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 , 2005 ; A. J. Wilson & Dehaene, 2007 ) and/or to access that number magnitude representation from numerical symbols ( Rousselle & No?l, 2007 ). 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.     

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.     

Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.     

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.     

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.     

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.     

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.     

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.     

小学一年级数感不良儿童的筛查与动态干预

首先编制测查小学一年级儿童数感发展水平的测验, 以筛查出数感发展不良儿童并进行数量转换和数量估计的动态干预。将数感不良儿童分为干预组(29人)和控制组(27人), 并以数感正常儿童作为对照组(40人), 以比较干预训练对儿童数感水平和与之密切相关的计算流畅性的促进作用。同时进一步考查数感和计算流畅性的作用方向。结果发现：(1)所编制的儿童数感发展测验信效度良好, 能有效评估一年级儿童的数感水平; (2)数感不良儿童经干预后, 其数感水平较控制组有了明显改善, 计算流畅性水平也显著提高, 甚至达到正常组儿童的水平; (3)数感对计算流畅性有明显的预测作用, 是计算流畅性的基础。     

Verbal rehearsal and selective attention in children with learning disabilities: A developmental lag

To investigate the development of verbal rehearsal strategies and selective attention in learning disabled children, Hagen's Central-Incidental task was administered to younger learning disabled (M CA = 8.68 years) and normal (M CA = 8.62 years) boys in Experiment 1 and to intermediate (M CA = 10.18 years) and older (M CA = 13.48 years) learning disabled boys in Experiment 2. Also, in Experiment 2, an experimentally induced verbal rehearsal condition was included to determine its effects on serial recall and selective attention performance. In Experiment 1, the serial postion curve of the normals revealed both a primacy and a recency effect, whereas that of the learning disabled revealed a recency effect only. In Experiment 2, both the intermediate and the older learning disabled exhibited both primacy and recency effects under both standard and rehearsal conditions. A developmental analysis of central recall for the three learning disabled groups revealed constant age-related increases in overall central recall and in primacy recall. That the normals recalled more central, but not more incidental, information than the learning disabled in Experiment 1 suggests that the learning disabled are deficient in selective attention. Correlational findings suggest that the selective attention of the learning disabled improves with age. The results were interpreted as support for the hypothesis of a developmental lag in the learning disabled population.     

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.

     

Verbal learning and memory as measured by the Rey-Auditory Verbal Learning Test: ADHD with and without learning disabilities

The primary purpose of the present study is to examine the effects of attention deficits, learning disability, and the combined effects of both on the learning and memory processes, as measured by the Rey Auditory Verbal Learning Test (AVLT). Thirty children (age range 12-17) diagnosed with attention deficit/hyperactivity disorder (ADHD), 18 children (age range 11-17) diagnosed with learning disabilities (LD), and 64 children (age range 12-17) diagnosed with ADHD as well as with LD, and 28, 18, and 62 matched controls, respectively, participated in this study. It was found that the children diagnosed with ADHD did not differ in any of the verbal learning and memory measures derived from the Rey AVLT. The group with LD was impaired in the overall number of words recalled across the learning phase. Performance of the children diagnosed with ADHD +LD showed a similar impairment as the group with LD (i.e., overall amount of words learned) and, in addition, their retrieval efficiency was also impaired. In conclusion, this study indicates that verbal memory is preserved in children with ADHD if they have no LD and their intelligence is in the normal range or above. LD by itself leads to difficulties in acquisition, but the combination of ADHD+LD leads to additional impairment in retrieval processes.     

Verbal learning and memory as measured by the Rey-Auditory Verbal Learning Test: ADHD with and without learning disabilities

The primary purpose of the present study is to examine the effects of attention deficits, learning disability, and the combined effects of both on the learning and memory processes, as measured by the Rey Auditory Verbal Learning Test (AVLT). Thirty children (age range 12–17) diagnosed with attention deficit/hyperactivity disorder (ADHD), 18 children (age range 11–17) diagnosed with learning disabilities (LD), and 64 children (age range 12–17) diagnosed with ADHD as well as with LD, and 28, 18, and 62 matched controls, respectively, participated in this study. It was found that the children diagnosed with ADHD did not differ in any of the verbal learning and memory measures derived from the Rey AVLT. The group with LD was impaired in the overall number of words recalled across the learning phase. Performance of the children diagnosed with ADHD +LD showed a similar impairment as the group with LD (i.e., overall amount of words learned) and, in addition, their retrieval efficiency was also impaired. In conclusion, this study indicates that verbal memory is preserved in children with ADHD if they have no LD and their intelligence is in the normal range or above. LD by itself leads to difficulties in acquisition, but the combination of ADHD+LD leads to additional impairment in retrieval processes.     

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.