The purpose of this closely aligned conceptual replication study was to investigate the efficacy of a Tier 2 kindergarten mathematics intervention. The replication study differed from the initial randomized controlled trial on three important elements: geographical region, timing of the intervention, and instructional context of the counterfactual. Similar to the original investigation, however, the current study tested the same intervention, used the same outcome measures and statistical analyses, and involved the same population of learners. A total of 319 kindergarten students with mathematics difficulties from 36 kindergarten classrooms participated in the study. Students who were randomly assigned to the treatment condition received the intervention in small-group formats, with 2 or 5 students per group. Control students participated in a no-treatment control condition. Significant effects on proximal and distal measures of mathematics achievement were found. Effect sizes obtained for all measures fell within or exceeded the upper bound of the effects reported in the initial study. Implications for systematically situating replication studies in larger frameworks of intervention research and reporting rates of treatment response across replication studies are discussed.

A critical aspect of intervention research is investigating the active ingredients that underlie intensive interventions and their theories of change. This study explored the rate of instructional interactions within treatment groups to determine whether they offered explanatory power of an empirically validated Tier 2 kindergarten mathematics intervention. Direct observations were conducted in 46 interventions groups, involving approximately 228 students. Multilevel structural equation models revealed that fall mathematics achievement significantly and negatively predicted the rate of academic feedback. Specifically, intervention groups with lower student mathematics achievement at the start of the kindergarten year received higher rates of academic feedback. Analyses also suggested that latent rates of instructional interactions were not significantly correlated with gains on student mathematics outcomes. Implications are discussed in relation to specifying the underlying mechanisms to intensify mathematics interventions, documenting local adaptation of intervention implementation, and examining possible threshold effects of instructional interactions.

There is a dearth of research on Tier 1 instruction designed to improve the mathematics achievement of English learners. This study examined the impact of a core kindergarten mathematics curriculum...

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities and the quality of explicit instruction served as treatment intensity metrics. A total of 465 kindergarten students with mathematics difficulties from 136 intervention groups participated. Results suggested comparable performances between the 2:1 and 5:1 intervention groups on six outcome measures. Observation data indicated that student practice differed by group size. Students in the 5:1 groups received more opportunities to practice with their peers, while students in the 2:1 groups participated in more frequent and higher quality individualized practice opportunities. Implications in terms of delivering Tier 2 interventions in small-group formats and engaging at-risk learners in meaningful practice opportunities are discussed.