Risk For Mathematics Difficulties Research Articles

Executive Functioning and Early Math Skills in Young Children at Risk for Mathematical Difficulties: Evaluation of Interventions Efficacy and Transfer Effects

ABSTRACT Research Findings: Executive Function (EF) and Early Math (EM) are foundational skills for children’s school success. Interventions have shown to foster these skills, but their effectiveness in less developed countries remains unknown. This study examined the initial efficacy of an eight-week EF and an EM skills program for young Iranian children at risk for mathematical difficulties. Participants included 88 five- to six-year-old children who were randomly assigned into three conditions: Business-As-Usual (BAU) control group, EF training group, or an EM training group. The experimental groups received 24 sessions over two months. In the EF group, children had significantly higher working memory and planning scores at posttest, which were stable five months later. No significant group difference was found on inhibitory control. In the EM group, children demonstrated stronger math performance compared to BAU children at the posttest and follow-up, suggesting stable math improvement. There was no significant effect of EF training on math performance or significant effect of math training on EF skills. Practice or Policy: Findings suggest that the EF training was related to stronger EF and EM training was related to better math performance. However, there were no significant transfer effects of EF on math and vice versa.

Teacher Qualification Typologies and Their Relationship With the Math Achievement of Adolescents At Risk for Math Difficulties: A Latent Class Analysis Study

This latent class analysis study used a bias-adjusted three-step approach to empirically identify mutually exclusive clusters of teacher professional qualifications based on commonly studied indicators of teacher quality. We then examined the relationship between cluster membership and the mathematics gains of adolescents at risk for mathematics difficulties (MD), including students with disabilities and those without disabilities. We identified students at risk for MD as those performing at or below the 25th percentile on the state exam. We empirically identified eight qualitatively distinct and interpretable teacher qualification clusters. Based on value-added models, we found that teachers in Cluster 5 had lower average math learning gains than their peers in clusters with the most experienced and credentialed teachers. Cluster 5 included teachers who were novice and early-career, traditionally prepared math majors. We observed significant effects for the end or grade scores for the middle grades but not the algebra scores of high school students, suggesting teacher cluster membership effects varied by grade level. We discuss limitations and offer implications for research and policy.

Examining the Role of Domain‐General Skills in Mathematics Learning and Intervention Response in Kindergarten

AbstractEffective early mathematics instruction is critical to support long‐term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors associated with intervention response, the current study explored how domain general cognitive skills were associated with intervention response for 621 kindergarten students with or at risk for mathematics difficulties. Results indicated that although domain general skills were associated with mathematics achievement, there was no evidence of differential response to intervention based on cognitive skills. When examining differences while holding initial mathematics skill constant, there was a non‐significant, but potentially important pattern of students with higher domain general skills demonstrating greater mathematics gains as a result of intervention participation. Implications for mathematics intervention and curriculum development, including potentially impactful instructional approaches and cognitive scaffolds are discussed.

Identifying Fraction Measures as Screeners of Mathematics Risk Status

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction measures for predicting which students would not meet state standards on the state mathematics test in fourth grade (n = 411), fifth grade (n = 362), and sixth grade (n = 304). A combined measure consisting primarily of fraction number line estimation items and general fraction concept items was the most accurate screener of risk status in fourth, fifth, and sixth grades (area under the curve [AUC] = .84, .81, and .85, respectively). To maximize efficiency for classroom use, the length of the combined screener was reduced using best subset automatic linear modeling. The study highlights the importance of fraction knowledge for predicting mathematics achievement more generally and validates an effective and practical screening tool for the intermediate grades.

Efficacy of a First-Grade Mathematics Intervention on Measurement and Data Analysis

Well-designed mathematics instruction focused on concepts and problem-solving skills associated with measurement and data analysis can build a foundational understanding for more advanced mathematics. This study investigated the efficacy of the Precision Mathematics Level 1 (PM-L1) intervention, a Tier 2 print- and technology-based mathematics intervention designed to increase first-grade students’ conceptual understanding and problem-solving skills around the areas of measurement and data analysis. Employing a randomized controlled trial, 96 first-grade students at risk for mathematics difficulties were randomly assigned within classrooms to either a treatment (PM-L1) or a control (business-as-usual) condition. A statistically significant positive effect was found on one of five outcome measures, with the other four showing positive but nonsignificant results. Results also suggested preliminary evidence of differential response based on students’ number sense and early literacy risk status. Implications for using mathematics interventions focused on measurement and data analysis to build comprehensive, multitiered service delivery models in mathematics are discussed.

Visual perceptive skills account for very preterm children's mathematical difficulties in preschool

BackgroundAlready in preschool, very preterm (VP) children perform worse than term born-children on preschool mathematical skills tests. Strong associations have been found between preschool mathematical skills, cognition and visual-motor integration. AimsTo compare VP children and their term-born peers on preschool mathematical achievement at the corrected age of five years, and determine whether cognitive, visual-perceptive, visual-motor, and motor-coordination skills, account for any significant differences observed. Study designSingle-center, consecutive cohort study with a term-born comparison group. Subjects54 five-year-old VP children and 28 term-born comparison children. Outcome measuresStandardized test for preschool mathematical skills (Dutch pupil monitoring system), cognitive skills (Wechsler Preschool and Primary Scale for Intelligence - third edition), visual-perception, visual-motor integration, and motor-coordination (Beery Visual-Motor Integration test - sixth edition). Group differences were analyzed with ANCOVAs, adjusting for maternal education, preschool grade, and time of assessment. Sobel's mediation analyses tested for possible mediation effects. ResultsPreschool mathematical skills and visual perceptive skills were significantly lower in VP children than in term-born children (Cohen's d = 0.63, p = 0.01; Cohen's d = 0.84, p < 0.01, respectively). Sobel's test indicated a significant mediating effect of visual perceptive skills on the association between VP birth and preschool mathematical skills. ConclusionsAt preschool age, VP children have poorer preschool mathematical skills compared to term-born peers; deficits that were fully accounted for by poor visual perceptive skills. Our findings indicate the relevance of screening visual perceptive skills at preschool age, enabling timely identification of children at risk for mathematical difficulties.

A Fraction Sense Intervention for Sixth Graders With or At Risk for Mathematics Difficulties

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 centered on a visual number line in the meaningful context of a color run race. Students were randomly assigned to the fraction sense intervention ( n = 25) or a business-as-usual control group ( n = 27). Students in the intervention condition received 21 lessons in small groups (45 min each) during their regular mathematics intervention period. Students in the intervention group performed significantly better than those in the control group on a measure of fraction number line estimation and a more general measure of fraction concepts, both at immediate posttest and delayed posttest, with large effect sizes; lesser effects were shown for fraction arithmetic.

Relations between preschoolers’ mathematical language understanding and specific numeracy skills

Understanding of mathematical language is critical for numeracy skill development. However, prior research has focused exclusively on relations between mathematical language and numeracy skills, broadly measured. Thus, the aim of the current study was to explore more targeted relations between preschoolers’ mathematical language and specific numeracy skills (e.g., cardinality, numeral comparison). The participants were 124 preschoolers aged 3.52 to 6.03 years (M = 4.78 years, SD = 0.53). Children were assessed on a battery of early numeracy skills and mathematical language as well as expressive vocabulary. Mixed-effects regression models were conducted, with school as a random effect and age, gender, and parental education as fixed effects covariates. Results indicated that mathematical language was significantly related to most numeracy skills, including verbal counting, one-to-one correspondence, numeral identification, cardinality, comparisons of sets and/or numerals, ordering numerals, and story problems. As hypothesized, mathematical language was not significantly related to either subitizing or formal addition because these skills are independent of general language ability. Importantly, mathematical language was generally more proximal to each of these numeracy skills than was general language. These results provide direction for future research, in particular for the development of more precise measures to identify children at risk for mathematics difficulties as well as the incorporation of focused mathematical language instruction within early mathematics interventions.

Early Number Skills Gains and Mathematics Achievement: Intervening to Establish Successful Early Mathematics Trajectories

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for mathematics difficulties in a kindergarten intervention study. Results indicated strong relationships between formal number skills gains and mathematics achievement across kindergarten and Grade 1. Intervention participants demonstrated larger informal and formal early number skills gains compared with their control peers, and relations between early number skills gains and first-grade mathematics achievement were moderated by intervention participation. Importantly, these findings suggest that formal and informal number skills gains may be critical components of later mathematics achievement for at-risk students. Implications for special education and intervention in tiered instructional systems are discussed.

Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance.

In this chapter, we address one potentially overlooked component of the relation between executive function (EF) skills and early mathematics, a relation for which there is widespread empirical support. Evidence for this relation has, thus far, been largely correlational. Here we emphasize that because positive correlations do not guarantee concordance among all members of a sample or population, a small but meaningful number of children may either fare well in mathematics despite poor EF skills, or may have strong EF skills despite weak mathematics skills. We propose that attention to different profiles of discordance for EF and mathematics may help identify individualized learning needs for students at risk for mathematics difficulties and disabilities.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test).

The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

Is Mathematical Representation of Problems an Evidence-Based Strategy for Students With Mathematics Difficulties?

The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to the Gersten et al. (2005) guidelines for group research studies. Results suggest that the representation of mathematical problems as a strategy is an evidence-based practice based on the criteria set by Gersten et al. Implications for research are discussed.

Early Identification of Students at Risk for Mathematics Difficulties :

Early Identification of Students at Risk for Mathematics Difficulties :

Self-Regulated Strategy Development Instruction for Teaching Multi-Step Equations to Middle School Students Struggling in Math

Six middle school students identified as having a specific learning disability or at risk for mathematical difficulties were taught how to solve multi-step equations by using the self-regulated strategy development (SRSD) model of instruction. A multiple-probe-across-pairs design was used to evaluate instructional effects. Instruction was provided 4 days per week, 45 min per session, for 12 weeks as part of the Response to Intervention (RtI) framework. Results showed a functional relation between SRSD instruction and students’ ability to solve multi-step equations. All but one student were able to maintain gains. Students’ self-efficacy increased as a result of instruction, instruction was provided with high degrees of fidelity by a special educator, and student interviews revealed an overall satisfaction with SRSD instructional procedures.

The Effects of a Supplemental Explicit Counting Intervention for Preschool Children

Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is successful in teaching students in preschool. More research needs to be conducted on brief explicit mathematic interventions that target the skill of counting and are supplemental to preschool mathematics core instruction. In this study, researchers examine the effects of using explicit instruction as an intervention to teach counting skills for four children who were at risk for mathematics difficulties or who received special education services for developmental delay in an inclusive preschool setting. The researchers find a functional relation for a 15-minute supplemental explicit intervention and counting skills. Implications of these findings are also discussed.

Introduction to the Special Series on Universal Design for Learning

In Issue 37.2 of the Learning Disability Quarterly (LDQ), Dr. Margaret (Peggy) King-Sears introduced the first articles in her special series on Universal Design for Learning (UDL) and learning disabilities (LD). Peggy’s special series concludes in this issue with the remaining two articles. In the first article, Hall, Cohen, Vue, and Ganley explore the ability of The Strategic Reader, a technology-based system that blends UDL with curriculum-based measurement, to improve students’ reading comprehension skills. The second article, by King-Sears, Johnson, Berkeley, Weiss, Peters-Burton, Evmenova, Menditto, and Hursh, examines the effectiveness of UDL when applied to chemistry instruction. This special series provides a unique concentrated effort to empirically examine the effectiveness of UDL with students who have disabilities, including those with LD. We are pleased that Dr. King-Sears and her colleagues chose the LDQ as an outlet for their scholarship. Also, in this issue are two articles that discuss findings from studies on other topics. In the first of these two articles, Doabler, Clarke, Fien, Baker, Kosty, and Cary describe an initial investigation of a recently developed supplemental mathematics curriculum designed to improve the mathematics performance of first-grade students who are at risk for mathematics difficulties. The curriculum integrates foundational concepts of whole number and validated-design principles of explicit and systematic instruction. In the next article, Al-Yagon compares the emotional and coping resources of two groups of parents who have children 8 to 12 years of age. One group has children with LD; the other group is composed of parents who have typically developing children. The study examines how mothers’ and fathers’ emotional resources may help explain their coping differences. As always, we appreciate the authors’ contributions to the LD literature.

A Review of Early Numeracy Interventions for Children at Risk in Mathematics

This study reviewed early numeracy interventions for four- to seven-year-old children at risk for mathematics difficulties. The search yielded 19 peer-reviewed studies with pre- and post-treatment control designs. The interventions were categorised as either core or supplemental instruction. The study analysed the effectiveness and identified the pedagogical components of the interventions: setting, duration, numeracy content used for intervention training and progress measurement, conductor and professional developmental support offered, and instructional design features. The interventions showed, to various degrees, the promising effect of improving the early numeracy skills of at-risk children. Results indicated that different types of instructional design features, including explicit instruction, computer-assisted instruction (CAI), game playing, or the use of concrete- representational-abstract levels in representations of math concepts, led to improvements in mathematics performance. The paper discusses the implications for practise and suggestions for future research. Key Words: At-risk children, early numeracy, intervention, mathematics, review.

The Science Behind Curriculum Development and Evaluation

The production of an effective mathematics curriculum begins with a scientific development, evaluation, and revision framework. The purpose of this study was to conduct an initial investigation of a recently developed Tier 2 mathematics curriculum designed to improve the outcomes of first grade students at risk for mathematics difficulties (MD). The curriculum, which is anchored to a scientific design framework and a well-specified theory of change, centers on the careful integration of foundational concepts of whole number and validated-design principles of explicit and systematic instruction. Four instructional groups, with each consisting of five first grade students with MD and one interventionist, participated in the study. Data related to the feasibility, usability, and promise of the curriculum to improve student mathematics achievement were collected using multiple methods. Results provide preliminary evidence in terms of these curriculum development and evaluation areas. Implications for instruction and design research are discussed.

Curriculum-Based Measurement and Standards-Based Mathematics

This purpose of this study was to examine the reliability and validity of a curriculum-based measure of word problem solving (CBM-WPS) as an indicator of performance and progress in a sample of 136 third-grade students at risk for mathematics difficulties (MDs) instructed in a standards-based mathematics curriculum. Students completed the CBM-WPS measure every 2 weeks across 12 school weeks. Results indicated that the CBM-WPS measure was reliable and significantly correlated with measures of arithmetic WPS, number combinations fluency, and a standardized test of mathematics achievement. Results of growth modeling indicated that students showed significant growth on the CBM-WPS measure, with an average increase of 0.33 problems correct per week. Additional analyses revealed that students identified as high at-risk demonstrated similar growth as students identified as low at-risk. Furthermore, the CBM-WPS growth slopes were a significant predictor of students’ spring performance on a standardized test of mathematics achievement, demonstrating their predictive validity. Implications for practice and future research for assessing mathematics skill development are discussed.

A Randomized Controlled Trial of the Impact of Schema-Based Instruction on Mathematical Outcomes for Third-Grade Students with Mathematics Difficulties

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive problems. All students at risk for MD identified through screening received a mathematics intervention in groups of 2–4 for 12 weeks across the school year. Results revealed that students in the SBI group outperformed students in the control group on a word problem solving (WPS) posttest (g = 0.46). The effect of SBI proved to be equivalent for students in both high and low at-risk subgroups. On a district-administered mathematics achievement test, SBI students scored significantly higher than control students (g = 0.34); however, there were no significant effects on the WPS retention test (8 weeks later).