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.

Using Direct Observation to Document "Practice-Based Evidence" of Evidence-Based Mathematics Instruction.

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a federally funded efficacy trial involving a Tier 2 first-grade mathematics intervention to examine whether the quantity and quality of explicit mathematics instruction was associated with the mathematics outcomes of 470 first-grade students with or at risk for mathematics learning disabilities. Associations between group-level pretreatment skill levels and the quality and quantity of explicit mathematics instructional practices used in the intervention were also explored. Findings suggested significant associations between positive gains in student mathematics outcomes and (a) lower rates of incorrectly answered mathematics-focused questions, and (b) the rate in which interventionists delivered group-level practice opportunities and offered academic feedback. Significant associations were also found between initial student mathematics performance and rates of student errors and the quality of explicit instruction. Implications for using direct observation to document enacted EBPs are discussed.