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.     

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.     

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 mathematical abilities of children with cochlear implants

Research has shown that cochlear implants give rise to improvements in speech recognition and production in children with profound hearing loss but very few studies have explored mathematical abilities in these children. The current study compared the mathematical abilities of 24 children with cochlear implants (mean age 10 years 1 month) to a control group of 22 hearing children (mean age 9 years 8 months). The math questions were categorized into questions that tapped into arithmetic or geometrical reasoning. It was predicted that the cochlear implant group would perform below the hearing group on the arithmetic questions but not the geometrical reasoning questions. Unexpectedly, the results showed that the cochlear implant group performed significantly below the hearing group on both types of math questions, but that this difference was mediated by language skill as assessed by vocabulary knowledge. The clinical implications of these results and possible future research results are considered.     

Religion and children with disabilities

Religion as a personal coping resource used by parents of infants and toddlers with disabilities has received some attention in recent literature. This exploratory study involved indepth interviews of 12 parents who had children with disabilities ranging in age from 15 months to 30 years. The ways in which religion can be used as a coping resource across the life-cycle are exemplified through excerpts from these interviews. Prayer, church attendance, and specific religious beliefs were identified as sources of support which helped some parents feel a growing sense of hope and strength. Suggestions for future research are discussed.Tess Bennett, Ph.D., is Assistant Professor in the University of Illinois College of Education, Department of Special Education; Deborah A. Deluca, B.A., is in the Department of Educational Psychology, and Robin W. Allen, M.S.W., is a doctoral candidate in the Department of Social Work at the same university.     

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.     

School adjustment of children with observable disabilities

This study investigated school behavior and achievement of children with mild degrees of observable physical disability. Children from two different disability types (cleft palate and cerebral palsy) were compared with each other and to a control group in order to determine potential similarities across disability types. Children (N=78) from each of the two disability groups were individually matched to each other and to a normal control group (N=39) by sex, IQ, socioeconomic status, age, and grade. They were compared on the basis of teachers' behavioral ratings and achievement test scores. All children attended regular public school classrooms. The two disability groups displayed significantly greater inhibition of impulse and lower educational achievement than did the controls. The implication of similar school adjustment across mild but observable subtypes is discussed.Parts of this article were presented at the meeting of the American Psychological Association, Washington, D.C., September 1976. The study was supported in part by PHS Grant DE-00853, the National Institute of Dental Research.     

The effect of reinforcement variables on inhibition in children with ADHD.

Behavioral inhibition, often cited as a central deficit in children with ADHD, has been shown to change in response to reinforcement. In this preliminary investigation, children with ADHD (n= 20) and matched controls (ages 7 to 12) completed a new version of the stop signal paradigm, the Fire Fighter Game, a measure of inhibition of a prepotent motor response, under three conditions: (1) no reinforcement; (2) immediate reinforcement; and (3) delayed reinforcement. In all conditions, the stop signal reaction time (SSRT) of children with ADHD was consistently longer than controls. Both groups improved significantly with reinforcement, and there was no strong evidence that immediate reinforcement was more effective than delayed reinforcement. However, it appeared that the reason for the changes in SSRT in response to reinforcement differed between the groups. Children in the control group responded faster on go trials, whereas children with ADHD improved their ability to inhibit responding with shorter stop delays. The relevance of these findings is discussed in terms of current theories of ADHD.     

Working memory in children with reading disabilities

This study investigated associations between working memory (measured by complex memory tasks) and both reading and mathematics abilities, as well as the possible mediating factors of fluid intelligence, verbal abilities, short-term memory (STM), and phonological awareness, in a sample of 46 6- to 11-year-olds with reading disabilities. As a whole, the sample was characterized by deficits in complex memory and visuospatial STM and by low IQ scores; language, phonological STM, and phonological awareness abilities fell in the low average range. Severity of reading difficulties within the sample was significantly associated with complex memory, language, and phonological awareness abilities, whereas poor mathematics abilities were linked with complex memory, phonological STM, and phonological awareness scores. These findings suggest that working memory skills indexed by complex memory tasks represent an important constraint on the acquisition of skill and knowledge in reading and mathematics. Possible mechanisms for the contribution of working memory to learning, and the implications for educational practice, are considered.     

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.     

Psychodynamic counselling with parents of children with developmental disabilities

A joint treatment of parents and child can be the treatment of choice when dealing with developmental disabilities. In our clinical experience, we have observed that psychoanalytically oriented support (developmental guidance), which involves the child and the parents together, answers the needs and addresses the difficult dynamics that are characteristic of developmental disabilities.     

Sociocultural studies of families of children with intellectual disabilities

This article reviews recent sociocultural studies of families of children with intellectual disabilities to introduce the range of research conducted from this perspective and to highlight the methodological, conceptual, and theoretical contributions of this approach to the study of mental retardation. Sociocultural studies examine families within their cultural, historical, and sociopolitical contexts. This type of research is comparative across different cultural groups, but is not limited to such comparisons. Sociocultural studies use varied theories and methods, but they share a focus on families' coproduction of meanings and practices related to intellectual disability; families' responses and adaptations to disability; and how their understandings and experiences are shaped within larger social institutions and inequities. Sociocultural approaches take into account community contexts that matter to families with members with mental retardation or developmental delay, and they examine the broader systems that define and position individuals with disabilities and their families. As a whole, these studies provide a more experiential and holistic view of families' beliefs and adaptations within sociopolitical worlds, and offer new tools by which to study the families of children with developmental delays within and across different cultural groups.     

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.

     

Life skills instruction for children with developmental disabilities

The Preschool Life Skills program is an intervention package designed to teach functional skills to prevent problem behavior in typically developing children. The purpose of the current study was to evaluate the effects of the instructional package (renamed “Life Skills”) with children with developmental disabilities. The program involved teaching 12 life skills to nine participants across four instructional units. The units were instruction following, functional communication, tolerance of denial and delay, and friendship skills. Teachers provided instruction through a three-tiered instructional approach, starting with class-wide instruction followed by small group and one-to-one instruction as necessary. We extended previous research by using visual prompts during all three tiers and progressively increasing intertrial intervals during one-to-one instruction. Results indicated that the intervention led to skill acquisition with all nine participants. The skills maintained 4 weeks after instruction ended.     

Supporting communication in young children with developmental disabilities

The behavior of parents, adult caregivers, and peers comprises the critical features of community support for the development of communication in young children with developmental disabilities. In a bio-ecological model of development, communication development is the result of the interactions of individuals with specific characteristics, in particular contexts over time. From the perspective of this model, foundational findings of intervention research to current views of communication development in children with developmental disabilities are summarized. The contributions of individual child characteristics to child-caregiver interactions that support language development are illustrated based on research with children who have autism, Williams syndrome, Down syndrome, and children who use augmentative communication systems. Parent-child interaction and the quality and quantity of parent talk are discussed as factors in children's language development. The effects of young children's delayed language on their interactions with peers, the contributions of peers to children's language learning and use, and the critical features of classroom settings that support child language development are reviewed. MRDD Research Reviews 7:143-150, 2001.     

The role of maternal responsivity in the development of children with intellectual disabilities

There is growing evidence that cumulative exposure to highly responsive parenting styles throughout the early childhood period may provide a variety of important child benefits in terms of language, cognitive, social, and emotional development. We view maternal responsivity as a dynamic construct of central importance to the development of children with intellectual disabilities just as it is for typically developing children. In this study, we selectively review the theoretical and conceptual evidence for the effects of responsivity on development, discuss factors known to influence responsivity including the nature of a child's disability, and review intervention approaches intended to enhance maternal responsivity. We conclude with a set of recommendations for future research.