, or proofs) rather than consuming it. In this paper, we argue that a production-centered view of inquiry is unnecessarily restrictive and limits the full range of disciplinary activity available to students. Drawing on Dewey’s notion of inquiry as transformation, we propose a broader definition of inquiry that centers on students’ use of disciplinary tools to bring clarity and coherence to unfamiliar or opaque mathematical objects, including existing proofs. We demonstrate how this lens both encompasses established inquiry models but also allows for different types of inquiry that do not rely on production but rather critical consumption. We share examples of students engaging in proof comprehension for the purpose of inquiring into general proof structures and for the purpose of inquiring into the concepts and relationships embedded in a specific complex theorem and proof. We suggest both researchers and instructors reflect on their views of inquiry and consider broader approaches.