Risky Business: Correlation and Causation in Developmental Studies- American Psychologist, in press

Developmental theories often posit that changes in children’s early psychological characteristics will affect much later psychological, social, and economic outcomes. However, tests of these theories frequently yield results that are consistent with plausible alternative theories that posit a much smaller causal role for earlier levels of these psychological characteristics. Our paper explores this issue with empirical tests of skill building theories, which predict that early boosts to simpler skills (e.g., numeracy or literacy) or behaviors (e.g, anti-social behavior or executive functions) support the long-term development of more sophisticated skills or behaviors. Substantial longitudinal associations between academic or socioemotional skills measured early and then later in childhood or adolescence are often taken as support of these skill-building processes. Using the example of skill-building in mathematics, we argue that longitudinal correlations, even if adjusted for an extensive set of baseline covariates, constitute an insufficiently risky test of skill-building theories. We first show that experimental manipulation of early math skills generates much smaller effects on later math achievement than the non-experimental literature has suggested. We then conduct falsification tests that show puzzlingly high cross-domain associations between early math and later literacy achievement. Finally, we show that a skill-building model positing a combination of unmeasured stable factors and skill-building processes is able to reproduce the pattern of experimental impacts on children’s mathematics achievement. Implications for developmental theories, methods, and practice are discussed.

Causal Impact of Early Math Learning- Child Development, 2017

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement, using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n= 410) that a standard-deviation of intervention-produced change at age 4 is associated with a 0.24 standard deviation gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly-controlled OLS regression models (Claessens et al., 2009; Watts et al., 2014) using national datasets. Implications for developmental theory and practice are discussed.

Early Math Intervention and Stable Learning Processes- JREE, 2017

Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children’s mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children’s mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group.

State and Trait Models of Math Achievement- Psychological Science, 2014

Substantial longitudinal relations between children’s early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children’s mathematics achievement across time. We hypothesized that individual differences in children’s later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children’s mathematics achievement over time. Latent trait effects on children’s mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed.

Early Growth in Math Learning and Later Achievement- Educational Researcher, 2014

Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multi-site longitudinal data. We find that preschool mathematics ability predicts mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics. Moreover, we find that growth in mathematical ability between age 54 months and first grade is an even stronger predictor of adolescent mathematics achievement. These results demonstrate the importance of prekindergarten mathematics knowledge and early math learning for later achievement.