Spatial transformation abilities and their relation to later mathematics performance

  • Andrea Frick
Original Article


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.



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.

Compliance with ethical standards

Conflict of interest

The author declares that she has no conflict of interest.

Ethical approval

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.

Informed consent

Informed consent was obtained for all individual participants included in the study.


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Authors and Affiliations

  1. 1.University of BernBernSwitzerland
  2. 2.Department of PsychologyUniversity of FribourgFribourgSwitzerland

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