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, ten years after the release of the Guidelines for the Assessment and Instruction in Statistics Education (GAISE) College Report (GAISE, 2005) and the subsequent movement to stress conceptual understanding and foster active learning in statistics classrooms, the sequence still remains a traditional, lectureintensive course. In this paper, 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. (Note: Supplementary materials, including code used to generate class plots and activity handouts, are available online.)

Improving student outcomes in high‐enrollment statistics classes with the structured writing approach

“…The structure of the writing assignment broadly follows stages of Bloom's taxonomy . Each component of the structured writing assignment is related to a different stage of learning and broadly follows a related “action verb.” Giving students the task to write a short explanation of a concept from the course and including a brief example, real‐life context, or scenario is not uncommon in statistics classrooms (eg, Callingham et al ; Stromberg & Ramanathan, ; Green and Blankenship ). The novelty of our assignment is its very specific imposed structure combined with the inclusion of a novice, lay audience.…”

“…Giving students the task to write a short explanation of a concept from the course and including a brief example, real-life context, or scenario is not uncommon in statistics classrooms (eg, Callingham et al [23]; Stromberg & Ramanathan, [19]; Green and Blankenship [24]). The novelty of our assignment is its very specific imposed structure combined with the inclusion of a novice, lay audience.…”

The Use of Technology in Statistics Courses

“…There have been many institutions that have used technology in these undergraduate calculus based statistics course. Some examples are the use of in-depth cases studies and statistical software [5], [6] and [7] and the use of statistical software to enhance students understanding of concepts [8] and [9]. Also another institution implementing the use of personal laptops in the classroom [10].…”

Math anxiety: the impact on traditionally underserved and marginalized adult female undergraduate students in elementary statistics

“…The researchers reported positive outcomes including a change in perception that statistics was not strictly mathematics as instruction but that it was focused on establishing "connections" (p. 324) to real world scenarios rather than simply delineating "disparate mathematical facts" (Green & Blankenship, 2015, p. 324). Additionally, despite the reduced association to the more linear mathematical concepts of statistics, students were well prepared, if they chose, to proceed to graduate statistical courses that were more mathematically concentrated (Green & Blankenship, 2015).…”

“…Green and Blankenship (2015) asserted that, although the 2005 GAISE reforms provided a plan for reform, lack of a concrete plan would slow implementation. The purpose of their study was to create awareness for educators of the role they play in integrating student understanding with pedagogy, and how best to accomplish that goal (Green & Blankenship, 2013).…”