Understanding numerical magnitude is critical to the development of mathematics proficiency. Math interventions targeting magnitude knowledge have been shown to improve outcomes for students with math learning difficulties across grade levels. However, while recent studies have found that growth in magnitude knowledge mediates fractions…

The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of initial variability within intervention groups using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics…

The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of pretest variability within intervention groups using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics…

Effective early mathematics instruction is critical to support long-term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors…

Effective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the…

Effective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the…

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 severe MD at kindergarten entry and examined whether these students improved…

Children enter kindergarten with a wide range of previous education experiences: Some have participated in pre-K programs: private, state-funded, or part of Head Start. Others have spent time in a family child care setting or in informal arrangements with family, friends, and neighbors. Regardless, this transition is fraught with stress and…

Opportunities for practice play a critical role in learning complex behaviors. In the context of explicit mathematics instruction, practice facilitates systematic opportunities for students with mathematics difficulties (MD) to learn new mathematics content and apply such knowledge and skills to novel mathematics problems. This study explored…

Opportunities for practice play a critical role in learning complex behaviors. In the context of explicit mathematics instruction, practice facilitates systematic opportunities for students with mathematics difficulties (MD) to learn new mathematics content and apply such knowledge and skills to novel mathematics problems. This study explored…

High-quality Tier 1 instruction is frequently conceptualized as the "foundation" for other tiers of intervention within multitiered systems of support (MTSS) models. However, the vast majority of Tier 2 intervention studies do not account for Tier 1 variables when examining intervention effectiveness. The purpose of this study was to…

Instructional interactions that occur between teachers and students around foundational mathematics topics are critical for supporting mathematical proficiency among students with mathematics learning disabilities (MLD). This study investigated whether the initial mathematics skill of 880 kindergarten students at risk of MLD predicted the quantity…

Instructional interactions that occur between teachers and students around foundational mathematics topics are critical for supporting mathematical proficiency among students with mathematics learning disabilities (MLD). This study investigated whether the initial mathematics skill of 880 kindergarten students at risk for MLD predicted the…

While the long-term societal costs for youth with disruptive behavior disorders are well documented, there is a dearth of information about the comprehensive costs of implementing even the most well-regarded early intervention programs, and the costs of scaling effective interventions are even less well understood. This study estimated the costs…

This paper reports the results of a randomized controlled trial evaluating "We Have Skills," a brief curriculum designed to teach early elementary students academic and social skills as well as improve teacher efficacy in classroom management. Intervention efficacy was tested with 127 teachers, randomly assigned to condition, and 2,817…