Advancing Students’ Proof Practices in Mathematics through Inquiry, Reinvention, and Engagement

Stephen Strand II
Assistant Professor
CSU, Chico

Need: While evidence is mounting in support of mathematics instruction that actively engages students, such approaches are still uncommon in post-secondary mathematics. There is also extensive literature demonstrating the struggles that students can have in transitioning to advanced mathematics.

Guiding Questions:
– How can instructors be supported in facilitating inquiry-based mathematics instruction?
– How can discourse protocols and other pedagogical strategies assist in realizing the potential of inquiry-based instruction to provide more equitable outcomes in advanced mathematics courses?
– How can students be supported in reinventing the foundational concepts, definitions, axioms, and theorems of introductory real analysis?
– How can artifacts and processes inspired by the history of mathematics be leveraged to support students’ reinvention of real analysis concepts?

Outcomes: Project deliverables include 1) two new proof modules to accompany existing modules focused on group theory and real analysis, 2) customizable online instructor support materials (OISM), 3) an online Wiki-style textbook (Wiki-text), and 4) a professional development workshop (PD workshop). The ASPIRE in Math materials are being developed using a design research methodology with the goal of supporting a network of individuals and institutions interested in providing their students with an engaging transition to advanced mathematics.

Broader Impacts: The project has the dual aims of 1) supporting students in transitioning to advanced mathematics and 2) supporting instructors in transitioning to inquiry-oriented instruction. The ASPIRE in Math resources are being intentionally designed to promote instruction that equitably engages students in mathematical inquiry thus broadening the impact of the innovative curricular materials inside each classroom. Recognizing the challenges in transitioning to this mode of instruction, our PD workshop is being intentionally designed to support instructors, both in working with our specific materials and in developing their own teaching practice to include more inquiry-oriented tools and perspectives.

The purpose of this poster will be to present the project’s current progress on our four project deliverables. In particular, for each deliverable we will 1) provide a description and example(s) that outline its goal and current form, 2) discuss our process for its design and redesign particularly highlighting the iterative process of the design research methodology, and 3) present reflections on the deliverable from students and/or instructors who have participated in a course that implemented our materials. Data for these reflections will come from post-interviews and surveys that were administered to both students and instructors after each course and PD workshop. These reflections will be used to highlight both how they informed redesigns of our material and the impact our materials have had on students’ and instructors’ perceptions of inquiry-oriented learning and teaching. We hope our poster provides an overview not only of our project’s work but also of the impact our projects’ deliverables can have on the future of proof-based mathematics courses.


Sean Larsen, Portland State University; Tenchita Alzaga Elizondo, Portland State University