Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students' reasoning about variability in different contexts. However, there is a lack of research on students' development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an introductory college-level statistics course. This exploratory case study conducted three interviews with each of the ten participants through a four-month period, at the beginning, middle, and end of the course. The Structure of Observed Learning Outcomes (SOLO) taxonomy was used to analyze participants' responses. Results indicated that overall the group of participants demonstrated a stable understanding of variability over the semester (i.e. lack of improvement). However, when examining each student's reasoning, four types of reasoning development paths were found: improvement, lack of change, decline, and inconsistent. This study provides implications in teaching college introductory statistics course and recommendations for future research.

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This study developed a teaching module that incorporated the Monty Hall problem to introduce conditional probability in a college introductory statistics course. This teaching module integrated a guess – experiment – discussion approach with game-based instruction. The researchers piloted this module and made modifications. The work of 20 non-mathematics major undergraduate students was examined for changes in their perceptions about conditional probability through a pre-and-post survey design. The Structure of the Observed Learning Outcome (SOLO) taxonomy was used for data analysis to show the quality of the student work. Findings suggest that most students’ perceptions were at higher levels after the teaching module.