This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (n = 198) were assigned to the treatment or control condition…

The purpose of this study was to conduct a replication study of a kindergarten mathematics intervention, ROOTS, delivered within the context of a research base core program. In the study, sixty two classrooms were randomly assigned to treatment (ROOTS) or a business as usual control. All classrooms implemented a research based core program (Early…

High-quality Tier 1 instruction is frequently conceptualized as the "foundation" for other tiers of intervention within multi-tiered systems of support (MTSS) models (Gersten et al., 2009). However, the vast majority of Tier 2 intervention studies do not account for Tier 1 variables when examining intervention effectiveness (Hill et al.,…

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…

A socioeconomic status- (SES-) related achievement gap in mathematics emerges prior to school entry, and increases as children move through elementary school. This gap makes implementation of demanding mathematics standards (e.g., the Common Core State Standards) an ongoing challenge. Early educational intervention is a strategy for addressing…

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's ability to discriminate nonsymbolic number (e.g. the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest it may be due to a sharpening numerical representation or an improved ability…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" (Green, 2008) of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data…

This study examined whether the efficacy of a 50 lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS, differed by group size and whether initial skill moderated intervention effects by group size. The study utilized a randomized block design with at-risk students (n = 1,251) within…

This study examined the cost effectiveness of a 50 lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS. The study utilized a randomized block design with 1,251 at-risk students within 138 classrooms randomly assigned to one of two active treatment conditions (small groups of either two…

A quasi-experimental design in six kindergarten classrooms (n = 123 students) was used to study the effects of the KinderTEK iPad-based math program on the math achievement of students in general education classrooms. Student math outcomes in three treatment ("early start") classrooms were compared to math outcomes for students in three…

Drawing from the developmental and cognitive mathematics literature, the purpose of this study was to investigate the reliability, validity, and diagnostic utility of a widely-researched number line task in kindergarten. Specifically, the Number Line Assessment 0-100 (NLA 0-100) as compared to an established kindergarten screening measure was…

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0-20 and NLA 0-100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test-retest reliability. The NLA 0-20 had low and the…

Students who demonstrate mathematics difficulties in the early grades are at risk for poor educational outcomes. Fortunately, strategic early mathematics intervention programs can improve academic outcomes for students with mathematics difficulties, and instructional technology has demonstrated promise in delivering targeted and individualized…

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…