Collaborative Research: Extending Inquiry-Oriented Linear Algebra

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With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by improving student learning in linear algebra. To accomplish this goal, the project will create research-based teaching and instructor support materials for linear algebra. This project is a collaboration between Virginia Polytechnic Institute and State University, Florida State University, Arizona State University, and Clayton State University. It aligns with national calls to engage students in learning through inquiry. To this end, it intends to help students learn mathematics by engaging in mathematical discussions, developing and testing conjectures, and explaining and justifying their thinking. The project has four main goals: (i) create four new units that integrate with and complement existing Inquiry-Oriented Linear Algebra materials; (ii) create instructional support materials for the four new units; (iii) contribute new 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. The two broad research questions for the project are: (i) What mathematical conceptions do students develop through their engagement with the tasks? (ii) What instructional moves facilitate student learning in this setting? The project has the potential to advance knowledge about and capacity for using inquiry-oriented approaches to improve undergraduate instruction in mathematics, particularly linear algebra.To accomplish its goals, the project will use a Design Research Cycle comprised of phases of Task Design, Paired Teaching Experiments (Steffe & Thompson, 2000), Classroom Teaching Experiments (Cobb, 2000), Online Working Groups (Fortune, Keene, & Hall, 2017), and Website Development. The project will extend the current Inquiry-Oriented Linear Algebra materials to include an entire introductory linear algebra course, providing a comprehensive set of supports to help instructors adopt an inquiry-oriented approach to teaching linear algebra. By focusing on new instructors and settings, the project has the potential to extend the impact of active learning and inquiry-oriented teaching to a larger number of students and institutions. Data to address the research questions will be collected from at least twelve institutions that vary in geographic location, institution type, size, and student demographics, thus enriching the diversity of the research population. Resources developed by the project and its research results will be disseminated through websites, workshops, and publications in both research and practitioner journals within mathematics and mathematics education. In addition, the project's consideration of and adherence to research recommendations regarding equity and access will promote and advance inquiry-oriented, equitable teaching practices. This work has the potential to benefit society by improving undergraduate mathematics instruction and extending the use of inquiry-oriented teaching. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.