Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude (Butterworth, 1999 Butterworth, B. 1999. The mathematical brain, London, , United Kingdom: Macmillan.  [Google Scholar], 2005 Butterworth, B. 2005. “Developmental dyscalculia”. In Handbook of mathematical cognition, Edited by: Campbell, J. I. D. 455–467. New York, NY: Psychology Press.  [Google Scholar]; A. J. Wilson &; Dehaene, 2007 Wilson, A. J. and Dehaene, S. 2007. “Number sense and developmental dyscalculia”. In Human behavior, learning, and the developing brain: Atypical development, 2nd, Edited by: Coch, D., Dawson, G. and Fischer, K. 212–237. New York, NY: Guilford Press.  [Google Scholar]) and/or to access that number magnitude representation from numerical symbols (Rousselle &; Noël, 2007 Rousselle, L. and Noël, M. P. 2007. Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3): 361–395. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.     

Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children with MLD failed to accurately name decimals, to correctly rank order decimals and/or fractions, and to identify equivalent ratios (e.g. 0.5 = 1/2); they also 'identified' incorrect equivalents (e.g. 0.05 = 0.50). Children with low math achievement but no MLD accurately named decimals and identified equivalent pairs, but failed to correctly rank order decimals and fractions. Thus failure to accurately name decimals was an indicator of MLD; but accurate naming was no guarantee of rational number knowledge - most children who failed to correctly rank order fractions and decimals tests passed the naming task. Most children who failed the ranking tests at 6th grade also failed at 8th grade. Our findings suggest that a simple task involving naming and rank ordering fractions and decimals may be a useful addition to in-class assessments used to determine children's learning of rational numbers.     

The developmental course of processing speed in children with and without learning disabilities

This study contrasted the development of processing speed in children with and without learning disabilities. We examined whether the same global mechanism presumed to be responsible for the normal developmental improvement in processing speed might also be associated with the processing speed deficiencies observed in children with learning impairments. One hundred and twenty-two children with learning disabilities in reading and/or math and 206 non-disabled community controls participated. There were no differences in relation of age to the development of processing speed for children with and without learning disabilities. We interpreted these results as suggesting that the underlying etiologies for the normal developmental change in processing speed and for the relative deficiencies in processing speed seen among children with learning disabilities were different.     

Memory strategies in children with learning disabilities

Memory strategies were examined among children, 7–13 years old, with diagnosed learning disabilities, in order to investigate whether they perform in appropriately active and efficient ways. The children were grouped at two age levels and administered tasks of serial recall and free recall. A strategy-training session was conducted on the second task. On the serial recall, neither age group showed evidence of rehearsal, in contrast to previous studies. On the free recall task, the younger children's performance was consistent with the mediation deficiency hypothesis, while the older children improved in sorting, clustering, and recall following training; i.e., they showed a typical production deficiency. There was support for considering this sample of learning disabled children as inactive learners, with potential developmental change. Serial recall improved with age, and the older children's production deficiences in free recall appeared to be ameliorated with training in organizational strategies.     

A multisource exploration of the friendship patterns of children with and without learning disabilities

Friendship patterns of 117 children with learning disabilities (LD) and 115 children without LD in Grades 4–8 were examined. In comparison with children without LD, boys with LD had fewer mutual friends, children with LD had more friends with learning problems and more younger friends, and children with LD in Grades 4–6 had less stable relationships. With regard to friendship quality, children with LD reported higher levels of conflict, lower levels of validation, and more problems with relationship repair than did children without LD. The findings were discussed in terms of factors that have been found to enhance friendship such as proximity and similarity, and the social skills difficulties that have been associated with learning disabilities.     

Selective attention in children with learning disabilities.

49 children, aged 11 to 14 yr., a learning disabled group and a normal group, performed a primary, reading-like, card-sorting task. After they completed the primary task, they were tested for memory of incidental materials presented during learning. While the normal children showed better recall of incidental materials related to the primary task, 24 children with disabilities showed superior recall of material irrelevant to the primary task. The results were discussed in terms of alternative "motivational" and "developmental lag" interpretations.     

The inhibition capacities of children with mathematical disabilities.

Several authors have argued that mathematical disabilities might result from difficulties in inhibiting irrelevant information. The present study addresses this issue by assessing three inhibition functions in 40 ten-year-old children: suppression of irrelevant information from working memory, inhibition of prepotent responses, and interference control. We found no significant differences between children with math disabilities and typically achieving controls, or between children with arithmetic facts disabilities and children with above-average arithmetic facts skills. These findings, along with other empirical evidence and with theoretical considerations, cast doubt on the inhibition deficit hypothesis.     

Depression and achievement in subgroups of children with learning disabilities

Eighty-five learning disabled children were assigned to four subgroups and administered measures designed to assess the relationship between depression and academic achievement. As a group, these children were more depressed than nondisabled children. The subgroups, which were identified as learning disabled only, learning disabled with low IQ, learning disabled with socio-emotional disturbance, and learning disabled with hyperactivity, did not differ in magnitude of depression; however, the relationships between depression and achievement and IQ were substantially different in each subgroup. For the two largest subgroups, learning disabled only and learning disabled with socio-emotional disturbance, it was suggested that depression is the consequence of learning failure in the former and a possible cause of learning failure in the latter. These findings underscore the importance of depression, a heretofore neglected variable, for the understanding and remediation of learning disabilities.     

WISC-IV GAI and CPI profiles in healthy children and children with learning disabilities

IntroductionIn addition to the FSIQ, the General Ability Index (GAI) and the Cognitive Proficiency Index (CPI) are two ancillary scores that can be calculated for the Wechsler Intelligence Scale. The GAI and the CPI have been proposed to assist in identifying cognitive strengths and weaknesses, and thus to provide different views into individual's cognitive abilities.ObjectiveThe purpose of the present study is to provide the frequency of GAI/CPI score difference by direction, the frequency of FSIQ/GAI score difference, and the frequency of FSIQ/CPI score difference, for the French Wechsler Intelligence Scale for Children and Adolescents–Fourth Edition (WISC-IV).MethodThese frequencies are provided for a sample of healthy children (n = 483), and for a sample of children with learning disabilities (LD, n = 370). The GAI comprises verbal comprehension and perceptual reasoning subtests, while CPI comprises working memory and processing speed subtests.ResultsResults indicated that the healthy sample performed better than the LD sample for all composite scores. The FSIQ was lower than the GAI for both groups and this difference was slightly larger for the LD sample (−1.35 points vs. −3.22 points). The GAI was higher than the CPI for both samples, but this difference was not significantly larger for the LD sample (4.2 points vs. 6.16 points). Finally, while the FSIQ was higher than the CPI for both groups, this difference was not larger for the LD sample (2.85 points vs. 2.95 points).ConclusionThese findings support the use of the GAI and the CPI, in addition to the FSIQ.     

Concrete operational thought in children with learning disabilities and children with normal achievement.

This study compared Piagetian cognitive development in normal achieving children and two groups of children with learning disabilities designated as either auditory-linguistic or visual-spatial on the basis of Verbal-Performance IQ differences on the Wechsler Intelligence Scale for Children-Revised (WISC-R; 1974). The two groups with learning disabilities were matched with normal achieving controls on intelligence, socioeconomic status, sex, race, and age. Piagetian tasks measuring conservation, seriation, and classification were administered to each child to determine level of operative thought. The auditory-linguistic group scored significantly below normal controls in operativity, and significantly fewer were at a concrete operational level on a conservation of length task than were normal achieving children. The visual-spatial group did not differ significantly from normal controls. These results suggest that auditory-linguistic disabilities may be more detrimental than visual-spatial disabilities to development of operativity.     

Academic engagement of elementary school children with learning disabilities

Variability of attention-to-task and its relation to instructional contexts for children with learning disabilities was investigated. Twenty-four mainstreamed children were observed in both the regular class and the resource room. Student behaviors relating to academic engagement and the situational contexts in which they occurred were coded. Significant differences in rate of engagement were found for classroom setting, type of instruction, and level of peer involvement, indicating that degree of attending is not stable but a function of the context in which it occurs. Implications for the assessment of attentional problems and instructional practices, especially as related to the resource room program, are discussed.     

Field dependence versus field independence of students with and without learning disabilities

The Group Embedded Figures Test of Oltman, Raskin, and Witkin was administered to 60 high school students (30 with learning disabilities and 30 without learning disabilities) to measure their cognitive styles of field dependence versus field independence. The analysis showed that the students with learning disabilities scored as more field dependent than those without learning disabilities.     

The relationship between phonological processing and arithmetic in children with learning disabilities

Phonological processing skills have not only been shown to be important for reading skills, but also for arithmetic skills. Specifically, previous research in typically developing children has suggested that phonological processing skills may be more closely related to arithmetic problems that are solved through fact retrieval (e.g., remembering the solution from memory) than procedural computation (e.g., counting). However, the relationship between phonological processing and arithmetic in children with learning disabilities (LDs) has not been investigated. Yet, understanding these relationships in children with LDs is especially important because it can help elucidate the cognitive underpinnings of math difficulties, explain why reading and math disabilities frequently co-occur, and provide information on which cognitive skills to target for interventions. In 63 children with LDs, we examined the relationship between different phonological processing skills (phonemic awareness, phonological memory, and rapid serial naming) and arithmetic. We distinguished between arithmetic problems that tend to be solved with fact retrieval versus procedural computation to determine whether phonological processing skills are differentially related to these two arithmetic processes. We found that phonemic awareness, but not phonological memory or rapid serial naming, was related to arithmetic fact retrieval. We also found no association between any phonological processing skills and procedural computation. These results converge with prior research in typically developing children and suggest that phonemic awareness is also related to arithmetic fact retrieval in children with LD. These results raise the possibility that phonemic awareness training might improve both reading and arithmetic fact retrieval skills.

Research Highlights

• Relationships between phonological processing and various arithmetic skills were investigated in children with learning disabilities (LDs) for the first time.
• We found phonemic awareness was related to arithmetic involving fact retrieval, but not to arithmetic involving procedural computation in LDs.
• The results suggest that phonemic awareness is not only important to skilled reading, but also to some aspects of arithmetic.
• These results raise the question of whether intervention in phonemic awareness might improve arithmetic fact retrieval skills.

     

Narrative comprehension and retelling abilities of children with nonverbal learning disabilities

Nonverbal learning disabilities (NLD) are characterized by weaknesses in narrative discourse. Thirty-three children (M ag e= 11.7 years), 15 girls and 18 boys, listened to stories to evaluate their narrative comprehension and retelling abilities. Children with NLD (n = 11) performed as poorly as children with verbal impairment (n = 10) on all narrative measures. Compared to typical controls (n = 12), the NLD group was poorer in comprehending inferences, but not facts. They included less of the original content than controls in their story retells, and there were strong trends suggesting fewer utterances and less variety in their vocabulary usage. Results are discussed regarding their implications for understanding the neuropsychological profile of NLD.     

Differences between children with attention deficit disorder,children with specific learning disabilities,and normal children

The study investigated the power of five measures to differentiate between children with Attention Deficit Disorder (ADD), children with Specific Learning Disabilities (SLD), and normal children. The measures employed were the Conners Parent Questionnaire (CPQ), the Conners Teacher Questionnaire (CTQ), the Matching Familiar Figures Test (MFFT), the Porteus Mazes Test (PMT), and the Jumbled Numbers Game (JNG). The results indicated that the Conners Parent Questionnaire, Conners Teacher Questionnaire, Matching Familiar Figures Test, and the Porteus Mazes Test significantly discriminated between groups. The Conners Questionnaires were able to discriminate between all three groups and the MFFT and PMT were able to discriminate between ADD and normal children. A discriminant analysis indicated that the CPQ was the best predictor of group membership, followed in order by the CTQ PMT, and MFFT.     

Counterfactual syllogistic reasoning in normal 4-year-olds, children with learning disabilities, and children with autism

Instruction encouraging imagery improves logical reasoning with counterfactual premises by normal preschool children. In contrast, children with autism have been reported to reason accurately with counterfactual premises in the absence of such instruction (F. J. Scott, S. Baron-Cohen, & A. M. Leslie, 1999). To investigate this pattern of findings, we compared the performance of children with autism, children with learning disabilities, and normally developing 4-year-olds, who were given reasoning problems both with and without instruction in two separate testing sessions 2 to 3 weeks apart. Overall, instruction to use imagery led to persistent logical performance. However, children with autism displayed a distinctive pattern of responding, performing around chance levels, showing a simple response bias, and rarely justifying their responses by elaborating on the premises. We propose that instruction boosts logical performance by clarifying the experimenter's intention that a false proposition be accepted as a basis for reasoning and that children with autism have difficulty grasping this intention.