Histograms: An educational eye

Abstract

Many high-school students are not able to draw justified conclusions from statistical data in histograms. A literature review showed that most misinterpretations of histograms are related to difficulties with two statistical key concepts: data and distribution. The review also pointed to a lack of knowledge about students’ strategies when solving histogram tasks. As the literature provided little guidance for the design of lesson materials, several studies were conducted in preparation. In a first study, five solution strategies were found through qualitative analysis of students’ gazes when solving histograms and case-value plot tasks. Quantitative analysis of several histogram tasks through a mathematical model and a machine learning algorithm confirmed these results, which implied that these strategies could reliably and automatically be identified. Literature also suggested that dotplot tasks can support students’ learning to interpret histograms. Therefore, gazes on histogram tasks were compared before and after students solved dotplot tasks. The "after" tasks contained more gazes associated with correct strategies and fewer gazes associated with incorrect strategies. Although answers did not improve significantly, students’ verbal descriptions suggest that some students changed to a correct strategy. Newly designed materials thus started with dotplot tasks. From the previous studies, we conjectured that students lacked embodied experiences with actions related to histograms. Designed from an embodied instrumentation perspective, the tested materials provide starting points for scaling up. Together, the studies address the knowledge gaps identified in the literature. The studies contribute to knowledge about learning histograms and use in statistics education of eye-tracking research, interpretable models and machine learning algorithms, and embodied instrumentation design.