Developing a novel preparation to analyze the onset of derived stimulus relations.

The experimental analysis of derived stimulus relations is a critical research area. A training-then-testing preparation nearly always is used to study derived relations. In the training phase, participants learn the relevant baseline discriminations via differential consequences (e.g., AB and AC relations). In the testing phase, they are presented with probe trials in the absence of differential consequences (e.g., BA and CA symmetry trials and BC and CB equivalence trials). High accuracy levels sometimes are observed from the start of testing such that it is unclear whether the participants learned these relations before testing. The present experiment reports data from a novel preparation that monitors the development of derived relations as trained relations are acquired. Three college students were presented with both training trials (AB, AC) and testing trials (BA, CA, BC, CB) in every session from the start of experimentation. Each participant learned each of the six discriminations by the end of experimentation. Most importantly, they learned the trained and symmetrical relations in close temporal proximity and the equivalence relations only after learning the symmetrical relations. These results are consistent with several findings demonstrating disparities between learning different forms of derived relational responding. The results validate the utility of the present preparation in the experimental analysis of derived relational learning.

Contributions of executive function and spatial skills to preschool mathematics achievement.

Early mathematics achievement is highly predictive of later mathematics performance. Here we investigated the influence of executive function (EF) and spatial skills, two generalizable skills often overlooked in mathematics curricula, on mathematics performance in preschoolers. Children (N=44) of varying socioeconomic status (SES) levels were assessed at 3 years of age on a new assessment of spatial skill (Test of Spatial Assembly, TOSA) and a vocabulary measure (Peabody Picture Vocabulary Test, PPVT). The same children were tested at 4 years of age on the Beery Test of Visual-Motor Integration (VMI) as well as on measures of EF and mathematics. The TOSA was created specifically as an assessment for 3-year-olds, allowing the investigation of links among spatial, EF, and mathematical skills earlier than previously possible. Results of a hierarchical regression indicate that EF and spatial skills predict 70% of the variance in mathematics performance without an explicit math test, EF is an important predictor of math performance as prior research suggested, and spatial skills uniquely predict 27% of the variance in mathematics skills. Additional research is needed to understand whether EF is truly malleable and whether EF and spatial skills may be leveraged to support early mathematics skills, especially for lower SES children who are already falling behind in these skill areas by 3 and 4 years of age. These findings indicate that both skills are part of an important foundation for mathematics performance and may represent pathways for improving school readiness for mathematics.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement.

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense.

Building Kindergartners' Number Sense: A Randomized Controlled Study.

Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to one of three groups (n = 44 in each group): a number sense intervention group, a language intervention group, or a business as usual control group. Accounting for initial skill level in mathematical knowledge, children who received the number sense intervention performed better than controls at immediate post test, with meaningful effects on measures of number competencies and general math achievement. Many of the effects held eight weeks after the intervention was completed, suggesting that children internalized what they had learned. There were no differences between the language and control groups on any math-related measures.