Abstract
Using a longitudinal approach, this study investigated the relational structure of different spatial transformation skills at kindergarten age, and how these spatial skills relate to children’s later mathematics performance. Children were tested at three time points, in kindergarten, first grade, and second grade (N = 119). Exploratory factor analyses revealed two subcomponents of spatial transformation skills: one representing egocentric transformations (mental rotation and spatial scaling), and one representing allocentric transformations (e.g., cross-sectioning, perspective taking). Structural equation modeling suggested that egocentric transformation skills showed their strongest relation to the part of the mathematics test tapping arithmetic operations, whereas allocentric transformations were strongly related to Numeric-Logical and Spatial Functions as well as geometry. The present findings point to a tight connection between early mental transformation skills, particularly the ones requiring a high level of spatial flexibility and a strong sense for spatial magnitudes, and children’s mathematics performance at the beginning of their school career.
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Notes
Test–retest reliability measures are reported where available; however, for some of the tasks, such measures were unobtainable. Measures based on inter-item correlations are misleading in these tasks, as items differ considerably in difficulty. For example, accuracy on items requiring mental rotation by a large angle is significantly lower than items requiring only a small mental transformation (Frick et al., 2013). Nevertheless, for the sake of completeness, Guttman’s Lambda 2 was calculated in these cases and was as follows: Ghost Rotation, 0.70; Perspective Taking, 0.70; Cross-sectioning, 0.56; Children’s Mental Transformation Task, 0.75; Diagrammatic Representations, 0.69; Spatial Scaling, .70; Proportional Reasoning, 0.88; Number-line Task, 0.87. For span tasks (both working memory tasks) and timed tasks (Card Rotation, Geometry task), inter-item correlations are meaningless as children solved different numbers of items.
In the case of map reading, changes in scale typically go hand in hand with changes in representational format, as maps typically are scaled two-dimensional representations of a three-dimensional space. To disentangle these two transformations, the Spatial Scaling Task used in the present study did not involve any changes in format—conversely, the Diagrammatic Reasoning Task did not involve changes in scale.
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Acknowledgements
This research was supported by research grants from the Swiss National Science Foundation # PZ00P1_131866 and # PP00P1_150486. Special thanks go to Wenke Möhring, Nora S. Newcombe, Laurenz L. Meier, Siegfried Macho, Claudia M. Roebers, Sarah Loher, Marianne Röthlisberger, and Annik E. Voelke for helpful comments, and to Denise Baumeler, Joël E. Bayard, Leunora Fejza, Ines Holzmann, and Lisa Odermatt for their help with data collection.
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All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Procedures were approved by the Institutional Review Board of the University. The manuscript does not contain clinical studies or patient data.
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Data of this project have been presented at the Society for Research in Child Development (SRCD) biennial meeting, as well as at the ‘Space and Mathematics’ conference in Chicago in 2015. Some of the data of the first waves of this longitudinal project have been published in two prior publications focusing on the relation between perspective taking and executive functioning in kindergarten (2016; https://doi.org/10.1007/s00426-016-0785-y), and between balance skills, spatial, and proportional reasoning (2016; https://doi.org/10.3389/fpsyg.2015.02049).
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Frick, A. Spatial transformation abilities and their relation to later mathematics performance. Psychological Research 83, 1465–1484 (2019). https://doi.org/10.1007/s00426-018-1008-5
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DOI: https://doi.org/10.1007/s00426-018-1008-5