Tyler W. Watts

What’s Past Is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement

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 multisite 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.

State and Trait Effects on Individual Differences in Children’s Mathematical Development

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.

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n = 1,362), this study tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first-grade and adolescent mathematics achievement was present (β = .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division serving as significant mediators.

Mathematics Content Coverage and Student Learning in Kindergarten

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998–1999 and 2010–2011 school years, they continued to place more emphasis on basic content. We find that time on advanced content is positively associated with student learning, whereas time on basic content has a negative association with learning. We argue that increased exposure to more advanced mathematics content could benefit the vast majority of kindergartners.

Risky Business: Correlation and Causation in Longitudinal Studies of Skill Development

Developmental theories often posit that changes in childrens 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 article 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., antisocial 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 nonexperimental 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 can reproduce the pattern of experimental impacts on childrens mathematics achievement. Implications for developmental theories, methods, and practice are discussed. (PsycINFO Database Record

Does Early Mathematics Intervention Change the Processes Underlying Children's Learning?

ABSTRACT 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 childrens 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 childrens mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group.

Differential effects of the classroom on African American and non-African American’s mathematics achievement.

We examined whether African American students differentially responded to dimensions of the observed classroom-learning environment compared with non–African American students. Further, we examined whether these dimensions of the classroom mediated treatment effects of a preschool mathematics intervention targeted at students from low-income families. Three observed dimensions of the classroom (teacher expectations and developmental appropriateness; teacher confidence and enthusiasm; and support for mathematical discourse) were evaluated in a sample of 1,238 preschool students in 101 classrooms. Using multigroup multilevel mediation where African American students were compared with non–African American students, we found that teachers in the intervention condition had higher ratings on the observed dimensions of the classroom compared with teachers in the control condition. Further, ratings on teacher expectations and developmental appropriateness had larger associations with the achievement of African American students than for non–African Americans. Findings suggest that students within the same classroom may react differently to that learning environment and that classroom learning environments could be structured in ways that are beneficial for students who need the most support.