Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

Concept-Focused and Procedure-Focused Instruction on the Algebra Performance of Grade 9 Students With and Without Mathematics Difficulty

Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement after 2.5 years, depending on students' mathematics difficulty (MD) status. Data for this study were drawn from the High School Longitudinal Study for the years 2009-2010 and 2011-2012 (N = 19,104). Multiple regression analyses indicated that students with MD who participated in Grade 9 mathematics classrooms where teachers self-reported the use of less CFI and more PFI were more positively associated with having higher algebra achievement after 2.5 years. Conversely, students without MD in classrooms where mathematics teachers self-reported the use of more CFI and less PFI were positively associated with having higher algebra achievement after 2.5 years. However, this study's findings do not suggest that teachers should disregard CFI and provide only PFI when teaching students with MD. Because the data set did not include any variable to discover whether teachers provided sufficient support (i.e., evidence-based practices) for students with MD, who have more constraints in their cognitive skills compared to students without MD, to benefit from CFI, the findings of this study should be interpreted cautiously. Directions for future research and practical implications are discussed.

Student and Teacher Characteristics on Student Math Achievement

Using data from the Programme for International Student Assessment (PISA), this study implements two statistical analyses to investigate the effects of student and teacher characteristics on students’ mathematical achievement. First, the authors conduct an exploratory factor analysis to explore the factor structure for the various student and teacher variables of interest in this study. Second, they perform hierarchical linear modeling to analyze students’ and teachers’ multilevel structure in a school. The results suggest that student characteristics such as mathematics interest, instrument motivation, mathematics self-efficacy, mathematics anxiety, mathematics self-concept, and out-of-school study time predicted 39.9% of mathematical achievement variance. The results also suggest that mathematics self-efficacy had the largest effect on mathematical achievement. Teacher characteristics such as teacher-directed instruction, cognitive activation, teacher support, classroom management, and student–teacher relations predicted 34.9% of mathematical achievement variance. This study’s results have implications for educators in fostering a positive learning environment to increase students’ mathematics interest and self-efficacy, and focus on specific teacher characteristics to increase students’ mathematical achievement.

The Causal Impact of Schooling on Children’s Development: Lessons for Developmental Science

Entry into formal schooling is a signature developmental milestone for young children and their families and represents an important period of cognitive, social, and emotional development. Until recently, few researchers have attempted to isolate the unique impact of schooling on children’s developmental and academic outcomes. The application of quasiexperimental methods has provided researchers with the tools to examine when and how schooling shapes children’s development. In this article, we summarize three main insights from this work: (a) Schooling produces major, unique changes in children’s growth across a wide range of psychological processes important for learning; (b) the effects of schooling are not universal across all domains; and (c) schooling impacts cognitive processes that are not explicitly taught. We also propose that a deeper look at classroom instruction and brain development can expand our understanding of how schooling influences academic success and positive life outcomes and provide a model for developmental science more broadly.

Student Practice Opportunities in Core Mathematics Instruction: Exploring for a Goldilocks Effect for Kindergartners With Mathematics Difficulties

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 whether there is an optimal amount of student practice that teachers should provide in core mathematics instruction to maximize the mathematics achievement of kindergarten students with MD, a so called "Goldilocks effect," as opposed to simply "more is better." Results from observation data collected in a large-scale efficacy trial supported the latter rather than the former. Specifically, we found that three individual practice opportunities for every explicit teacher demonstration of mathematical content was associated with increased mathematics achievement for students with MD relative to fewer practice opportunities. Implications for facilitating frequent student practice opportunities during core mathematics instruction and designing professional development for teachers who work with students with MD are discussed.

Parent-Child Math Talk About Fractions During Formal Learning and Guided Play Activities

This study examined parent-child math talk within three contexts (formal learning; guided play; unguided play) in order to identify characteristics of activities supporting high-quality math engagement. Seventy-two dyads of parents and 4- and 5-year-olds were observed using a set of toy foods; instructions and materials varied across conditions. Parents and children engaged in the most math talk in formal learning; guided play also yielded more math talk than unguided play. Parents rated the formal learning and guided play activities as equally supportive of math learning, but rated the guided play activity as more enjoyable than the formal learning activity. The findings have implications for how parents should be encouraged to support preschoolers' math learning.

Kindergarten Children's Executive Functions Predict Their Second-Grade Academic Achievement and Behavior

Whether and to what extent kindergarten children's executive functions (EF) constitute promising targets of early intervention is currently unclear. This study examined whether kindergarten children's EF predicted their second-grade academic achievement and behavior. This was done using (a) a longitudinal and nationally representative sample (N = 8,920, M_age  = 97.6 months), (b) multiple measures of EF, academic achievement, and behavior, and (c) extensive statistical control including for domain-specific and domain-general lagged dependent variables. All three measures of EF-working memory, cognitive flexibility, and inhibitory control-positively and significantly predicted reading, mathematics, and science achievement. In addition, inhibitory control negatively predicted both externalizing and internalizing problem behaviors. Children's EF constitute promising targets of experimentally evaluated interventions for increasing academic and behavioral functioning.

Specific learning disability in mathematics: a comprehensive review

Math skills are necessary for success in the childhood educational and future adult work environment. This article reviews the changing terminology for specific learning disabilities (SLD) in math and describes the emerging genetics and neuroimaging studies that relate to individuals with math disability (MD). It is important to maintain a developmental perspective on MD, as presentation changes with age, instruction, and the different models (educational and medical) of identification. Intervention requires a systematic approach to screening and remediation that has evolved with more evidence-based literature. Newer directions in behavioral, educational and novel interventions are described.

Using assessment to individualize early mathematics instruction

Accumulating evidence suggests that assessment-informed personalized instruction, tailored to students' individual skills and abilities, is more effective than more one-size-fits-all approaches. In this study, we evaluate the efficacy of Individualizing Student Instruction in Mathematics (ISI-Math) compared to Reading (ISI-Reading) where classrooms were randomly assigned to ISI-Math or ISI-Reading. The literature on child characteristics X instruction or skill X treatment interaction effects point to the complexities of tailoring instruction for individual students who present with constellations of skills. Second graders received mathematics instruction in small flexible learning groups based on their assessed learning needs. Results of the study (n=32 teachers, 370 students) revealed significant treatment effects on standardized mathematics assessments. With effect sizes (d) of 0.41-0.60, we show that we can significantly improve 2nd graders' mathematics achievement, including for children living in poverty, by using assessment data to individualize the mathematics instruction they receive. The instructional regime, ISI-Math, was implemented by regular classroom teachers and it led to about a 4-month achievement advantage on standardized mathematics tests when compared to students in control classrooms. These results were realized within one school year. Moreover, treatment effects were the same regardless of school-level poverty and students' gender, initial mathematics or vocabulary scores.

A longitudinal study on predictors of early calculation development among young children at risk for learning difficulties

The purpose of this study was to explore domain-general cognitive skills, domain-specific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical competence, incoming calculations, socioeconomic status, and gender at the beginning of first grade and on calculation performance at four time points: the beginning of first grade, the end of first grade, the end of second grade, and the end of third grade. Latent growth modeling analysis showed that numerical competence, incoming calculation, processing speed, and decoding skills significantly explained the variance in calculation performance at the beginning of first grade. Numerical competence and processing speed significantly explained the variance in calculation performance at the end of third grade. However, numerical competence was the only significant predictor of calculation development from the beginning of first grade to the end of third grade. Implications of these findings for early calculation instructions among young at-risk children are discussed.

The Interaction of Learning Disability Status and Student Demographic Characteristics on Mathematics Growth

This study examined mathematics achievement growth of students without disabilities (SWoD) and students with learning disabilities (LD) and tested whether growth and LD status interacted with student demographic characteristics. Growth was estimated in a statewide sample of 79,554 students over Grades 3 to 7. The LD group was significantly lower in achievement in each grade and had less growth than the SWoD group. We also found that student demographic characteristics were significantly related to mathematics growth, but only three demographic characteristics were statistically significant as interactions. We found that LD-SWoD differences at Grade 3 were moderated by student sex, while Black race/ethnicity and free or reduced lunch (FRL) status moderated LD-SWoD differences at all grades. These results provide practitioners and policy makers with more specific information about which particular LD students show faster or slower growth in mathematics. Our results show that simply including predictors in a regression equation may produce different results than direct testing of interactions and achievement gaps may be larger for some LD subgroups of students than previously reported.