A Meta‐Analysis of Empirical Research on Teaching Students with Mathematics Learning Difficulties

This article quantitatively summarizes experimental and quasi‐experimental studies on teaching students with mathematics difficulties (MD) published between 2000 and 2014, research that was available following earlier syntheses. It reports the analysis of effect sizes of 25 intervention studies on participant characteristics, intervention parameters, domains of mathematics interventions, and instructional approaches and components. Results indicate that several participant characteristics (e.g., grade level and level of mathematics difficulties) and intervention parameters (e.g., methodological soundness, intervention agent, and grouping) mediated the treatment effects. In addition, different types of instructional approaches and several instructional components contributed to the improvements in mathematics performance in students with MD.     

Challenges in identifying target skills for math disability screening and intervention

Gersten, Jordan, and Flojo (in this series) review their research on math difficulties, with an emphasis on applying current knowledge to inform practices of early identification and intervention. On a practical level, educators are in dire need of empirically based screening and intervention tools. From a scientific perspective, it is important to recognize the need to clearly define what we seek to identify and remediate, and to acknowledge that we are currently far from achieving this goal despite recent advances in the field. Among the studies reviewed by Gersten et al., as well as other studies by several other researchers, there is much variability in how mathematics difficulties are defined and measured, and even in the terms used to refer to them. I address the degree of consensus and controversy currently characterizing the state of math learning disabilities research, with an emphasis on the usefulness of a developmental perspective in appraising this young field.     

Clock reading: an underestimated topic in children with mathematics difficulties

Recent studies have shown that children with mathematics difficulties (MD) have weaknesses in multiple areas of mathematics. Andersson, for example, recently found that children with MD perform significantly worse than other children on clock reading tasks. The present study builds on this recent finding and aims at a more profound understanding of the difficulties that children with MD experience with telling time. Therefore, clock reading abilities of 154 children with MD were compared to the abilities of 571 average achieving children, and a qualitative error analysis was performed. The results of this study confirm the earlier findings of Andersson that children with MD perform worse on clock reading than average achieving children and also show that children with MD especially struggle with the combination of procedural and retrieval strategies that are needed to read complex 5-min and 1-min clock times. Children with MD make more errors, which reflects immature counting strategies and deficits in memory retrieval. This finding is in line with Geary's theory of subtypes in MD, which argues that children with MD have problems with mathematical procedures and semantic memory retrieval.     

Phonological Awareness and Rapid Naming Skills of Children with Reading Disabilities and Children with Reading Disabilities Who Are At Risk for Mathematics Difficulties

Limited research has examined the skills of children with a reading disability (RD) and children with RD and a mathematics disability (MD). Even less research has examined the phonological awareness (PA) and rapid automatized naming (RAN) skills in these two groups of children and how these skills relate to reading and math achievement. Additionally, various classification criteria are frequently implemented to classify children with MD. The purpose of this study, therefore, was to examine the PA and RAN skills in children who met different criteria for RD only and children with RD who are at risk for mathematics difficulties (MDR). Participants were 114 second‐ or third‐grade students with RD from public elementary schools in three large metropolitan areas. Students were classified as at risk for mathematics difficulties utilizing a 25th‐percentile cutoff and a 15th‐percentile cutoff as assessed by the KeyMath‐Revised Test ( Connolly, 1988 ). A series of PA and RAN measures were administered along with a range of reading and mathematics measures. Hierarchical regression analyses indicated that children with RD only evidenced a different pattern of results compared to children with RD + MDR. Additionally, using a more stringent criterion to classify children at risk for mathematics difficulties resulted in a differential pattern of results when compared to a less stringent classification criterion.     

Mathematical thinking in second-grade children with different forms of LD

Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving.     

Making the Case for Early Identification and Intervention for Young Children at Risk for Learning Disabilities

The early identification of children with learning disabilities (LD) is difficult but can be accomplished. Observation of key behaviors which are indicators of LD by preschool and kindergarten teachers can assist in this process. This early identification facilitates the use of intervention strategies to provide a positive early experience for children at risk for academic difficulties.     

Early years practitioners’ views on early personal,social and emotional development

Current policy guidance stresses the need for early identification of obstacles to learning and appropriate intervention. New standards for learning (Early Years Foundation Stage) place personal, social and emotional development (PSED) as central to learning and development. This paper reports a survey and follow-up interviews with early years practitioners on early identification and intervention of young children with difficulties in PSED. As previous research with primary and secondary colleagues has shown, practitioners find low-level disturbance occurring most frequently. Although aggressive behaviour (hurting others, kicking, hitting and biting) is a concern, not attending or listening and immature social skills (lack of sharing and turn-taking, and inability to relate to other children) is a bigger challenge. Practitioners report a range of strategies for formally teaching relevant skills but point to the greater challenge of supporting recent immigrants where different cultural and social norms need to be understood.     

我国数学学习困难儿童的教育与干预研究回顾与展望

近年来,我国对数学学习困难儿童的表现、诊断、认知特点等有了较多的研究,这为数学学习困难儿童的干预策略提供了基础。通过对我国数学学习困难儿童的教育干预研究进行综述,发现主要有知觉加工干预策略、工作记忆干预策略、问题表征干预策略和元记忆干预策略,并在借鉴国外数学学习困难研究的基础上,对我国未来数学学习困难的研究提供若干建议。     

Role of cognitive theory in the study of learning disability in mathematics

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.     

Differences in the Mathematics‐Vocabulary Knowledge of Fifth‐Grade Students With and Without Learning Difficulties

The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics‐vocabulary understanding of fifth‐grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and general vocabulary measures, students were categorized with no learning difficulty (i.e., typical), mathematics difficulty without reading difficulty (MD‐only), reading difficulty without mathematics difficulty (RD‐only), and combined mathematics and reading difficulties (MDRD). On the mathematics‐vocabulary measure, students with MD‐only or RD‐only scored significantly lower than typical students, and students with MDRD demonstrated significantly lower performance than students with MD‐only or RD‐only.     

Baseline assessment,value-added and the prediction of reading

Value-added approaches aim to make fair comparisons of the academic progress of pupils in different settings. They rest on measurements at two time points and it has been suggested that the assessment of 4-year-olds cannot provide a sufficiently strong base from which to make comparisons at the end of Key Stage 1. Data on a range of potential predictors from the Performance Indicators in Primary Schools (PIPS) are related to measures of reading and mathematics in Year 2. The questions addressed include: a) To what extent is it possible to predict the reading of 7-year-olds? b) Which measures of 4-year-olds are the most predictive of later success? c) What are the implications for baseline assessment nationally? The results suggest that on-entry assessments, which last about 20 minutes, can predict the reading and mathematics scores of seven-year-olds with correlations around 0.7. Several measures are identified as potential predictors. The quickest to administer reliably include digit and letter identification, counting, writing and doing simple sums. The analysis suggests that value-added measures are possible for schools but that individual pupil predictions remain problematic.     

Response to intervention for reading difficulties in the primary grades: some answers and lingering questions

The purpose of this article is to describe the current research base and identify research needs related to response to intervention (RTI) frameworks in primary-grade reading. Research is reviewed on early reading instruction and intervention, the implementation of multitiered reading interventions, and the determination of intervention responsiveness. Areas identified as in need of research include (a) the conditions under which early reading interventions are most effective in RTI contexts, (b) multitiered interventions for students with limited English proficiency, (c) reading instruction for students who make limited progress in Tier 3 intensive interventions, (d) criteria for determining intervention responsiveness, and (e) the effects of fully implemented RTI frameworks. Although RTI research may be expensive and difficult to implement, it may contribute to improved reading outcomes for many students who are otherwise at risk of serious negative life consequences.     

Representation of situations involving changes sequence: A didactic interdisciplinary intervention

Our previous research, conducted in various fields, demonstrates the obvious difficulties children encounter when they must achieve, in a collective game situation, coordinated motor actions (Garnier, 1989) or solve additive problems in mathematics involving changes sequence (Bednarz Schmidt, & Dufour-Janvier, 1989b; Poirier & Bednarz. 1991a, b). These investigations show the children’s extreme centration on the states, and a global non anticipation of the situations that lead them to act punctually and sequentially. The didactic intervention that was developed in view of these difficulties, integrating sociomotor and mathematics activity, aims to develop the cognitive processes of decentration and anticipation on the basis of the resolution of these situations. In the pedagogical approach undertaken on 30 grade three children (8–9 years old), the social actions and interactions played a major part in the development of the aimed processes and in the elaboration of the representation of underlying relations to the situations involved (games and problems). A sociomotor examination (collective game) and a written examination in mathematics, carried out before and after the experiment, show, along with the qualitative analysis achieved during the intervention, the evolution of the child jaced with the aimed processes.     

数学学习困难学生数学技能干预效果的元分析

探索干预对提升数学学习困难学生数学学业表现的有效性及其调节因素.通过系统检索文献获得纳入符合标准的30篇文献,应用CMA2.0软件进行元分析,并检验被试特征、干预方案、干预目标、干预方法的调节效应.随机效应模型表明数学干预对数困生数学表现的合并效应量Hedges'g为0.438(p＜0.001),对数困生干预效果呈中等...     

Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use

Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between numerical magnitude representations and children's strategy use during single‐digit arithmetic. Our findings reveal that children's symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming, and general mathematics achievement are additionally controlled for. All this indicates that particularly the access to numerical meaning from Arabic symbols is key for children's arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent.     

The effects of strategic counting instruction,with and without deliberate practice,on number combination skill among students with mathematics difficulties

The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone versus MD with reading difficulty) and site (proximal versus distal to the intervention developer) and then randomly assigned to control (no tutoring) or 1 of 2 variants of NC remediation. Both remediations were embedded in the same validated word-problem tutoring protocol (i.e., Pirate Math). In 1 variant, the focus on NCs was limited to a single lesson that taught strategic counting. In the other variant, 4–6 min of practice per session was added to the other variant. Tutoring occurred for 16 weeks, 3 sessions per week for 20–30 min per session. Strategic counting without deliberate practice produced superior NC fluency compared to control; however, strategic counting with deliberate practice effected superior NC fluency and transfer to procedural calculations compared with both competing conditions. Also, the efficacy of Pirate Math word-problem tutoring was replicated.     

An Evolution of Mathematical Beliefs: A Case Study of Three Pre-K Teachers

This case study involved examination of the evolution of mathematical beliefs of three prekindergarten teachers. The researcher followed three teachers at one school in west Alabama over the course of 6 months as they implemented a new mathematics curriculum in their pre-K classrooms. Interviews were conducted prior to implementation and at the end of the school year. Classroom observations were done throughout the implementation process. Three themes emerged from the data (a) math resources for the pre-K classroom, (b) pushing beyond—thinking mathematically, and (c) instructional strategies used the pre-K classroom. These themes revealed how all of the teachers' perceptions of early childhood mathematics curriculum and instruction evolved during the course of the study. These findings have implications for early childhood teacher education programs and professional development.     

Principles for the Prevention and Intervention of Mathematics Difficulties

Three levels of prevention and intervention in the area of mathematics are addressed: (a) primary prevention focusing on universal design, (b) secondary prevention focusing on adaptations, and (c) tertiary prevention focusing on intensive and explicit contextualization of skills‐based instruction. The purpose of this paper is to identify and discuss principles of prevention and intervention in the area of mathematics. First, we identify research‐based principles associated with primary prevention. Second, we turn our attention to secondary prevention, with a focus on prereferral intervention. We identify principles that serve to differentiate primary and secondary prevention and specify instructional variables that are promising for use within a secondary prevention mode. Finally, we discuss intervention. We identify principles of effective intervention, which include individually referenced decision making, instructional intensity, and deliberate contextualization of skills‐based instruction.     

Mathematics-related emotions among Finnish adolescents across different performance levels

This study examined the relation of mathematics performance and gender with seven mathematics-related emotions (enjoyment, pride, anger, anxiety, shame, hopelessness and boredom) among adolescents. Using strict and lenient mathematics performance cut-off scores, respective groups of adolescents with mathematics difficulties (MD, n = 136), low (LA, n = 166) and typical mathematics performance (TA, n = 1056) were identified. Our results revealed that the MD group reported more shame than the LA group. The MD group also reported more negative emotions and less positive emotions than the TA group, with the exception of boredom, for which there was no statistically significant difference. The interaction effect between mathematics performance group and gender on emotions was significant. Only females with MD showed significantly higher levels of hopelessness and shame than females with LA, while males with LA even reported more boredom than males with MD. Concerning gender differences, males reported slightly more pride and enjoyment than females. However, the direction and magnitude of the gender differences showed great variance among mathematics performance groups. The practical implications of the results are discussed.     

Intensive Intervention in Mathematics

Students who demonstrate persistent mathematics difficulties and whose performance is severely below grade level require intensive intervention. Intensive intervention is an individualized approach to instruction that is more demanding and concentrated than Tier 2 intervention efforts. We present the elements of intensive intervention that teachers should consider when planning for, implementing, and monitoring intensive intervention in mathematics. Each of these elements is based on evidence from validated interventions. We also highlight strategies for intensifying instruction. We provide two examples of intensive intervention, one of which launches from a Tier 2 intervention platform and the other which is completely generated by a teacher. We conclude with considerations for intensive intervention in mathematics.