Mathematics & Down Syndrome Abstracts

J Intellect Disabil Res 49 (10): 761-5 (2005 Oct)

Numeracy for adults with Down syndrome: it's a matter of quality of life

Faragher R¹, Brown RI²
¹James Cook University, School of Education, Townsville Qld, Australia. ²Child and Youth Care, University of Victoria, BC, Canada

BACKGROUND: Numeracy development is widely accepted as critical for adults in the general community which is equally the case for adults with Down syndrome. This paper reports some of the findings of a study including the research question: What is the justification for numeracy development for adults with Down syndrome? Investigating this question led to the search for a framework to support the ongoing development of numeracy. METHOD: The research used a case study methodology. Five adults were observed and interviewed in two contexts each. The data were analyzed to identify links to the quality of life model. RESULTS: The research illustrates how a quality of life approach can be used to justify and guide the lifelong development of numeracy. Data from the case studies linked numeracy to quality of life under the principles of personal contexts, variability, life-span perspective, values, choices and personal control, perceptions and self-image. CONCLUSIONS: The principles of quality of life can provide a framework for the development of numeracy in the context of adulthood and Down syndrome. Preparation for the numeracy needs of a long and satisfying adulthood should begin in early childhood, continue in schools with the teaching of underlying mathematics concepts and skills, and be modified and refined throughout adulthood by the use of a numeracy development plan. Carers and professionals interacting in the contexts need to adopt a teaching role for numeracy.
Down Syndrome Research and Practice 7 (2): 68-78 (2001)

Counting and cardinal understanding in children with Down syndrome and typically developing children

Nye, Joanna; Fluck, Michael; Buckley, Sue

This study compares the procedural counting ability (independently and with parental support) and conceptual understanding of cardinality of a group of children with Down syndrome and a group of typically developing children, matched for non-verbal mental age. Participants were 23 children with Down syndrome (chronological age range: 3.5 - 7 years; mental age range: 2.5 - 4 years) and 20 typically developing children (chronological age range: 2 - 4 years; mental age range: 2.5 - 4 years), and their main caregiver. The children were asked to count sets of toys (assessing procedural counting skills) and to give sets of toys (assessing understanding of cardinality), with set sizes between 2 and 18 items. The counting task was performed in two conditions, with and without parental support. The children were also asked to say the count word sequence aloud, to assess sequence production independent from object counting. The typically developing children produced significantly more number words altogether, longer standard number sequences and could count larger sets than the children with Down syndrome. Support from an adult improved performance on the count task significantly for both groups of children, and there was no significant difference between the groups in the degree of improvement, i.e. the zone of proximal development. No significant differences were found between the frequency of children (approximately one third) in each group who used counting to solve the give task, indicating an understanding of cardinality.
Down Syndrome Research and Practice 6 (2): 85-94 (1999)

Learning to count: A difficult task

Porter, Jill
School of Education, University of Birmingham, UK

This article is concerned with the acquisition of counting skills in pupils with Down syndrome. Data from a larger survey of pupils with severe learning dificulties is explored to investigate the types of errors children make at the earliest stages of learning to count. The pattern of responding was consistent tasks utilising auditory sequential memory, in this case learning the number string. The practical implications of these findings are discussed.
Special! The official journal of the National Association for Special Educational Needs (Spring): 30-2 (1999)

Thinking in Figures

Lorenz, Stephanie
Downright. 26 Worsley Rd., Worsley, Manchester M28 2GQ England

Teaching the basics of maths to children with Down's syndrome means adapting lessons to use mainly visual methods. This article outlines some straightforward teaching approaches that can be used effectively in both mainstream and special classrooms. It covers ways of teaching the language of maths, improving memory skills and overcoming fine motor problems. Examples of typical teaching programmes are given as well as tips for teachers.
Journal of Developmental and Learning Disorders 1 (2): 299-319 (1997)

Mediated Learning and its Application to the Enhancement of Mathematical Abilities in Children with Down Syndrome

Klein, Pnina S.; Arieli, Mary
Bar Ilan University, Baker Center of the Study of Developmental Disorders in Infants and Children, Ramat Gan 52900, Israel

Commonly used methods for developing math readiness in young children frequently do not meet the needs of children with various developmental disorders. Furthermore, children may learn to use skills (such as counting by rote memory) that may be misued and actually interfere with the future development of their mathematical thinking. This study presents a model for designing a remedial approach for a population of children with special needs, including children with severe problems involving the understanding of numbers. The Mediational Intervention in Math (MIM) shifts the focus of training the auditory sequential mode to the visual simultaneous mode ("right hemisphere"). In addition, the MIM approach exemplifies the use of a mediational approach in math. Subjects were thirty children with Down Syndrome, 5 to 7 years old. The subjects were randomly divided into two groups. Group 1 received weekly training using MIM approach, Group 2 did not participate in the program but their parents participated in MIM counseling including general information about the development of math skills and the MIM. Group 3 included children who were involved in an ongoing language and math enrichment program for one to three years. The MIM training lasted about 6 months. Six months following the intervention, a significant difference in children's performance on the Key Math Diagnostic Arithmetic Test was found in favor of Group 1. The children in Group 1 demonstrated a better understanding of basic mathematical concepts and problem solving abilities that the children in both other groups.
Research in Developmental Disabilities 17 (3): 185-201 (1996)

Basic Money-Counting Skills of Children with Mental Retardation

Stith, Laura E.; Fishbein, Harold D.
University of Cincinnati, Department of Pyschology, Cincinnati, OH 45221-0376

The thought processes involved in counting and comparing small amounts of money among children and adolescents with Down syndrome (n=17), other children and adolescents with mental retardation of unknown etiologies (n=17) and normally developing first graders (n=15) were examined. Three different tasks that progressively reduced the cognitive demands placed on the children were used. Although not generally different from each other, the two groups of children with mental retardation had far greater difficulties with the tasks than normals. Also, as the complexity of the counting task increased, the number of comparison errors made by the children with mental retardation increased. Based on the findings, a program for teaching money principles with children with mental retardation was proposed.
Down Syndrome Research and Practice 3 (3): 92-102 (1995 Oct)

Numerical ability, general ability and language in children with Down syndrome

Nye, Joanna; Clibbens, John; Bird, Gillian
Department of Psychology, University of Portsmouth, UK

The aims of this study were to investigate the relationship between numerical and general ability and the contribution that receptive language makes to numerical ability in children with Down syndrome. Sixteen children with Down syndrome were tested on the following measures: two nonstandardised tests of numerical ability, two standardised numerical tests, two measures of receptive language and an IQ scale. Only one of the sixteen children attained a score on the IQ measure so the relationship between general and numerical ability in this population could not be assessed. All four numerical measures significantly correlated (positively) with each other, and receptive grammar (but not vocabulary) was found to significantly correlate (positively) to numerical skills. Details of the children's performance on the two main numerical measures under investigation are presented.
Down Syndrome Research and Practice 2 (3): 597-101 (1994 Oct)

Attainments in Reading and Number of Teenagers and Young Adults with Down Syndrome

Shepperdson, Billie
Nuffield Community Care Studies Unit, University of Leicester, UK

Studies were made of the reading and number abilities of two cohorts of people with Down syndrome. One cohort consisted of people who were born in the sixties, and the other of people who were born in the seventies. Both cohorts were seen in their teens, and the sixties cohort were also seen in their mid-twenties. The studies confirmed that some people with Down syndrome are able to master 'academic' skills, and that some people not only retain skills, but continue to improve into the adult years. Comparing the two cohorts at teenage, more of the seventies cohort possessed 'academic' skills, compared with the sixties cohort at the same chronological age, but the skills of the seventies cohort were not of a substantially higher order. Looking specifically at reading, in both cohorts teenage language scores were significantly related to reading scores but, for the sixties cohort, there was no relationship between language and reading scores by the mid-twenties. In the sixties cohort more girls than boys could read. In the teens this difference was not significant but it became so in adulthood. This difference between girls and boys was not found in the seventies cohort.
Early Child Development and Care 81: 1-13 (1992)

Process of Development in Understanding of Length in Individuals with Down's Syndrome

Lister, Caroline; Lee, Sheila
University of Newcastle upon Tyne and Dewsbury Health Authority, UK

An investigation of processes in development of understanding of length was carried out with children who have Down syndrome extending an approach used with non-retarded children. The study revealed similarities and differences and was effective in developing children's understanding. Forty-eight individuals (aged 5 years to 26 years) with Down syndrome were pretested on tasks involving conservation of number and length. Two groups each of 17 subjects were matched in particular for understanding of conservation of length. The experimental group was given individual experiences and explanations building understanding of length. Processes of development in understanding length and its conservation were clarified by the training procedure. Posttested after two weeks, the experimental group showed significantly greater progress than the control group (p<0.001). The increased understanding of the experimental group was generalised. The findings of similarity and difference and of an effective approach with Down syndrome children have both theoretical and practical implications.
Journal on Mental Retardation 95 (5): 575-583 (1991 Mar)

Counting by Children with Down Syndrome

Caycho, L.; Gunn, P.; Siegel, M.
Fred and Eleanor Schonell Special Education Research Centre, University of Queensland, St. Lucia, Australia

Children's understanding of one-to-one, stable order, and cardinal principles was tested through error-detection and self-performance counting tasks. Gelman's modified counting task was used to test understanding of the order irrelevance principle. There were no significant differences between the mean task scores of 15 children with Down syndrome and 15 preschoolers with similar revised Peabody Picture Vocabulary test (PPVT-R) scores (mean age equivalent, 4 years, 7 months). Partial correlations showed several significant associations between counting principles and PPVT-R that were independent of chronological age. The results support the view that counting by children with Down syndrome can be guided by counting principles and that developmental level rather than the syndrome is associated with counting behavior.
Education and Treatment of Children 14 (2): 128-141 (1991 May)

Teaching Children with Down Syndrome to Add by Counting-On

Irwin, Kathryn C.
Department of Education, Univeristy of Auckland, New Zealand

Eight students with Down syndrome, aged 11 through 13, who had been adding by counting all objects for at least a year, were taught to use the more advanced technique of adding by counting-on, in a teaching program that lasted 5 days. These students had the prerequisite skills of counting to 9 consistently, being able to read and write numerals, and understanding the operation of adding. Teaching included instruction in the three component skills identified by Secada, Fuson, and Hall (1983) and the use of precision teaching techniques. A multiple baseline design across school settings showed that all students, and one other who ahd been taught the procedure by his mother, continued to use the technique 6 months later. All the students generalized the use of the technique to materials other than those used in instruction when assessed at the end of the teaching period, and all by two continued to do so 6 months later.
Early Child Development and Care 49: 57-66 (1989)

The Development of Understanding of Quantity in Children with Down's Syndrome

Lister, Caroline; Leach, Chris; Riley, Elaine
University of Newcastle upon Tyne and University of Leeds

Thirty-six chidren with Down's syndrome were pretested on tasks involving conservation of discontinous and continous quantity. Their order of development of understanding was compared with that of twenty non-retarded children who had been given exactly the same tasks. Similarity in sequence of development was clear and supported by scalogram analysis. From the sample of Down's children, two groups, each of eight children, were matched for understanding of conservation and for age. None of these children recognized conservation of continuous quantity. The experimental group was given individual teaching, experiences and explanations, building understanding of conservation for its components. Post tested immediately after teaching and again two weeks later, all the experimental group recognized conservation of continuous as well as continuous quantity. Their understanding was generalised and durable. The control group childen did not show such understanding of either post test. The difference between the two group's performance was highly significant for both post tests. The findings have clear educational implications.
Australian Journal of Early Childhealth 4 (1): 15-20 (1979 March)

Early Number Experiences for Preschool Down's Syndrome Children

Thorley, BJ; Woods, VM
Macquarie University, Australia

This report on the development and trialling during 1978 of a basic number curriculum for pre-school Down's children represents a synthesis of our previous instructional efforts with what appeared to us to be significant recent developments in understanding how children acquire number skills. The success achieved by the children in this initial attempt encourages us to believe that with continued improvements in teaching technology and with more frequent practice opportunities, the "minimal objectives" represent a viable goal for Down's children in a model pre-school. The long term educational significance of an earlier than normal start with number teaching, in the context of a pre-school program for the intellectually handicapped, remains to be determined. It would appear to depend upon a number of factors. Firstly, where subsequent enrolment in a regular class takes place, as distinct from enrolment in a segregated class for the moderately retarded, the extent to which the momentum is maintained may depend upon a continuing access to short individualized teaching sessions. In this respect, special teachers who otherwise would have been providing a total segregated educational service might supply the essential back-up support in basic skills within the regular classroom. Secondly, the children's future progress will probably depend upon the extent to which the present program articulates with other teachers' plans for teaching number. Much of the present teaching of number to five and six year olds in the regular schools seems to be based on unsupported theoretical implications and the logic of advanced mathematics. If such thinking prevents or delays our graduating children from engaging in the type of number activities described in this paper, then the results of our efforts may well be dissipated. All in all, the early progress obtained by the present Down's children in basic skills extends considerably beyond traditional predictions. As further data become available from other children in the program and from our follow-up of the pre-school graduates, a clearer picture of the educational significance of the early learning of basic skills should emerge.
American Journal of Mental Deficiency 79 (2): 179-190 (1974)

Development of Language, Abstraction, and Numerical Concept Formation in Down's Syndrome Children

Cornwell, AC
Albert Einstein College of Medicine, Yeshiva College, New York, New York

Earlier findings (Cornwell & Birch, 1969) suggested the hypothesis that a marked discrepancy between verbal receptive and performance abilities exists in home-reared children with Down's syndrome. This was tested developmentally in 38 Down's syndrome children, 5 to 19 years old. The data showed differences between verbal items requiring extensive language expression (designation) and recognition of visually presented objects. Language expression was also assessed in numerical concepts and skills and concept formation. Developmentally, this population revealed a slow accretion of certain rote skills and progressive improvement in other abilities, but severe limitations in concept formation, abstraction, and higher level integrative abilities regardless of age.