Small number estimation in undergraduate college students and applications to understanding fluid-Earth science

The geoscience education research community has invested in research of students’ understanding of large magnitudes as it applies to deep time and worked to apply findings to improve teaching and learning in geology courses. Building on this research and encouraged by efforts to expand beyond studies of solid Earth science, we posit that fluid-Earth sciences such as oceanography and atmospheric science require facility with small numbers and suggest that parallel investigations of students’ understanding of small numbers would broadly support geoscience education, while adding to emerging cognitive science theory of how individuals conceptualize and estimate small magnitudes. We reviewed textbooks from oceanography, atmospheric science, and geology as proxies for small number use in introductory courses. We found in the introductory level textbooks we reviewed, oceanography and atmospheric science use small numbers and small units at a rate of two to three times that found in geology. We conducted two number line experiments (Experiment 1, N = 185; Experiment 2, N = 80) to identify student errors with small number estimation and compared error patterns to large number estimation and previous work. Our findings include a pattern of overestimation at smaller values and underestimation at larger values within small magnitude categories. These patterns are consistent with less variability when estimating familiar magnitudes and greater variability when estimating unfamiliar magnitudes. We conclude that learning about small scale Earth processes may be as challenging for students as learning about geological time scales and propose that investigations into student understanding of small numbers are likely to yield education and cognitive science insights as valuable as those from prior investigations of large numbers.