Eye-tracking measures as indicators for a local vs. global view of data

Abstract

Comparing data distributions is a fundamental activity in statistics and a motivating learning opportunity in schools to initiate statistical thinking. Research has shown that many students tend to perceive a data distribution as a collection of individual values rather than as a conceptual entity that has certain features such as center, spread, and shape. These difficulties are reflected in students’ tendency to focus on local details of the distribution (so-called local view of data) instead of referring to differences between the distributions as a whole (so-called global view of data). While many authors refer to school students’ conceptions and difficulties related to their view of data, there is, to the best of our knowledge, no empirical study that investigated their actual viewing behavior (local vs. global) when comparing distributions. The central assumption of this study is that specific eye-tracking measures constitute indicators for the perceiving and processing of local vs. global distributional features. For this purpose, hypotheses for differences in certain eye-tracking measures (fixation count, saccade amplitude, and saccade direction) between students with a local and global view of data were theoretically derived and empirically investigated using a methodological combination of eye-tracking and stimulated recall interviews. We analyzed data of 25 sixth-grade students who each completed four items on distributional comparisons. The results showed strong positive inter-item correlations for all eye-tracking measures, indicating high internal consistency in participants’ gaze behavior across all items. Based on the analysis of the eye-tracking stimulated recall interviews, we split our sample into those students who perceived and processed global features in half or more of the items (global view) and those below that threshold (local view). In line with our theoretically derived hypotheses, students with a global compared to a local view of data had on average significantly fewer fixations, longer saccade amplitudes, and a higher relative number of horizontal saccades. These results suggest that eye-tracking can assist in identifying students’ conceptions and difficulties related to a local vs. global view of data. Implications for school practice and further research are discussed.