Longitudinal Relations Among Spatial and Numerical Skills in Pre-k to Fourth Grades

• In Event: 3-133 - Associations Between Space and Number Across Development

Integrative Statement

Correlations among spatial and numerical skills are well-established at all ages (e.g., Mix & Cheng, 2012). However, it is important to understand how specific spatial skills (e.g., mental rotation, mental transformation, proportional reasoning, and visuospatial working memory [VSWM]) relate to numerical skills. Cross-sectional evidence suggests some specificity. In one study, mental rotation was most strongly related to math among kindergarteners, whereas VSWM was most related to math among 6th-graders (Mix et al., 2016). Building on this foundation, this longitudinal study tested: 1) whether initial spatial skills predict growth rates in numerical skills, 2) whether spatial development is characterized by stable individual differences or influences of prior skill on later skill, and 3) whether relations among spatial and numerical skills are time-general (i.e., relations among stable individual differences) or time-specific (e.g., later math skill predicted by prior spatial skill).
We conducted a cross-sequential study of 511 students (281 female) initially in pre-k to 3rd grades. Participants completed 4 time-points across 2 school years (T1-T4). Each time-point involved assessments of mental rotation, mental transformation, proportional reasoning, VSWM, number line (NL) estimation, calculation, and reading (Figure 1).
We first tested whether spatial skills predicted growth in NL estimation and calculation, controlling for reading, gender, and socioeconomic status (SES). In a latent growth model, initial VSWM and proportional reasoning significantly related to initial NL estimation (ps≤.001), and growth in NL estimation was significantly predicted by initial mental transformation skill (p=.034). In a separate model, initial calculation performance was uniquely predicted by initial levels of all four spatial skills (ps≤.01); however, growth in calculation was not related to initial spatial skills.
We next investigated whether prior skill predicted later skill (autoregressive relations) after accounting for stable individual differences (trait-like factors), for each skill separately (Figure 2). For spatial skills and NL estimation, autoregressive relations were non-significant (with one exception, T3 to T4 rotation) after accounting for stable trait-like factors. (Note that these skills were not stagnant - children significantly improved over time.) In contrast, reading achievement involved significant autoregressive effects.
Finally, we examined whether spatial-numeric relations were primarily time-invariant or time-specific, using a random-intercepts cross-lagged panel model (RI-CLPM; Hamaker et al., 2015). We included autoregressive and cross-lagged effects among all measures (α=.005 to account for multiple comparisons). Only one cross-lagged effect was significant (T2 calculation predicting T3 transformation). However, trait-like factors were significantly correlated between all spatial and numerical skills (ps≤.001).
In sum, initial mental transformation predicted NL estimation growth, consistent with Gunderson et al. (2012). Spatial development was characterized by stable individual differences; prior spatial skills did not predict later skills after accounting for individual differences. Finally, spatial-numeric relations were large in terms of stable individual differences, but there was little evidence that prior spatial skills predicted later numerical skills, or vice versa (consistent with Bailey, 2017). Future research should investigate sources of stable individual differences in spatial skills, which could result from time-invariant internal and external factors (e.g., home and school environments, engagement in spatial activities, cognitive skills, and heritable factors).

Author

• Elizabeth Gunderson, Temple University
  Presenting Author