Students’ Initial Cognitive Processes While Comparing Two Data Sets: An Approach to Foster Conceptual Knowledge About Boxplots

Boxplots can be used to compare distributions. However, many students do not acquire conceptual knowledge relevant for such comparisons because instructional approaches often focus on procedural knowledge. In a digital learning environment, seventeen eighth-graders (unfamiliar with boxplots) faced the problem of estimating two long jumpers’ performance based on dot plots. We investigated students’ naïve preconceptions. Findings indicate that meaningful comparisons were made if students evaluated both distributions using the same criteria. Often, performance was not evaluated with just one criterion, but several were contrasted in the responses. Two intuitive ways to quantify data variability could be identified. Although many students determined which part of the distribution lies in a defined interval, only a few students intuitively considered the spread of a fixed proportion of the distribution.