Need: This project aims to serve the national interest by improving student learning in linear algebra. It aligns with national calls to engage students in learning through inquiry. To this end, it helps students learn mathematics by engaging in mathematical discussions, developing and testing conjectures, and explaining and justifying their thinking.Guiding Question: The project has four main goals: (i) create four new units that integrate with existing Inquiry-Oriented Linear Algebra materials; (ii) create instructional support materials for the four new units; (iii) build knowledge through empirical research about student reasoning and effective inquiry-oriented instructional practices in linear algebra; and (iv) foster inquiry-oriented instructional practices in undergraduate mathematics. To accomplish its goals, the project introduces the Design Research Spiral comprised of five phases: Task Design based on Realistic Mathematics Education (Freudenthal, 1991), Paired Teaching Experiments (Steffe & Thompson, 2000), Classroom Teaching Experiments (Cobb, 2000), Online Working Groups (Fortune & Keene, 2021), and Website Development. The project extends the current Inquiry-Oriented Linear Algebra materials, providing supports for instructors adopting an inquiry-oriented approach to teaching linear algebra. The project’s broad research questions are: (i) What mathematical conceptions do students develop through their engagement with the tasks? (ii) What instructional moves facilitate student learning in this setting? Outcomes: Thus far, the team has designed and tested student-facing materials for all four instructional units focused on solutions to linear systems, determinants, subspaces, and least squares; final refinements of these materials are underway. The team has drafted instructional support materials for three of the four units, and it anticipates completing these for all four units within the next year. The team has disseminated findings through one published practitioner article, one book chapter accepted for publication, one research paper under review, and two peer-reviewed conference papers. Additionally, over a dozen presentations at national and regional conferences, two workshops, and four online workgroups have been conducted by the research team to disseminate project findings. Through these efforts we have fostered inquiry-oriented practices in linear algebra, and we aim to continue this work over the next year.Broader Impacts: This project works to benefit society by improving undergraduate mathematics instruction and extending the use of inquiry-oriented teaching. By extending the current curriculum products and instructor support materials to comprise an entire introductory linear algebra course, we provide a more comprehensive set of supports for instructors who want to adopt an inquiry-oriented approach to teaching linear algebra. By working to impact new instructors and settings, we have the potential to increase the impact of active learning and inquiry-oriented teaching to both a larger number of students and institutions. The project enhances the infrastructure for research and education by fostering collaborations among the four U.S. academic institutions of the PI team. In addition data has been collected at institutions which vary in geographic location, institution type, size, and student demographics providing diversity in the research population. The project’s consideration of and adherence to research recommendations regarding equity and access will promote and advance inquiry-oriented, equitable teaching practices.
Michelle Zandieh, Arizona State University; Christine Andrews-Larson, Florida State University; David Plaxco, Clayton State University