The Effects of Algebraic Equation Solving Intervention for Students With Mathematics Learning Difficulties.

The purpose of this study was to examine the effects of algebraic equation solving intervention for sixth graders with mathematics learning difficulties (MD). A total of 48 students with MD were randomly assigned to either the algebraic equation solving intervention, Mystery Math (n = 24) or control condition (n = 24). The multicomponent intervention was based on the principles of explicit instruction and focused on improving conceptual and procedural knowledge of algebraic equation solving using concrete manipulatives. Students in the intervention group received instruction in pairs, 30 min per session, 3 sessions per week for 5 weeks (i.e., 15 sessions). The results indicated that the main effect of intervention was significant for 2 proximal measures of mathematics vocabulary, and conceptual and procedural understanding of algebraic equation solving with large effect sizes. However, the main effect of intervention was not significant for distal measures of comprehensive pre-algebra skills and whole-number computations. The findings demonstrate that grade-level standards can be successfully taught to students with MD. Implications for practice are discussed.

Examining the mutual relations between language and mathematics: A meta-analysis.

This study presents a meta-analysis of the relation between language and mathematics. A moderate relation between language and mathematics was found in 344 studies with 393 independent samples and more than 360,000 participants, r = .42, 95% CI [.40, .44]. Moderation and partial correlation analyses revealed the following: (a) more complicated language and mathematics skills were associated with stronger relations between language and mathematics; after partialing out working memory and intelligence, rapid automatized naming showed the strongest relation to numerical knowledge; (b) the relation between language and mathematics was stronger among native language speakers than among second-language learners, but this difference was not found after partialing out working memory and intelligence; (c) working memory and intelligence together explained over 50% of the variance in the relation between language and mathematics and explained more variance in such relations involving complex mathematics skills; (d) language and mathematics predicted the development of one another even after controlling for initial performance. These findings suggest that we may use language as a medium to communicate, represent, and retrieve mathematics knowledge as well as to facilitate working memory and reasoning during mathematics performance and learning. With development, the use of language to retrieve mathematics knowledge may be more important for foundational mathematics skills, which in turn further strengthens linguistic thought processes for performing more advanced mathematics tasks. Such use of language may boost the mutual effects of cognition and mathematics across development. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

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.

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.

Cognitive Predictors of Calculations and Number Line Estimation with Whole Numbers and Fractions among At-Risk Students.

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 7 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and incoming calculation skill at the start of 4th grade. Then, they were assessed on whole-number and fraction calculation and number line estimation measures at the end of 4th grade. Structural equation modeling and path analysis indicated that processing speed, attentive behavior, and incoming calculation skill were significant predictors of whole-number calculations whereas language, in addition to processing speed and attentive behavior, significantly predicted fraction calculations. In terms of number line estimation, nonverbal reasoning significantly predicted both whole-number and fraction outcome, with numerical working memory predicting whole-number number line estimation and language predicting fraction number line estimation. Findings are discussed in terms of distinctions between whole-number and fraction development and between calculations and number line learning.

Early Numerical Competencies of Students with Different Forms of Mathematics Difficulty.

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on measures of addition and word-problem skill, second grade students (N = 332) were classified in terms of MD status. Then, students were assessed on three early numerical competency measures (Number Line Estimation, Number Sets Test, and Counting Knowledge) as well as a measure of subtraction. On Number Line Estimation and Number Sets Test, students with CD and those with PD scored comparably, but both outperformed students with CDPD. On Counting Knowledge-Double First, students with CDPD scored lower than the three contrasting groups. On subtraction, students with CD outperformed those with PD, and students with PD and those with CDPD performed comparably. Findings are discussed in terms of differential performance as a function of difficulty status and implications for understanding and teaching subtypes of MD.

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.

Toddlers with elevated autism symptoms show slowed habituation to faces.

We explored social information processing and its relation to social and communicative symptoms in toddlers with Autism Spectrum Disorder (ASD) and their siblings. Toddlers with more severe symptoms of autism showed slower habituation to faces than comparison groups; slower face learning correlated with poorer social skills and lower verbal ability. Unaffected toddlers who were siblings of children with ASD also showed slower habituation to faces compared with toddlers without siblings with ASD. We conclude that slower rates of face learning may be an endophenotype of ASD and is associated with more severe symptoms among affected individuals.