Spatial Foundations of Science Education: The Illustrative Case of Instruction on Introductory Geological Concepts

Abstract To study the role of spatial concepts in science learning, 125 college students with high, medium, or low scores on a horizontality (water-level) spatial task were given information about geological strike and dip using existing educational materials. Participants mapped an outcrop's strike and dip, a rod's orientation, pointed to a distant building and north, and completed 3-dimensional horizontality and verticality tasks. Many students, particularly those with low water-level scores, experienced difficulty on both field and laboratory tasks and failed to use good field-observation strategies. Error patterns implicated roles of cognitive regularization of the environment, embodied spatial cognition, and map experience. Data relating performance to participants' spatial skills, gender, self-reported confidence in responses, spatial awareness, and strategy use suggest a range of instructional approaches. ACKNOWLEDGMENTS The research reported here was funded by the National Science Foundation in grants to Liben and Kastens (REC04-11686 and REC04-11823, respectively). All opinions, findings, conclusions, and recommendations are those of the authors and no endorsement from the National Science Foundation should be inferred. This is Lamont-Doherty Earth Observatory Contribution No. 7418. Portions of this research were presented at meetings of the Association for Psychological Science, New York; American Educational Research Association, New York; National Science Foundation, Arlington; Geological Society of America, Philadelphia; and the Workshop on Spatial Cognition, Evanston. The authors thank Linda Pistolesi for preparing the figures; Eva Pell, Rodney Erikson, and the Office of Physical Plant for facilitating the outcrop installation at Penn State; John Sindt of the Lamont-Doherty Instrument Shop, for machining the models for the laboratory tasks; the Penn State Cognitive and Social Development lab—especially Kevin Fomalont, Michael Kilcoyne, and Hillary O'Neill—for their dedicated work in data collection, scoring, and entry; Hoben Thomas for his expert consultation on statistical analyses; and two anonymous reviewers for their helpful and thought-provoking comments. Lynn S. Liben and Adam E. Christensen are with the Department of Psychology at The Pennsylvania State University. Kim A. Kastens is with the Lamont-Doherty Earth Observatory and Department of Earth & Environmental Sciences at Columbia University. Notes Because forming WLGs on the basis of average degree error created groups that did not universally differ with respect to the total number correct (within 10°), we also created "purer" groups by using conjoint criteria and dropping data from participants when the two criteria would have assigned them to different groups. Under this system, to be placed in the high WLG, average degrees error had to be less than 10° and 5–6 responses had to be correct; for medium, average error had to fall between 10° and 20° with 2–4 correct, and for low, average error had to be greater than 20° with 0–1 correct. Using these conjoint criteria, 7 males and 9 females could not be included, leaving, respectively in the high, medium, and low groups, 29, 11, and 16 males, and 20, 16, and 17 females. All ANOVAs reported in the text were run twice, once with the full data set (N = 125) and once with the reduced data set (N = 109). The pattern of results was identical, and thus, only data from the full sample are reported. In addition, data were analyzed with regressions using the continuous average degree-error. These analyses revealed the same pattern of results as the ANOVAs and thus are not described further. As explained in the next section, many dip lines were not perpendicular to the strike. Thus, as an alternative way to examine participants' performance, we used dip lines as the primary data: An orthogonal to the drawn dip line was used to infer the strike line. (Note that when the drawn dip line was [correctly] perpendicular to the drawn strike line, the inferred strike line was identical to the drawn strike line.) We then analyzed inferred strike lines similarly to the way we had analyzed drawn strike lines. Although the absolute values were affected, the general picture of participants' dramatic errors and the patterns of group level effects remained unchanged, and to avoid redundancy, we have thus omitted details of these analyses here. Three participants estimated dip angles that were greater than 90°, which are not legal values given the definition of dip. One may argue such errors demonstrate that these participants completely misunderstood the task, and thus that their data should be excluded from the analyses. Removing these three subjects' data, however, left all results on dip angle unchanged. As mentioned when initially describing the map used in this research, the visitor maps used for this campus do not have north directly at the top of the map; instead the map is oriented so that the top of the map is approximately 45° counterclockwise from true north. To test whether participants might have been pointing systematically to this "campus north" rather than to true north, we recalculated errors using campus north as the correct value. All patterns of results remained identical, with the obvious exception that the values of the mean errors changed. One might argue that the responses for the 3D shoreline and drop tasks should have been scored by projecting participants' lines down onto the horizontal plane. The argument for such a scoring procedure would be that projections of this kind are necessary when one records strike on a map. Thus, although participants were not actually asked to record their shorelines on a 2D map, we used this scoring method as an alternative way to examine the data. To do so, we calculated the projected lines for each participant's response for each of the six models. For shoreline, the angle of the projected line was calculated as arctan (tan θ × cos α), where θ is the participant's degree of error and α is the dip of the appropriate model. A similar calculation was used for the drop task except that complementary angles were used because the correct answer is a vertical rather than horizontal line. The resulting angular data were then used as the dependent variables for analyses parallel to those described in the text proper. Patterns from these analyses were comparable to those reported in the text in which the angles drawn on the planar surfaces of the models were measured directly.