Mathematical Learning Disabilities Research Articles

Cognitive Processing and Mathematical Achievement

This investigation analyzed the relation between cognitive functioning and mathematical achievement in 114 students in fourth, fifth, and sixth grades. Differences in cognitive performance were studied concurrently in three selected achievement groups: mathematical learning disability group (MLD), low achieving group (LA), and typically achieving group (TA). For this purpose, performance in verbal memory and in the PASS cognitive processes of planning, attention, and simultaneous and successive processing was assessed at the end of the academic course. Correlational analyses showed that phonological loop and successive and simultaneous processing were related to mathematical achievement at all three grades. Regression analysis revealed simultaneous processing as a cognitive predictor of mathematical performance, although phonological loop was also associated with higher achievement. Simultaneous and successive processing were the elements that differentiated the MLD group from the LA group. These results show that, of all the variables analyzed in this study, simultaneous processing was the best predictor of mathematical performance.

Cognitive and Emotional Factors in Children with Mathematical Learning Disabilities

Emotional and cognitive factors were examined in 18 children with mathematical learning disabilities (MLD), compared with 18 normally achieving children, matched for chronological age, school level, gender and verbal IQ. Working memory, short‐term memory, inhibitory processes, speed of processing and level of anxiety in mathematics were assessed in the two groups. The results corroborated the hypothesis that children with MLD are impaired in working memory capacity, inhibitory ability, and speed of processing. However, no impairment was found in short‐term memory tasks requiring passive storage of verbal and numerical information. Moreover, while the children with MLD showed higher levels of anxiety in mathematics, their anxiety levels in other school subjects were similar to those of normal achievers. Implications for identifying underlying emotional and cognitive deficits in children with MLD are discussed, along with possible approaches to treatment.

Coherent motion sensitivity predicts individual differences in subtraction

Recent findings suggest deficits in coherent motion sensitivity, an index of visual dorsal stream functioning, in children with poor mathematical skills or dyscalculia, a specific learning disability in mathematics. We extended these data using a longitudinal design to unravel whether visual dorsal stream functioning is able to predict individual differences in subsequent specific mathematical skills, i.e., single-digit subtraction and multiplication. We measured children's sensitivity to coherent motion in kindergarten (mean age: 5 years 8 months) and evaluated their subtraction and multiplication skills in third grade (mean age 8 years 3 months). Findings revealed an association between subtraction but not multiplication performance and coherent motion sensitivity. This association remained significant even when intellectual ability and reading ability were additionally controlled for. Subtractions are typically solved by means of quantity-based procedural strategies, which reliably recruit the intraparietal sulcus. Against the background of a neural overlap between the intraparietal sulcus and visual dorsal stream functioning, we hypothesize that low-level visuospatial mechanisms might set constraints on the development of quantity representations, which are used during calculation, particularly in subtraction.

Fact Retrieval Deficits in Low Achieving Children and Children With Mathematical Learning Disability

Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA–mild fact retrieval; n = 97) and severe (LA–severe fact retrieval; n = 18) fact retrieval deficits and mathematically learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted developing retrieval competence from second to fourth grade with developing competence in executing arithmetic procedures, in fluency of processing quantities represented by Arabic numerals and sets of objects, and in representing quantity on a number line. The retrieval deficits of LA–severe fact retrieval children were at least as debilitating as those of the children with MLD and showed less across-grade improvement. The deficits were characterized by the retrieval of counting string associates while attempting to remember addition facts, suggesting poor inhibition of irrelevant information during the retrieval process. This suggests a very specific form of working memory deficit, one that is not captured by many typically used working memory tasks. Moreover, these deficits were not related to procedural competence or performance on the other mathematical tasks, nor were they related to verbal or nonverbal intelligence, reading ability, or speed of processing, nor would they be identifiable with standard untimed mathematics achievement tests.

Can we predict mathematical learning disabilities from symbolic and non‐symbolic comparison tasks in kindergarten? Findings from a longitudinal study

The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. The current study addressed the predictive value of non-symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sixteen children with mathematical disabilities (MD), 64 low achievers (LA), and 315 typical achieving (TA) children were followed from kindergarten till grade 2. The association of comparison skills with arithmetical skills in grades l and 2 was studied. The performances of MD, LA and TA children were compared. Regression analyses showed that non-symbolic skills in kindergarten were predictively related to arithmetical achievement 1 year later and fact retrieval 2 years later. AN comparison was predictively related to procedural calculation 2 years later. In grade 2, there was an association between both symbolic tasks and arithmetical achievement. Children with MD already had deficits in non-symbolic and symbolic AN comparison in kindergarten, whereas in grade 2 the deficits in processing symbolic information remained. The combination of non-symbolic and symbolic deficits represents a risk of developing MD.

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics.

Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving

Although various studies support the multicomponent nature of visuospatial working memory, to date there is no general consensus on the distinction of its components. A difference is usually proposed between visual and spatial components of working memory, but the individual roles of these components in mathematical learning disabilities remains unclear. The present study aimed to examine the involvement of visual and spatial working memory in poor problem-solvers compared with children with normal level of achievement. Fourth-grade participants were presented with tasks measuring phonological loop, central executive, and visual versus spatial memory. In two separate experiments, both designed to distinguish visual and spatial component involvement, poor problem-solvers specifically failed on spatial—but not visual or phonological—working memory tasks. Results are discussed in the light of possible working memory models, and specifically demonstrate that problem-solving ability can benefit from analysis of spatial processes, which involves ability to manipulate and transform relevant information; instead, no benefit is gained from the analysis of visual pictorial detail.

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 mathematical 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.

Understanding the Cognitive Processes and Metacognitive Strategies that Work with Mathematical Learning Disabilities

Understanding the Cognitive Processes and Metacognitive Strategies that Work with Mathematical Learning Disabilities

Math Anxiety and Math Ability in Early Primary School Years.

Mathematical learning disabilities (MLDs) are often associated with math anxiety, yet until now, very little is known about the causal relations between calculation ability and math anxiety during early primary school years. The main aim of this study was to longitudinally investigate the relationship between calculation ability, self-reported evaluation of mathematics, and math anxiety in 140 primary school children between the end of first grade and the middle of third grade. Structural equation modeling revealed a strong influence of calculation ability and math anxiety on the evaluation of mathematics but no effect of math anxiety on calculation ability or vice versa-contrasting with the frequent clinical reports of math anxiety even in very young MLD children. To summarize, our study is a first step toward a better understanding of the link between math anxiety and math performance in early primary school years performance during typical and atypical courses of development.

Predicting Mathematical Achievement and Mathematical Learning Disability with a Simple Screening Tool

The Number Sets Test was developed to assess the speed and accuracy with which children can identify and process quantities represented by Arabic numerals and object sets. The utility of this test for predicting mathematics achievement and risk for mathematical learning disability (MLD) was assessed for a sample of 223 children. A signal detection analysis of first grade Number Sets Test scores provided measures of children's sensitivity to number and their response bias. The sensitivity measure, d', but not the response bias measure was predictive of third grade mathematics achievement scores, above and beyond the influence of intelligence, working memory, and first grade achievement scores. Further analyses assessed the sensitivity and specificity of the test and revealed that first grade d' scores identified 2 out of 3 children diagnosed as MLD in third grade and correctly identified about 9 out of 10 children who were not at risk for MLD.

This Month in Anesthesiology

The investigators studied the association between anesthetic exposure before age 4 and the development of learning disabilities (LD) in reading, written language, and mathematics. Educational and medical records of all children born to mothers residing in five townships were examined. A single exposure to anesthesia (n = 449) was not associated with an increased risk of LD (hazard ratio = 1.0; 95% confidence interval, 0.79–1.27). However, children receiving two anesthetics (n = 100) or three or more anesthetics (n = 44) were at increased risk for LD (hazard ratio = 1.59; 95% confidence interval, 1.06–2.37, and hazard ratio = 2.60; 95% confidence interval 1.60–4.24, respectively). The authors noted they cannot determine whether anesthesia itself may contribute to LD, or whether the need for multiple anesthetics is a marker for other unidentified factors that contribute to LD.The authors hypothesized that natriuretic peptide system gene variants independently predict risk of ventricular dysfunction (VnD) after primary coronary artery bypass grafting. A total of 139 haplotype-tagging single nucleotide polymorphisms (SNPs) within 7 natriuretic peptide system genes were genotyped. Seven natriuretic SNPs were associated with decreased risk of postoperative VnD (odds ratios = 0.44–0.55; P = 0.010–0.036) and four natriuretic SNPs were associated with increased risk of postoperative VnD (odds ratios = 3.89–4.28; P = 0.007–0.034). Knowledge of natriuretic peptide system gene variants may result in a better understanding of postoperative VnD after primary coronary artery bypass grafting. These variants may also predict those patients at high risk for VnD so that preventative interventions can be explored. See the accompanying Editorial View on page 693 Exposure to anesthetics administered to young animals causes neurohistopathologic changes including apoptosis, a form of programmed cell death. The investigators examined isoflurane-mediated apoptosis in isolated neuronal tissues in vitro. The authors focused their investigation on a precursor of mature brain-derived neurotrophic factor (BDNF), called proBDNF, and its receptor, the p75 neurotrophin receptor (p75NTR). Inhibition of the proBDNF–p75NTRsignaling pathway blocked isoflurane-mediated neuronal apoptosis in cultured neurons from the developing rodent brain. If exposure to anesthesia and surgery in early life impairs neural development, the proBDNF–p75NTRsignaling pathway may be a target for future therapeutic intervention. See the accompanying Editorial View on page 709 The authors examined the association between preoperative executive function, depression, and other established clinical predictors of postoperative delirium among 998 patients undergoing major noncardiac surgery. Patients were screened prospectively using the Confusion Assessment Method as well as by retrospective chart review. Thirty-five patients developed delirium postoperatively (3.5%). Preoperative executive dysfunction (P = 0.007) and greater levels of depression (P = 0.049) were associated with a greater incidence of postoperative delirium. Complex tests for executive function were more strongly associated with postoperative delirium than simpler tests. In the future, preoperative screening of patients at risk for delirium may facilitate testing of preventative interventions.The pursuit of excellence should always be the number one agenda item for all anesthesiologists. See the accompanying Editorial View on page 712 A preoperative screening tool for obstructive sleep apnea and postanesthesia care unit monitoring identified patients at risk for later adverse postoperative respiratory events.Independent predictors of impossible mask ventilation were determined.Keys for safe perioperative airway management of obese patients with obstructive sleep apnea are reviewed.

Classification, Seriation, and Counting in Grades 1, 2, and 3 as Two-Year Longitudinal Predictors for Low Achieving in Numerical Facility and Arithmetical Achievement?

Previous research stresses the importance of seriation, classification, and counting abilities that should be assessed in kindergarten, when looking for crucial predictors of mathematical learning disabilities in Grade 1. This study examines ( n = 158) two-year-long predictive relationships between children's seriation, classification, procedural counting knowledge, and conceptual counting knowledge, and their numerical facility and arithmetical achievement in Grades 3, 4, and 5. Path analyses reveal a relationship between procedural counting knowledge in Grades l and 3 and numerical facility, and between conceptual counting knowledge in Grade l and arithmetical achievement in Grades 1 and 2. In addition, procedural counting knowledge correlates with seriation, and conceptual counting knowledge correlates with classification as well as with seriation in Grade 1. Clinicians are encouraged to select early arithmetic subtests with caution when assessing and predicting arithmetic and arithmetical disabilities.

Mathematical learning disabilities in special populations: Phenotypic variation and cross‐disorder comparisons

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to mathematical learning difficulties and disabilities presented across the reviews. Specifically we consider how each of the reviews contributes to identifying the MLD phenotype by specifying the range of assets and deficits in mathematics, identifying sources of individual variation, and characterizing the natural progression of MLD over the life course. We show how principled comparisons across disorders address issues about the cognitive and behavioral co-morbidities of MLD, and whether commonalities in brain dysmorphology are associated with common mathematics performance profiles. We project the status of MLD research ten years hence with respect to theoretical gains, advances in methodology, and principled intervention studies.

Mathematical learning disability in girls with Turner syndrome: A challenge to defining MLD and its subtypes

Turner syndrome is a common disorder with a prevalence of 1:2,500 live female births. Although not associated with mental retardation, there is an increased risk of learning difficulties in this population. In particular, mathematical learning difficulties among girls with Turner syndrome are prevalent, significant, and persistent. As such, the study of mathematical performance in girls with Turner syndrome presents opportunities to advance our knowledge of mathematics ability, disability, and disability subtypes. Moreover, the Turner syndrome phenotype illustrates the challenges faced when defining mathematical learning disability (MLD) and characterizing MLD subtypes because the cognitive phenotype is aligned with several proposed MLD subtypes. There is some evidence linking MLD in Turner syndrome with spatial deficits, with executive dysfunction, and with deficient numerosity skills. Yet there is also conflicting evidence as to whether any of these explanations underlies MLD in Turner syndrome. Most mathematical difficulties in girls with Turner syndrome, as a group, occur on timed tests or on complex problems. On untimed tests, achievement test scores may be age appropriate. Therefore, the inclusion of MLD in the Turner syndrome cognitive phenotype reminds us that we cannot rule out MLD solely on the basis of performance on an untimed calculations subtest, and it poses a challenge to the widespread practice in which many researchers engage, that is, defining MLD on the basis of broad mathematics achievement test outcomes.

Mathematical learning disabilities in children with 22q11.2 deletion syndrome: A review

Mathematical learning disabilities (MLD) occur frequently in children with specific genetic disorders, like Turner syndrome, fragile X syndrome and neurofibromatosis. This review focuses on MLD in children with chromosome 22q11.2 deletion syndrome (22q11DS). This syndrome is the most common known microdeletion syndrome with a prevalence of at least 1:4000 to 1:6000 live births. Although the clinical presentation of 22q11DS is quite variable, its major characteristics include velopharyngeal abnormalities, congenital cardiac anomalies, mild facial dysmorphism and learning difficulties. Children with 22q11DS show considerable difficulties in mathematics, despite relatively normal reading performance. While fact retrieval seems to be preserved, impairments in procedural calculation and word problem solving are particularly prominent. Children with 22q11DS also have substantial difficulties in understanding and representing numerical quantities, possibly related to poor visuospatial attention, which all might stem from their underlying abnormalities in the inferior parietal cortex. This review ends with a discussion on how research on genetic disorders might aid our understanding of MLD in general.

Potential influences on mathematical difficulties in children and adolescents with neurofibromatosis, type 1

Neurofibromatosis, type 1 (NF-1) is a common genetic disorder affecting 1 in 3,500-4,000 individuals in the world. Mutations of the NF-1 gene produce a myriad of physical, medical, and psychological manifestations. Although there is a very high degree of variability in the manifestations between individuals with NF-1, the majority of children and adolescents with NF-1 encounter difficulties that negatively impact their educational attainment. NF-1 is associated with a very high incidence of cognitive deficits and learning disability, sometimes including mathematical learning disabilities (MLD). A number of possible inter-related etiologies for MLD specific to children and adolescents with NF-1 are discussed, including the high incidence of attention deficit hyperactivity disorder, visual spatial impairment, morphological and functional brain abnormalities. Thus NF-1 exemplifies the wide ranging sources of potential influences on mathematical learning and MLD.

A review of mathematical learning disabilities in children with fragile X syndrome

The prevalence rate of mathematical learning disabilities (MLD) among children with fragile X syndrome who do not meet criteria for intellectual and developmental disabilities (approximately 50% of female children) exceeds the rate reported in the general population. The purpose of this article is two-fold: (1) to review the findings on MLD in persons with fragile X syndrome; and (2) to discuss fragile X syndrome as a possible model for understanding pathways to MLD.

Case Study: Transitioning From Insulin to Glyburide in Permanent Neonatal Diabetes: Medical and Psychosocial Challenges in an 18-Year-Old Male

D.R., an 18-year-old man diagnosed with insulin-dependent diabetes as an infant, was identified as an appropriate candidate for genetic testing based on publications identifying a monogenic cause of diabetes in patients diagnosed in the first 6 months of life.1,2 As a 2.78-kg full-term infant (in the third percentile for weight with intrauterine growth retardation), D.R. initially presented in the Emergency Department at 3 weeks of age with a blood glucose level of 571 mg/dl after 1 week of increased irritability, crying, and decreased oral intake. He was initiated on conventional split-mixed insulin (NPH/regular) twice daily and has been followed ever since by the diabetes team in a large pediatric hospital. Notable history includes moderate developmental delays in reading, writing, and fine and gross motor skills and an identified learning disability in mathematics. Medical history is significant for two presumed hypoglycemic seizures. At the time of D.R.'s diagnosis, permanent neonatal diabetes mellitus (PNDM) was medically treated as type 1 diabetes. However, in 2004, a specific genetic mutation (KCNJ11 gene) was identified as the cause of neonatal diabetes, and ensuing research confirmed that high doses of oral sulfonylureas are successful in managing neonatal diabetes in selected patients.1,2 When D.R. was 18 years old, PNDM attributed to the KCNJ11 R201H (heterozygous) mutation was confirmed by a saliva sample sent for Institutional Review Board-approved research-based analysis at the University of Chicago Diabetes Research and Training Center and follow-up serum analysis performed by the Clinical Laboratory Improvement Amendments-approved University of Chicago Genetics Services Laboratory. Treatment options were discussed and, after informed consent, D.R. chose a longer outpatient transition rather than completing the transition in an inpatient clinical research unit. Thereafter, the transition from insulin to glyburide was initiated based on the outpatient protocol described by Pearson et al.2 …

First-grade predictors of mathematical learning disability: A latent class trajectory analysis

Kindergarten to third grade mathematics achievement scores from a prospective study of mathematical development ( n = 306) were subjected to latent growth trajectory analyses. The four corresponding classes included children with mathematical learning disability (MLD, 6% of sample), and low (LA, 50%), typically (TA, 39%) and high (HA, 5%) achieving children. The groups were administered a battery of intelligence (IQ), working memory, and mathematical-cognition measures in first grade. The children with MLD had general deficits in working memory and IQ and potentially more specific deficits on measures of number sense. The LA children did not have working memory or IQ deficits but showed moderate deficits on these number sense measures and for addition fact retrieval. The distinguishing features of the HA children were a strong visuospatial working memory, a strong number sense, and frequent use of memory-based processes to solve addition problems. Implications for the early identification of children at risk for poor mathematics achievement are considered.