Student Understanding of Linear Algebra across Quantum Information Science

About This Grant

Research in quantum information sciences (QIS) across a spectrum of forefronts, including education, is important for the advancement and national security of the United States. With the necessary rise of QIS, an important challenge in undergraduate STEM education is understanding how university students make sense of the foundational interconnectedness of mathematics in quantum, and how professors can best facilitate both deep physical and mathematical understanding in quantum instruction to ensure that all students succeed in their degree programs and have access to the quantum workforce. The purpose of the Student Understanding of Linear Algebra across Quantum Information Science project is to conduct fundamental basic research regarding student understanding at the intersection of mathematics and quantum information science across disciplines. This project has the potential to benefit society by increasing what is known about students' interdisciplinary understanding of mathematics and quantum information science, generating insight into student cognition that will be relevant to subject matter, courses, and disciplines across STEM beyond those directly investigated in the project. Results have the potential to inform best practices in QIS instruction, which in turn, supports the growth of the quantum workforce--a workforce that is increasingly critical to international competitiveness in information technology during the coming century. The project research questions are: How do students understand various linear algebra concepts that are central to quantum information science concepts across disciplines? How do students reason about and symbolize linear algebra concepts in coordination with quantum information science concepts across disciplines? These questions are pursued through qualitative analyses of interviews conducted with and written work collected from students enrolled in four QIS-focused courses that are part of an interdisciplinary Quantum Information Science and Engineering minor. These four courses include a lower-division and an upper-division physics course, a chemistry course, and a computer science course. Each of the four courses relies on a similar throughline of core linear algebra concepts, such as linear combination, matrix equations and linear operators, unitary and Hermitian matrices, orthonormality, basis and change of basis, inner product, and tensor product, and eigentheory, as well as Dirac notation and matrix notation. Data analyses will aim to characterize students' meanings for these linear algebra concepts, as well as how students leverage linear algebra in their understanding of quantum topics such as qubits and entanglement. Thus, answering the project research questions will produce explanatory, research-based knowledge about how humans make sense of core mathematical concepts and their interconnectedness with QIS beyond disciplinary lines, in contexts that underly STEM in the modern world. This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad, and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. 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.