Jessica M. Namkung

Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge.

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across Grades 2-3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems.

Fraction Intervention for Students With Mathematics Difficulties: Lessons Learned From Five Randomized Controlled Trials

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on fractions magnitude understanding may improve learning. They then describe an intervention that relies strongly on this type of understanding about fractions instruction, and they provide an overview of the intervention’s overall effects. This is followed by an overview of 5 intervention components for which the authors isolated effects. They conclude by discussing some of the lessons learned from this research program.

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.

Understanding the Cognition Related to Mathematics Difficulties: A Meta-Analysis on the Cognitive Deficit Profiles and the Bottleneck Theory

The current study investigated the cognitive deficit profiles among individuals with mathematics difficulties (MD) and potential moderators and mechanism for these profiles. Seventy-five cognitive profiling studies on MD were included, representing a total of 13,001 individuals and 126 independent samples. Results showed that compared with typically developing individuals, individuals with MD showed deficits (from most severe to less severe) in phonological processing, processing speed, working memory, attention, short-term memory, executive functions, and visuospatial skills. Moderation analyses indicated that comorbidity (with reading disabilities) and types of MD screening affected the cognitive deficits. Severity of MD was related to processing speed deficits. Deficits in phonological processing and attention were more severe in younger individuals with MD. Deficits in processing speed and working memory were most severe in the numerical domain. Deficits in low-level cognitive skills (i.e., processing speed and short-term memory) could not completely explain the deficits in high-level skills (i.e., working memory, attention, and executive functions), partially supporting the bottleneck theory. These findings, taken together, suggest that (a) deficits in processing speed and working memory are most salient and stable cognitive markers of MD, (b) numerical-processing deficit and the cognitive deficits of MD are relatively independent from each other, and (c) MD may be a discrete construct with heterogeneity reflected by MD subtypes and age. Implications for incorporating cognition in the diagnosis and the interventions for MD are discussed.

Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill?

The purposes of this study were to (a) explore whether early fractions understanding at 4th grade is differentially challenging for students with versus without adequate whole-number competence and (b) identify specific whole-number skill associated with difficulty in fractions understanding. Based on initial whole-number competence, 1,108 4th graders were classified as having (a) adequate whole-number competence (n = 775), (b) less severe whole-number difficulty (n = 201), and (c) severe whole-number difficulty (n = 132). At the end of 4th grade, they were assessed on fractions understanding and further classified as with versus without difficulty in fractions understanding. Multi-level logistic regression indicated that compared to students with adequate whole-number competence, those with less severe whole-number difficulty were almost 5 times as likely to experience difficulty with fractions understanding whereas those with severe whole-number difficulty were about 32 times as likely to experience difficulty with fractions understanding. Students with severe whole-number difficulty were about 7 times as likely to experience difficulty with fractions understanding compared to those with less severe whole-number difficulty. Among students with adequate whole-number competence, the pretest whole-number skill distinguishing those with versus without difficulty in fractions understanding was basic division facts (i.e., 2-digit dividend ÷ 1-digit divisor) and simple multiplication (i.e., 3-digit × 1-digit without regrouping). The role of whole-number competence in developing initial fractions understanding and implications for instruction are discussed.

Exploring Growth Trajectories of Informal and Formal Mathematics Skills Among Prekindergarten Children Struggling With Mathematics

Growth in two subscales, Informal and Formal Mathematics Skills, of the Test of Early Mathematics Abilitity–3 (TEMA-3) was explored in a sample of 281 children. Children were identified as either typically developing (TYP; n = 205) or having mathematics difficulties (MD; n = 76) based on their total TEMA-3 score at the end of prekindergarten. Their average level of informal and formal mathematics skills, growth rate over time, and rate of acceleration of growth were estimated using conventional growth modeling while controlling for the effects of gender. Results indicated that children with MD had significantly lower informal and formal mathematics knowledge than did TYP children at the end of kindergarten. However, for informal mathematics skills, children with MD grew at a significantly faster rate than did TYP children, and the rate of acceleration was also significantly faster for children with MD. In contrast, both the rate of growth and acceleration of growth in formal mathematics skills were significantly faster for TYP children than they were for children with MD. Implications for early MD identification and interventions are discussed.