Math Teaching Seminar

Join the Math Department and the Center for Teaching, Learning, and Outreach for this math-focused, educational seminar by Juma Zevick Otieno. This talk will be about the use of STACK (System for Teaching and Assessment using a Computer Algebra Kernel) to support the teaching and learning of mathematical proof in undergraduate mathematics in Kenya and Italy. Learn about a series of initiatives that address the challenge of assessing proof understanding at scale, particularly in high-enrollment courses with limited instructional resources. At Maseno University (Kenya), we focus on the assessment of proofs in large service courses, often enrolling up to 1,000 students and taught by a single lecturer. We describe the design and implementation of STACK-based proof assessment tasks across five undergraduate courses: Linear Algebra, Measure Theory, Foundations of Pure Mathematics, Complex Analysis, and Calculus I and II. These tasks emphasize students' ability to interpret, evaluate, and reason about proofs rather than produce complete written proofs.

At the University of Trieste (Italy), we developed a collection of 22 STACK-based proof tasks for a first-year Linear Algebra course, covering topics such as diagonalisation, algebraic and geometric multiplicities, the Basis and Dimension Theorems, Gram–Schmidt, the Spectral Theorem, Grassmann's formula, and the Rouché–Capelli Theorem. The talk reflects on how the constraints of electronic assessment systems shift instructional focus from proof writing toward proof assessment and comprehension, and how this shift can support student learning outcomes in proof-based courses. We conclude by highlighting opportunities for cross-continental collaboration and future research on digital approaches to teaching and assessing mathematical proof.