Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties

Profiles of mathematical deficits in children with dyslexia

Despite a high rate of concurrent mathematical difficulties among children with dyslexia, we still have limited information regarding the prevalence and severity of mathematical deficits in this population. To address this gap, we developed a comprehensive battery of cognitive tests, known as the UCSF Mathematical Cognition Battery (MCB), with the aim of identifying deficits in four distinct mathematical domains: number processing, arithmetical procedures, arithmetic facts retrieval, and geometrical abilities. The mathematical abilities of a cohort of 75 children referred to the UCSF Dyslexia Center with a diagnosis of dyslexia, along with 18 typically developing controls aged 7 to 16, were initially evaluated using a behavioral neurology approach. A team of professional clinicians classified the 75 children with dyslexia into five groups, based on parents' and teachers' reported symptoms and clinical history. These groups included children with no mathematical deficits and children with mathematical deficits in number processing, arithmetical procedures, arithmetic facts retrieval, or geometrical abilities. Subsequently, the children underwent evaluation using the MCB to determine concordance with the clinicians' impressions. Additionally, neuropsychological and cognitive standardized tests were administered. Our study reveals that within a cohort of children with dyslexia, 66% exhibit mathematical deficits, and among those with mathematical deficits, there is heterogeneity in the nature of these deficits. If these findings are confirmed in larger samples, they can potentially pave the way for new diagnostic approaches, consistent subtype classification, and, ultimately personalized interventions.

Cognitive Predictors of the Overlap of Reading and Math in Middle School

Math and reading skills are known to be related, and predictors of each are well researched. What is less understood is the extent to which these predictors, uniquely and collectively, overlap with one another, are differentially important for different academic skills, and account for the overlap of math and reading. We examined 20 potential predictors from four domains (working memory, processing speed, attention, and language) using latent variables and both timed and untimed achievement skill, in a sample (N=212) of at-risk middle schoolers, half of whom were English learners. The predictors accounted for about half of the overlap among achievement skills, suggesting that other factors (e.g., domain specific skills) might also be relevant for the overlap. We also found some differential prediction (language for reading, working memory for math). The present results extend and refine our understanding of the contribution of these cognitive predictors for reading and math.

Iodine Intake and Related Cognitive Function Impairments in Elementary Schoolchildren

Iodine deficiency, the most common cause of preventable mental impairment worldwide, has been linked to poorer intellectual function in several studies. However, to our knowledge, no studies have been performed in moderate iodine-deficient schoolchildren using the complete form of Wechsler Intelligence Scale for Children (WISC-III; Portuguese version). The main purpose of this study was to ascertain whether moderate iodine deficiency would affect the cognitive function of schoolchildren (7-11 years old; 3rd and 4th grades). Raven's Colored Progressive Matrices (CPM; Portuguese version) were used for measuring the intelligence quotient (IQ) of the total population (n = 256; median UIC = 66.2 μg/L), and the WISC-III was used to study two selected subgroups: one moderately iodine-deficient (n = 30) and the other with adequate iodine intake (n = 30). WISC-III was shown to be the prime instrument for cognitive function assessment among moderate iodine-deficient schoolchildren; this subgroup had a Full-Scale IQ 15.13 points lower than the adequate iodine intake subgroup, with a magnitude effect of d = 0.7 (p = 0.013). Significant differences were also registered in 6 of the 13 Verbal-Performance IQ subtests. Moderate iodine deficiency has a substantial impact on mental development and cognitive functioning of schoolchildren, with significant impairment in both Performance IQ and Verbal IQ spectrum, adversely impacting their educational performance.

Applying an Individual Word-Problem Intervention to a Small-Group Setting: A Pilot Study's Evidence of Improved Word-Problem Performance for Students Experiencing Mathematics Difficulty

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (N = 76) were randomly assigned to word-problem intervention (n = 56) or business-as-usual comparison (n = 20). Intervention occurred for 13 weeks, 3 times per week, 30 min per session. Multilevel models revealed the intervention condition significantly outperformed the BaU on a proximal word-problem outcome, corroborating results from our prior individual intervention. When comparing student performance in the individual versus small-group intervention, findings suggest students received added benefit from the individual intervention. The word-problem intervention successfully translated to a small-group setting, which holds important implications for educators working with students in supplemental, targeted, or Tier 2 mathematics intervention settings.

A Network Analysis of Children's Emerging Place-Value Concepts

Examining how informal knowledge systems change after formal instruction is imperative to understanding learning processes and conceptual development and to implementing effective educational practices. We used network analyses to determine how the organization of informal knowledge about multidigit numbers in kindergartners (N = 279; mean age = 5.76 years, SD = 0.55; 135 females) supports and is transformed by a year of in-school formal instruction. The results show that in kindergarten, piecemeal knowledge about the surface properties of reading and writing multidigit numbers and the use of base-10 units to determine large quantities are strongly associated with each other and connected in a stringlike manner to other emerging skills. After a year of instruction, each skill becomes connected to the "hub" abilities of reading and writing multidigit numbers, which also become strongly connected to more advanced knowledge of base-10 principles. These findings provide new insights into how partial knowledge provides the backbone on which explicit principles are learned.

The development of place value concepts: Approximation before principles

Place value concepts were measured longitudinally from kindergarten (2017) to first grade (2018) in a diverse sample (n = 279; Mage  = 5.76 years, SD = 0.55; 135 females; 41% Black, 38% White, 8% Asian, 12% Latino). Children completed three syntactic tasks that required an explicit understanding of base-10 symbols and three approximate tasks that could be completed without this explicit understanding. Approximate performance was significantly better in both age groups. A factor analysis confirmed that syntactic and approximate tasks tapped separate latent variables in kindergarten, but not in first grade. Path analyses indicated that only kindergarten approximate performance predicted overall first-grade place value understanding. These findings suggest that explicit understanding of base-10 principles develops from implicit, partial knowledge of multidigit numbers.

Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature

Mathematical performance implies a series of numerical and mathematical skills (both innate and derived from formal training) as well as certain general cognitive abilities that, if inadequate, can have a cascading effect on mathematics learning. These latter skills were the focus of the present systematic review. Method: The reviewing process was conducted according to the PRISMA statement. We included 46 studies comparing school-aged children’s performance with and without math difficulties in the following cognitive domains: processing speed, phonological awareness, short- and long-term memory, executive functions, and attention. Results: The results showed that some general cognitive domains were compromised in children with mathematical difficulties (i.e., executive functions, attention, and processing speed). Conclusions: These cognitive functions should be evaluated during the diagnostic process in order to better understand the child’s profile and propose individually tailored interventions. However, further studies should investigate the role of skills that have been poorly investigated to date (e.g., long-term memory and phonological awareness).

Mathematical Difficulties vs. High Achievement: An Analysis of Arithmetical Cognition in Elementary School

This study analyzed the contribution of cognitive processes (planning, attention, simultaneous and successive processing) and domain-specific skills (counting, number processing and conceptual comprehension) to the arithmetic performance achieved in the last three grades (4th, 5th, and 6th) of elementary school. Three groups of students with a different arithmetic achievement level were characterized. The predictive value of the cognitive processes and the math specific skills are explored through diverse covariance and discriminant analyses. Participants were 110 students (M = 10.5 years, SD = 1.17) classified in three groups: mathematical difficulties (MD; n = 26), high achieving (HA; n = 26), and typical achieving (TA; n = 58). Cognitive processes and domain-specific skills were evaluated in two individual sessions at the end of the school year. Nonverbal intelligence was assessed in a final collective session with each class. The mathematical difficulties group's achievement was deficient in simultaneous and successive processing, number processing, and conceptual comprehension compared to the typical achievement group. High achievement children obtained significantly better results than the typical achievement children in simultaneous processing, counting, number processing, and conceptual comprehension. Number processing and conceptual comprehension were the most consistent classifiers, although successive and simultaneous processing, respectively, also contributed to identifying students with mathematical difficulties and high achievement. These findings have practical implications for preventive and intervention proposals linked to the observed profiles.

Place-value computation in children with mathematics difficulties

Recent research has provided initial evidence that children with math difficulties (MD) experience problems in processing place-value information in basic numerical tasks. However, it remains unclear whether these problems generalize to basic arithmetic operations. For instance, multi-digit addition problems with carryover specifically require the computation of place-value information. Yet little is known about the carry effect in children with MD. Therefore, the current study investigated whether problems in processing place-value information among third-grade children with MD (n = 29 9-year-olds) compared with an age-matched control group (n = 50) generalize to two-digit addition. The results indicate an increased carry effect for response latencies and error rates in children with MD. These findings suggest that deficits in processing place-value information among children with MD generalize to place-value computations in multi-digit arithmetic. Potential contributions of strategy use and working memory for difficulties in processing place-value information are discussed.

Cognitive Profiles Associated With Responsiveness to Fraction Intervention

This study examined differences in cognitive processing between 4^th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or inadequate responders, using as the cut-point the control-group mean on pre-to-post improvement on the relevant measure. Between-group differences identified reasoning, concept formation, and listening comprehension related to all 3 fraction outcomes. On the number-line outcome, within-group profile analysis indicated that inadequate responders experienced low reasoning ability relative to their other forms of cognitive processing.

Math Error Types and Correlates in Adolescents with and without Attention Deficit Hyperactivity Disorder

Objective: The aim of this study was to examine the types of errors made by youth with and without a parent-reported diagnosis of attention deficit and hyperactivity disorder (ADHD) on a math fluency task and investigate the association between error types and youths’ performance on measures of processing speed and working memory.

Method: Participants included 30 adolescents with ADHD and 39 typically developing peers between 14 and 17 years old matched in age and IQ. All youth completed standardized measures of math calculation and fluency as well as two tests of working memory and processing speed. Math fluency error patterns were examined.

Results: Adolescents with ADHD showed less proficient math fluency despite having similar math calculation scores as their peers. Group differences were also observed in error types with youth with ADHD making more switch errors than their peers.

Conclusion: This research has important clinical applications for the assessment and intervention on math ability in students with ADHD.

Error Patterns with Fraction Calculations at Fourth Grade as a Function of Students' Mathematics Achievement Status

The goal of the present study was to describe fraction-calculation errors among 4^th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We specifically addressed whether mathematics-achievement status was related to students' tendency to operate with whole number bias. We extended this focus by comparing low-performing students' errors in two instructional settings that focused on two different types of fraction understandings: core instruction that focused on part-whole understanding vs. small-group tutoring that focused on magnitude understanding. Results showed students across the sample were more likely to operate with whole number bias on problems with unlike denominators. Students with low or average achievement (who only participated in core instruction) were more likely to operate with whole number bias than students with low achievement who participated in small-group tutoring. We suggest instruction should emphasize magnitude understanding to sufficiently increase fraction understanding for all students in the upper elementary grades.

Behavioral Executive Functions Among Adolescents With Mathematics Difficulties

This study investigates behavioral executive functions (EFs) in the mathematics classroom context among adolescents with different mathematics performance levels. The EF problems were assessed by teachers using a behavioral rating inventory. Using cutoff scores on a standardized mathematics assessment, groups with mathematics difficulties (MD; n = 124), low mathematics performance (LA; n = 140), and average or higher scores (AC; n = 355) were identified. Results showed that the MD group had more problems with distractibility, directing attention, shifting attention, initiative, execution of action, planning, and evaluation than the LA group, whereas the differences in hyperactivity, impulsivity, and sustaining attention were not significant. Compared to the AC group, the MD group showed more problems with all behavioral EFs except hyperactivity and impulsivity, while the LA group showed more problems only with shifting attention. Male adolescents showed more behavioral EF problems than female adolescents, but this gender difference was negligible within the MD group. The practical implications of the results are discussed.

Distinct influences of affective and cognitive factors on children's non-verbal and verbal mathematical abilities

Individual differences in children's math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children's math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving.

[Formula: see text]Cognitive and behavioral rating measures of executive function as predictors of academic outcomes in children

Interrelations of two measurement methods (cognitive versus behavioral ratings) for executive function (EF) were examined and related to reading comprehension and math calculations in fourth and fifth grade students (n = 93) in the context of a diverse urban student population. Relations among measures within four EF processes (working memory, planning, inhibition and shifting) were modest; relations to academics were stronger. EF measures contributed to both academic outcomes even in the context of relevant covariates (age, language and educational program). Working memory was particularly important for reading comprehension across measurement type. Cognitive measures from all EF processes, particularly inhibition and planning, and behavioral ratings of working memory were important for math.

Alterações Fonoaudiológicas no Transtorno de Déficit de Atenção e Hiperatividade: revisão sistemática de literatura

RESUMO Objetivo revisar sistematicamente as produções científicas acerca das relações entre o Transtorno de Déficit de Atenção e Hiperatividade e a Fonoaudiologia e analisar, metodologicamente, os estudos observacionais sobre a temática. Estratégia de pesquisa trata-se de revisão sistemática de literatura, realizada nas bases de dados Medical Literature Analysis and Retrieval System on-line (MEDLINE, EUA), Literatura Latino-Americana e do Caribe em Ciências da Saúde (LILACS, Brasil) e Indice Bibliográfico Español de Ciencias de la Salud (IBECS), na qual foram utilizados os descritores “Linguagem”, “Desenvolvimento da Linguagem”, “Transtorno do Déficit de Atenção com Hiperatividade”, “TDAH” e “Percepção Auditiva”. Critérios de seleção foram selecionados artigos publicados entre 2008 e 2013. Os critérios de inclusão foram: artigos completos, publicados em periódicos nacionais e internacionais, no período de 2008 a 2013. Como critério de exclusão, foram considerados os artigos que não apresentavam, como foco principal, as alterações fonoaudiológicas presentes no Transtorno de Déficit de Atenção e Hiperatividade. Análise dos dados foi realizada a leitura dos artigos na íntegra e a extração de dados para caracterização da metodologia e do conteúdo das pesquisas. Resultados foram encontrados 23 artigos, os quais foram separados de acordo com dois eixos temáticos, relacionados à Fonoaudiologia e ao Transtorno de Déficit de Atenção e Hiperatividade. Conclusão o estudo das produções científicas revelou que as alterações fonoaudiológicas mais abordadas foram os distúrbios de leitura e que há poucas publicações acerca da relação entre o processamento auditivo e o transtorno, bem como a respeito da atuação do fonoaudiólogo na avaliação e no tratamento de crianças com Transtorno de Déficit de Atenção e Hiperatividade.

Basic numerical processing, calculation, and working memory in children with dyscalculia and/or ADHD symptoms

Abstract. Objective: Deficits in basic numerical skills, calculation, and working memory have been found in children with developmental dyscalculia (DD) as well as children with attention-deficit/hyperactivity disorder (ADHD). This paper investigates cognitive profiles of children with DD and/or ADHD symptoms (AS) in a double dissociation design to obtain a better understanding of the comorbidity of DD and ADHD. Method: Children with DD-only (N = 33), AS-only (N = 16), comorbid DD+AS (N = 20), and typically developing controls (TD, N = 40) were assessed on measures of basic numerical processing, calculation, working memory, processing speed, and neurocognitive measures of attention. Results: Children with DD (DD, DD+AS) showed deficits in all basic numerical skills, calculation, working memory, and sustained attention. Children with AS (AS, DD+AS) displayed more selective difficulties in dot enumeration, subtraction, verbal working memory, and processing speed. Also, they generally performed more poorly in neurocognitive measures of attention, especially alertness. Children with DD+AS mostly showed an additive combination of the deficits associated with DD-only and A_Sonly, except for subtraction tasks, in which they were less impaired than expected. Conclusions: DD and AS appear to be related to largely distinct patterns of cognitive deficits, which are present in combination in children with DD+AS.


Old/New Effect of Digital Memory Retrieval in Chinese Dyscalculia

This study reports the neurophysiological and behavioral correlates of digital memory retrieval features in Chinese individuals with and without dyscalculia. A total of 18 children with dyscalculia (ages 11.5-13.5) and 18 controls were tested, and their event-related potentials were digitally recorded simultaneously with behavior measurement. Behavioral data showed that the dyscalculia group had lower hit rates and higher false rates than the control group. The electroencephalography results showed that both groups had a significant old/new effect and that this effect was greater in the control group. In the 300 to 400 ms processing stages, both groups showed significant differences in digital memory retrieval in the frontal regions. In the 400 to 500 and 500 to 600 ms epochs, the old/new effect in the control group was significantly greater than it was in the dyscalculia group at the frontal, central, and parietal regions. In the 600 to 700 ms processing stages, both groups showed significant differences in digital memory retrieval in the frontal, central, parietal, and occipital regions. These results suggest that individuals with dyscalculia exhibit impaired digital memory retrieval. Extraction failure may be an important cause of calculation difficulties.

Neurocognitive predictors of mathematical processing in school-aged children with spina bifida and their typically developing peers: Attention, working memory, and fine motor skills

OBJECTIVE

Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated.

METHOD

Participants were 9.5-year-old children with SBM (n = 44) and typically developing children (n = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM.

RESULTS

Children with SBM performed similarly to peers on exact arithmetic, but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention, but not on alerting and executive attention. Multiple mediation models showed that fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study.

CONCLUSION

Results are discussed with reference to models of attention, WM, and mathematical cognition.

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 4^th-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 4^th grade. Then, they were assessed on whole-number and fraction calculation and number line estimation measures at the end of 4^th 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.

Longitudinal relations among inattention, working memory, and academic achievement: testing mediation and the moderating role of gender

Introduction. Behavioral inattention, working memory (WM), and academic achievement share significant variance, but the direction of relationships across development is unknown. The aim of the present study was to determine whether WM mediates the pathway between inattentive behaviour and subsequent academic outcomes. Methods. 204 students from grades 1-4 (49.5% female) were recruited from elementary schools. Participants received assessments of WM and achievement at baseline and one year later. WM measures included a visual-spatial storage task and auditory-verbal storage and manipulation tasks. Teachers completed the SWAN behaviour rating scale both years. Mediation analysis with PROCESS (Hayes, 2013) was used to determine mediation pathways. Results. Teacher-rated inattention indirectly influenced math addition fluency, subtraction fluency and calculation scores through its effect on visual-spatial WM, only for boys. There was a direct relationship between inattention and math outcomes one year later for girls and boys. Children who displayed better attention had higher WM scores, and children with higher WM scores had stronger scores on math outcomes. Bias-corrected bootstrap confidence intervals for the indirect effects were entirely below zero for boys, for the three math outcomes. WM did not mediate the direct relationship between inattention and reading scores. Discussion. Findings identify inattention and WM as longitudinal predictors for math addition and subtraction fluency and math calculation outcomes one year later, with visual-spatial WM as a significant mediator for boys. Results highlight the close relationship between inattention and WM and their importance in the development of math skills.

Cognitive and mathematical profiles for different forms of learning difficulties

The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive measures (e.g., working memory and language) and on mathematics measures of foundational numerical competencies, computation, and problem solving. Results revealed expected level differences among groups in both domains: NoLD outperformed RD, and MD outperformed MDRD. Profile differences were noted among pairs of subgroups on cognitive measures. On mathematics measures, profile differences were noted between RD and other subgroups, but not between MD and MDRD subgroups. The most discriminating cognitive measures were processing speed and language; the most discriminating mathematics measures depended on the subgroups being compared. Results were further evaluated according to more severe (< 10th percentile) criteria for MD and RD, which generally affected level differences more than the profile patterns. Results have implications for understanding comorbid MD and RD and for conceptualizing core deficits in MD.

Mathematics development and difficulties: the role of visual-spatial perception and other cognitive skills

Several neurocognitive abilities, including visual-spatial and language-based processes, attention, and fine motor/finger skills, are thought to play important roles in mathematical development and disability. Evidence for relations of specific neurocognitive skills and mathematical development and disability is presented, with a particular emphasis on findings from longitudinal studies. Why these particular neurocognitive skills are related to math is also discussed. We suggest that mathematics learning in children with congenital and acquired neurodevelopmental disorders, including children treated for cancer, is particularly vulnerable to disruption because these disorders often affect one or more of the neurocognitive systems that support math learning and performance. Implications for assessment of and interventions for math difficulties are discussed. The article ends with implications for mathematical functioning in children treated for acute lymphoblastic leukemia and brain tumors.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense.

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills such as number system knowledge and estimation. This study of 3rd graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in 3 significant arithmetic skills: basic calculation fluency, written multidigit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill, and their contributions are independent of both each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: Most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multidigit skills. These findings indicate that many factors matter but multidigit skills matter most in 3rd grade mathematical achievement.

Prediction and stability of mathematics skill and difficulty

The present study evaluated the stability of math learning difficulties over a 2-year period and investigated several factors that might influence this stability (categorical vs. continuous change, liberal vs. conservative cut point, broad vs. specific math assessment); the prediction of math performance over time and by performance level was also evaluated. Participants were 144 students initially identified as having a math difficulty (MD) or no learning difficulty according to low achievement criteria in the spring of Grade 3 or Grade 4. Students were reassessed 2 years later. For both measure types, a similar proportion of students changed whether assessed categorically or continuously. However, categorical change was heavily dependent on distance from the cut point and so more common for MD, who started closer to the cut point; reliable change index change was more similar across groups. There were few differences with regard to severity level of MD on continuous metrics or in terms of prediction. Final math performance on a broad computation measure was predicted by behavioral inattention and working memory while considering initial performance; for a specific fluency measure, working memory was not uniquely related, and behavioral inattention more variably related to final performance, again while considering initial performance.

Rethinking ADHD and LD in DSM-5: proposed changes in diagnostic criteria

The Diagnostic and Statistical Manual of Mental Disorders (DSM) is currently undergoing revision that will lead to a fifth edition (DSM-5) in 2013. This article first provides a brief synopsis of the DSM-5 administrative structure, procedures, and guiding principles to enhance understanding of how changes are made in the DSM. The next two sections (on attention-deficit/hyperactivity disorder and learning disorders, respectively) highlight the major concerns and controversies surrounding the DSM-IV diagnostic criteria for these two disorders and provide a rationale for the proposed changes to the criteria, along with a commentary on the empirical evidence on which the proposed changes were based.

Mathematical Cognition Deficits in Children With Learning Disabilities and Persistent Low Achievement: A Five-Year Prospective Study

First- to fifth-grade mathematics and word reading achievement were assessed for children with mathematical learning disability (MLD, n = 16), persistent low achievement (LA, n = 29), and typical achievement (n = 132). Intelligence, working memory, processing speed, and in-class attention were assessed in 2 or more grades, and mathematical cognition was assessed with experimental tasks in all grades. The MLD group was characterized by low school-entry mathematics achievement and poor word reading skills. The former was mediated by poor fluency in processing or accessing quantities associated with small sets of objects and corresponding Arabic numerals, whereas the latter was mediated by slow automatized naming of letters and numbers. Both the MLD and LA groups showed slow across-grade growth in mathematics achievement. Group differences in growth were mediated by deficits or delays in fluency of number processing, the ability to retrieve basic facts from long-term memory and to decompose numbers to aid in problem solving, and by the central executive component of working memory and in-class attention.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics

The goals of the review are threefold: (a) to highlight the educational and employment consequences of poorly developed mathematical competencies; (b) overview the characteristics of children with mathematical learning disability (MLD) and with persistently low achievement (LA) in mathematics; and (c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms underlying these learning disabilities and associated cognitive interventions. Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Poor mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, ∼ 7% of children and adolescents have MLD and another 10% show persistent LA in mathematics, despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in learning mathematical procedures. These deficits and delays cannot be attributed to intelligence but are related to working memory deficits for children with MLD, but not LA children. These individuals have identifiable number and memory delays and deficits that seem to be specific to mathematics learning. Interventions that target these cognitive deficits are in development and preliminary results are promising.

Mathematical Disabilities: Reflections on Cognitive, Neuropsychological, and Genetic Components

The collection of articles in this special issue and related studies over the past decade provides a fine example of the substantial progress that has been made in our understanding and remediation of mathematical learning disabilities and difficulties since 1993 (Geary, 1993). The originally proposed procedural and retrieval deficits have been supported and a number sense deficit has been identified. There is evidence for visuospatial contributions to some aspects of mathematical learning, but identification of a core visuospatial deficit underlying some forms of mathematics learning disabilities and difficulties has been elusive. The contributions of working memory to the development and expression of these deficits is more nuanced than I originally proposed as are the brain systems supporting mathematical learning. Although much has been learned about children's difficulties in learning mathematics, but there is just as much and likely more than remains to be discovered.

Sources of Group and Individual Differences in Emerging Fraction Skills

Results from a two year longitudinal study of 181 children from fourth through fifth grade are reported. Levels of growth in children's computation, word problem, and estimation skills using common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency. Comparisons of 55 participants identified as having mathematical difficulties to those without mathematical difficulties revealed that group differences in emerging fraction skills were consistently mediated by attentive classroom behavior and conceptual knowledge about fractions. Neither working memory nor arithmetic fluency mediated group differences in growth in fraction skills. It was also found that the development of basic fraction skills and conceptual knowledge are bidirectional in that conceptual knowledge exerted strong influences on all three types of basic fraction skills, and basic fraction skills exerted a more modest influence on subsequent conceptual knowledge. Results are discussed with reference to how the identification of potentially malleable student characteristics that contribute to the difficulties that some students have with fractions informs interventions and also will contribute to a future theoretical account concerning how domain general and domain specific factors influence the development of basic fraction skills.