Melissa M. Murphy

Cognitive Characteristics of Children With Mathematics Learning Disability (MLD) Vary as a Function of the Cutoff Criterion Used to Define MLD

Researchers of mathematics learning disability (MLD) commonly use cutoff scores to determine which participants have MLD. Some researchers apply more restrictive cutoffs than others (e.g., performance below the 10th vs. below the 35th percentile). Different cutoffs may lead to groups of children that differ in their profile of math and related skills, including reading, visual—spatial, and working memory skills. The present study assesses the characteristics of children with MLD based on varying MLD definitions of math performance either below the 10th percentile (n = 22) or between the 11th and 25th percentile (n = 42) on the Test of Early Math Ability, second edition (TEMA-2). Initial starting levels and growth rates for math and related skills were examined in these two MLD groups relative to a comparison group (n = 146) whose TEMA-2 performance exceeded the 25th percentile. Between kindergarten and third grade, differences emerged in the starting level and growth rate, suggesting qualitative differences among the three groups. Despite some similarities, qualitative group differences were also observed in the profiles of math-related skills across groups. These results highlight differences in student characteristics based on the definition of MLD and illustrate the value of examining skill areas associated with math performance in addition to math performance itself.

Mathematics learning disability in girls with Turner syndrome or fragile X syndrome

Two studies were carried out to examine the persistence (Study 1) and characteristics (Study 2) of mathematics learning disability (MLD) in girls with Turner syndrome or fragile X during the primary school years (ages 5-9 years). In Study 1, the rate of MLD for each syndrome group exceeded the rate observed in a grade-matched comparison group, although the likelihood of MLD persisting through the primary school years was comparable for all three groups. In Study 2, formal and informal math skills were compared across the syndrome groups, a normative group, and children from the normative group who had MLD. Few differences were observed between the Turner syndrome and normative groups. Despite having rote counting and number representation skills comparable to those in the normative group, girls with fragile X had difficulty with counting rules (e.g., cardinality, number constancy). However, this difficulty did not distingush them from the MLD group. Overall, counting skills appear to distinguish the Turner syndrome and fragile X groups, suggesting that the specificity of math deficits emerges earlier for fragile X than Turner syndrome.

Signaling Noncomprehension of Language: A Comparison of Fragile X Syndrome and Down Syndrome

Signaling noncomprehension of the spoken messages of others was examined for youth with fragile X or Down syndrome in comparison with each other and nonverbal MA-matched typically developing children. A direction-following task was used in which some of the directions were inadequate. Both syndrome groups signaled noncomprehension less often than did the typically developing children. The ability to signal noncomprehension appropriately was related to a measure of receptive vocabulary and syntax. Preliminary analyses indicated that males with fragile X syndrome signaled noncomprehension less often than did their female peers, even after controlling for differences in nonverbal MA.

Indirect Genetic Effects and the Early Language Development of Children With Genetic Mental Retardation Syndromes: The Role of Joint Attention

Mental retardation is typically associated with substantial delays in language. Researchers have been interested in the possible differences in the extent or nature of these delays across genetic syndromes, such as fragile X, Down, and Williams syndromes. This article addresses how genetic factors and environmental characteristics interact to produce specific language outcomes. We suggest that episodes of joint attention provide a means by which genetic anomalies can have indirect effects on some facets of language development. In doing so, we explain the nature of indirect effects and their influence on development; illustrate the link between joint attention and later language ability; discuss how joint attention may account for the characteristics associated with genetic syndromes, with special attention on fragile X syndrome; and consider implications for intervention.

Rote numeric skills may mask underlying mathematical disabilities in girls with fragile X syndrome

Mathematical learning disabilities (MLD) have been reported for elementary school age girls with fragile X syndrome who do not have mental retardation. Yet girls with fragile X demonstrate age-appropriate rote math skills, sometimes outperforming other children with MLD. We examined whether MLD and strengths in rote math skills persist during middle school among girls with fragile X. Middle school children were individually administered the Ranking Proportions Task (RPT), which involves fractions and decimals. Such problems, although difficult for many students, yield different performance profiles between children with versus without MLD. We hypothesized that girls with fragile X would outperform children with MLD on rote skills (e.g., naming decimals) despite conceptual difficulties, regardless of effects of FSIQ. To address the influence of fragile X versus MLD or FSIQ, several comparison groups were included. Children from a normative sample outperformed girls with fragile X on conceptual, but not rote, skills. However, their performance resembled that of children with MLD on conceptual skills, such as identifying equal quantities with different symbols (e.g., 0.5 and 1/2). Fragile X syndrome provides a compelling model of the heterogeneity of MLD, as the associated profile resembles that of both children with or without MLD. In terms of applications to serving girls with fragile X, it is important to consider that efficient rote skills may not only fail to enhance math achievement, they may hinder achievement by masking underlying conceptual deficiencies.

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.

Research on Language Development and Mental Retardation: History, Theories, Findings, and Future Directions**

In this chapter, we briefly review some of the theoretical shifts and most important findings to emerge in the study of language development in individuals with mental retardation since the inception of the Gatlinburg Conference on Mental Retardation Research and Theory in 1968. This period corresponds to an especially vibrant era of research on language and mental retardation, and one that has been shaped in profound ways by the nativist theory espoused first by Noam Chomsky (1965) and later by Fodor (1983), Pinker (1996), and others. Research on language development among those with mental retardation has not only been shaped by nativist theory but this research has also yielded data that have proven important for evaluating the merits of the theory, as in the case of research on Williams syndrome (Bellugi, Lai, & Wang, 1997). In our review, we have by necessity been selective, focusing largely on those concerns and findings that have been motivated by, or are relevant to, the claims of nativist theory or the alternative theories that have risen in prominence in recent years. The alternatives we consider are the social‐interactionist (Bruner, 1983) and emergentist (MacWhinney, 1999) approaches, which grew out of work in typical child development and cognitive science, respectively, and the genetic syndromes approach (Hodapp & Dykens, 1994), which emerged from work within the field of mental retardation. Our goal is to provide a brief history of research on language and mental retardation, demonstrate the bidirectional relationships between that research and the dominant theoretical approaches of our time, and outline future directions for research.

Genetic Syndromes as Model Pathways to Mathematical Learning Difficulties

Abstract The difficulties that children with mathematics learning disability (MLD) experience are linked to both numerical and nonnumerical skills. At issue is that the combination of difficulties experienced by any one child varies across cases of MLD. An approach to identifying distinct pathways to MLD is to study genetic disorders for which well-described cognitive phenotypes include poor math achievement. Using this approach, we summarize research on three common genetic disorders: fragile X, Turner, and chromosome 22q11.2 deletion syndromes. Evidence from these studies suggests that children with numerical and arithmetic impairments differ in the specificity of their difficulties as well as the relation between their math and executive function skills. In light of these and other differences, the notion that a single cognitive impairment is common to each disorder is not supported. The findings summarized in this chapter add to the growing body of evidence that MLD is heterogeneous, and counters notions that a single core deficit underlies MLD.