Proficiency With Number Concepts and Operations: Replicating the Efficacy of a First-Grade Mathematics Intervention.

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240 first-grade students with mathematics difficulties in a new geographical region. Participating students were randomized into one of three conditions: (a) 2:1 mathematics intervention group, (b) 5:1 mathematics intervention group, or (c) business-as-usual instruction. Relative to the original study, findings from the replication varied. When comparing the treatment groups to the control, results suggested positive effects on all outcome measures, including a follow-up assessment administered one year later. However, differences between the two treatment groups based on group size were not found in the mathematics outcome measures. Both groups also received commensurate levels of observed instructional interactions. Implications for unpacking contextual differences between original research and their replications as well as using future research to explore the quantity and quality of instructional interactions as ways to explain variation in findings of group size are discussed.

Kindergarteners at Risk for Severe Mathematics Difficulties: Investigating Tipping Points of Core Mathematics Instruction.

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated risk for severe MD at kindergarten entry and examined whether these students improved from a category of high MD risk (i.e., <10th percentile) to a lower risk of MD (i.e., norm-referenced performance at or above the 10th, 20th, 30th, and 40th percentiles) between the fall and spring of kindergarten. Differential response to the program based on the classroom-level proportion of students with severe MD was also explored. A total of 795 kindergarteners with severe MD from 122 classrooms were included in the analyses. Results suggested students with severe MD in treatment classrooms improved from fall to spring at a greater rate than their control peers. Treatment students also demonstrated higher rates of improvement from below the 10th percentile to a performance at or above the 20th, 30th, and 40th percentiles across the school year. No evidence of differential efficacy of the program by the classroom-level proportion of students with severe MD was found. Implications for using explicit mathematics programs to thwart the onset of severe MD among academically vulnerable students are discussed.