Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding the premise of a LT approach--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. This hypothesis was evaluated for an empirically-validated…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

Powell, Berry, et al. (in press) conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a…

This article assesses the likely generalizability of educational treatment-effect estimates from regression discontinuity designs (RDDs) when treatment assignment is based on academic pretest scores. Our assessment uses data on outcome and pretest measures from six educational experiments, ranging from preschool through high school, to estimate…

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (n = 76) were randomly assigned to word-problem intervention (n = 56)…

This article summarizes findings from a two-year randomized control trial, focusing on a subset of 194 fourth graders with reading comprehension scores at or below the 15th percentile. Students in the treatment condition received an average of 94 daily 30-min sessions of small group intervention implemented with fidelity by well-trained research…

Researchers have shown that children's social-emotional growth is inextricably connected to academic learning. We developed the Social-Emotional Learning Foundations (SELF) intervention, a Grade K-1 curriculum merging social-emotional learning (SEL) and literacy instruction, to promote language supported self-regulation, specifically for primary…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

This study examined differences in cognitive processing between 4th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or…

This study evaluated the efficacy of the Word Learning Strategies (WLS) supplementary program to improve elementary students' vocabulary skills and reading comprehension. The study used a multi-site cluster randomized, experimental design, which randomly assigned 92 4th grade classrooms (n=2558 students) from two cohorts to a treatment or control…

Social interdependence is a key concept in CSCL research. However, investigations of students' positive and negative interdependence during collaborative activities have often relied on self-report, rather than dialogue analysis. Bringing together politeness and social interdependence theory, we assessed "dialogue indicators" of positive…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…

Using a randomized control trial, this study examined the causal evidence of cross-language transfer of phonological awareness and letter knowledge (names and sounds) using data from multilingual 1st-grade children (N = 322) in Kenya. Children in the treatment condition received an 8-week instruction on phonological awareness and letter knowledge…