Fostering Conceptual Understanding in Mathematical Statistics

Abstract

In many undergraduate statistics programs, the two-semester calculus-based mathematical statistics sequence is the cornerstone of the curriculum. However, 10 years after the release of the Guidelines for the Assessment and Instruction in Statistics Education (GAISE) College Report, 2005, and the subsequent movement to stress conceptual understanding and foster active learning in statistics classrooms, the sequence still remains a traditional, lecture-intensive course. In this article, we discuss various instructional approaches, activities, and assessments that can be used to foster active learning and emphasize conceptual understanding while still covering the necessary theoretical content students need to be successful in subsequent statistics or actuarial science courses. In addition, we share student reflections on these course enhancements. The course revision we suggest doesn't require substantial changes in content, so other mathematical statistics instructors can implement these strategies without sacrificing concepts in probability and inference that are fundamental to the needs of their students. Supplementary materials, including code used to generate class plots and activity handouts, are available online.