A Review of Mathematical Learning Disabilities in Children with Fragile X

DEVELOPMENTAL DISABILITIES RESEARCH REVIEWS 15: 21 – 27 (2009)

AREVIEW OF MATHEMATICAL LEARNING DISABILITIES IN CHILDREN WITH FRAGILE XSYNDROME

Melissa M. Murphy* Education Department, College of Notre Dame of Maryland, Baltimore, Maryland

The prevalence rate of mathematical learning disabilities (MLD) final section, fragile X syndrome is discussed as a model of among children with fragile X syndrome who do not meet criteria for potential pathways to MLD. intellectual and developmental disabilities (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 OVERVIEW OF FRAGILE X SYNDROME model for understanding pathways to MLD. ' 2009 Wiley-Liss, Inc. Dev Disabil Res Rev 2009;15:21–27. Neural development, such as synaptic maturation and neuronal pruning, relies in part on the presence of a specific protein called the Fragile X Mental Retardation Protein [FMRP, Key Words: fragile X syndrome; mathematical learning disability; genetic Oostra, 1996; Greenough et al., 2001]. FMRP is coded for by syndrome a single gene on the long arm of the X chromosome. If the production of this protein is disrupted, optimal neural development is impeded resulting in fragile X syndrome. As the leading genetic cause of inherited IADD, fragile X syndrome affects approximately 1 in 4,000 to 1 in 8,000 ifficulty with mathematics is well documented among live births [Crawford et al., 2001]. The majority of male indi- children and adults with fragile X syndrome [Grigsby viduals with fragile X syndrome, but only about half of female Det al., 1990; Brainard et al., 1991; Bennetto et al., individuals, meet criteria for IADD [Rousseau et al., 1994; 2001; Mazzocco, 1998, 2001]. Also apparent are deficits in Bailey et al., 1998]. The range of cognitive abilities among the areas of cognitive ability that are associated with mathematics, remaining 50% of female individuals without IADD can vary such as executive function, visual spatial ability, and reading- from no noticeable cognitive deficits to learning disabilities related skills [as reviewed by Mazzocco and McCloskey, [Rousseau et al., 1994]. 2005]. The poor mathematics performance associated with Variability in the amount of FMRP produced may affect fragile X syndrome may reflect a primary deficit resulting from the extent to which syndrome characteristics are manifest the syndrome or a deficit secondary to difficulty in requisite within and across gender groups. Male individuals have only cognitive skills. Alternatively, a specific profile of mathematical one X chromosome in every cell; whereas female individuals and cognitive deficits associated with fragile X syndrome may have two X chromosomes. Although only one of the two X be independent of general impairment, as has been proposed chromosomes is active in a female’s cells [Lyon, 1972], cells for other developmental disorders (e.g., Williams syndrome, where the unaffected X chromosome is active can still produce this issue). Regardless of the specificity with which it emerges, FMRP. Thus, female individuals with fragile X syndrome gen- the fragile X syndrome mathematical learning disability erally, produce more FMRP relative to male individuals, and (MLD) profile is a possible model for understanding pathways so may be less affected [Hagerman, 1999]. There can also be to MLD [Mazzocco and McCloskey, 2005; Mazzocco et al., variability in the extent to which male individuals with fragile 2007; Murphy et al., in press]. X syndrome produce FMRP [as reviewed by Hagerman, The present review focuses on describing MLD in chil- 1999]. Male individuals who have a mosaic pattern of fragile dren with fragile X syndrome with a specific emphasis on X syndrome have a combination of affected and unaffected female individuals without intellectual and developmental dis- cells, and so may produce more FMRP than those individuals abilities (IADD) (Throughout this review, the term intellectual and developmental disabilities (IADD) is used in lieu of the term mental retardation to reflect the change in terminology taking *Correspondence to: Dr. Melissa Murphy, Education Department, 4701 North place in the field of developmental disabilities research and Charles St., Baltimore, MD 21209. E-mail: [email protected] practice). Cognitive correlates related to MLD, such as execu- Received 17 December 2008; Accepted 22 December 2008 Published online in Wiley InterScience (www.interscience.wiley.com). tive function, visual spatial skills, and reading-related skills, are DOI: 10.1002/ddrr.49 also discussed in the context of fragile X syndrome. In the

' 2009 Wiley -Liss, Inc. Table 1. Summary of Implicated Strengths and Challenges in Mathematics and Related Skills in Female and Male Individuals with Fragile X Syndromea

Females Males

Strengthb Challengeb Strengthb Challengeb

Mathematics skills Number sense Reading/writing Visual/verbal magnitude judgments One-to-one correspondence numbersc when counting Rote countingc: Mental number line judgments Forward by ones Counting 8 pictured items Backward by ones Applied counting: Forward by tens 1-to-1 correspondenced Next number in Number constancy series Identifying Nth in set

Arithmetic operations Adding sets less than 10 Early math skills as assessed by WJ-R, Applied Problems subtest Related skills Executive function Working memory Performance declines as working Memory for meaningful Sequential processing memory demands increase information presented in context Limited changes in brain activation in Inhibition, selective and sustained response to increasing task difficulty attention

Visual spatial Visual perceptual ability; difficulty Visual spatial skills, visual-motor recalling object location in array coordination

WJ-R = Woodcock Johnson-Revised. aTable highlights areas of known strength and challenge as well as areas where evidence regarding mathematics and related skills is lacking. bBased on comparisons to children with no known syndrome. cPerformance exceeds that of children with MLD. dIndicates area of challenge relative to children with MLD.

with a higher affected to unaffected cell characterized by areas of relative under review], which suggests that cer- ratio [Bailey et al., 2001]. strength in verbal skills, such as vocabu- tain tasks may be more effortful for girls The majority of research on MLD lary [Jakala et al., 1997], and aspects of with fragile X syndrome relative to and fragile X syndrome has focused on visual perception, such as identifying their peers [Murphy and Mazzocco, individuals without IADD to investigate missing parts of concrete objects [Ben- under review]. aspects of the cognitive phenotype inde- netto and Pennington, 1996] and iden- pendent of global deficits that are associ- tifying shapes embedded within designs Male Individuals with FXS ated with IADD. As a result, this review [Mazzocco et al., 2006]. As a group, male individuals with focuses primarily on MLD among female Areas of weakness include visual fragile X syndrome tend to have more individuals with fragile X syndrome. perceptual skills, such as recalling the pronounced cognitive deficits than However, the mathematical abilities and location of an object within an array female individuals [Rousseau et al., challenges for individuals with fragile X [Mazzocco et al., 2006], and executive 1994; Jakala et al., 1997]. However, syndrome who meet criteria for IADD is function [e.g., Mazzocco et al., 1993; areas of strength and weakness are still included whenever possible. Bennetto et al., 2001]. Executive func- present. Similar to female individuals Table 1 summarizes what is tion includes a range of cognitive abil- with fragile X syndrome, relative known about the areas of strength and ities related to planning and goal- strengths among male individuals are challenge associated with mathematical directed behavior. Specific aspects of apparent in verbal skills [Jakala et al., skills among female and male individu- executive function that are impaired in 1997] and memory for meaningful in- als with fragile X syndrome. The fol- fragile X syndrome include working formation that is presented in context lowing section briefly reviews the phe- memory [Mazzocco et al., 1993; Kwon [e.g., remembering pictures rather than notypic characteristics associated with et al., 2001], inhibition, sustained atten- sequences of numbers [Munir et al., fragile X syndrome that are relevant to tion, and controlled switching of atten- 2000]. Areas of weakness include short- mathematical ability. A complete review tion [Cornish et al., 2004]. Processing term memory, visual spatial skills, and of the physical and behavioral character- speed per se does not appear to distin- visual-motor coordination [Cornish istics associated with the syndrome is guish girls with fragile X syndrome et al., 1999], as well as aspects of execu- beyond the scope of this article. The from their peers [Kirk et al., 2005; tive function such as inhibition reader is referred to Cornish et al. Mazzocco et al., 2006; Murphy and [Wilding et al., 2002; Scerif et al., [2007] and Hagerman [2002] for addi- Mazzocco, 2008a]. However, the per- 2004], and selective and sustained atten- tional information. formance of girls with fragile X syn- tion [Cornish et al., 2001]. Along with drome on working memory tasks the select executive function deficits, Female Individuals with FXS declines as the working memory processing sequential information is an The cognitive profile of female demands of the task increase [Kirk area of relative weakness that may individuals with fragile X syndrome is et al., 2005; Murphy and Mazzocco, contribute to mathematics performance,

22 Dev Disabil Res Rev MATHEMATICAL LEARNING DISABILITIES IN FRAGILE X MURPHY such as counting [Daniel et al., unpub- et al., 2001], but not all aspects of strate relative strengths in written num- lished data]. mathematics are impaired. Mathematics ber representation (e.g., reading and ability in fragile X syndrome is charac- writing numbers) and rote counting skills MLD IN FRAGILE X SYNDROME terized by a profile of strengths and (e.g., counting forward or backwards by challenges, especially in the areas of one). In fact, rote counting knowledge Female Individuals with number sense (e.g., counting) and in fragile X syndrome is comparable to Fragile X Syndrome rational number knowledge [as that in the general population and reviewed by Mazzocco et al., 2007]. exceeds the performance of children Prevalence of MLD Understanding this profile of mathemat- with MLD [Murphy et al., 2006]. As early as kindergarten, girls ics ability and its relation to specific The strength in rote counting with fragile X syndrome are at an cognitive abilities can inform under- contrasts with weakness in applied increased risk for MLD relative to their standing of MLD both in fragile X syn- counting knowledge, such as recogniz- peers from the general population drome and in the general population. ing that rearranging items in a set does [Mazzocco, 2001]. We have found that In studying mathematics perform- not change the quantity of items the percentage of girls with fragile X ance among girls with fragile X syn- (number constancy), understanding or- syndrome who scored in the MLD drome, four types of comparison groups dinal numbers (e.g., the ability to cor- range, at least once during annual have been employed. The performance rectly identify the Nth position in an assessments between kindergarten and ofgirlswithfragileXsyndromehasbeen array), and understanding one-to-one 3rd grade, was greater (87%) than the compared to that of: (1) children from a correspondence when counting (i.e., rate observed in the K-3rd grade gen- normative sample of the general popula- recognizing that each object in a set can eral population (44%) [Murphy et al., tion (general population); (2) children have only one number name). Overall, 2006]. Even relative to an age and IQ from the general population who do not girls with fragile X syndrome and chil- matched comparison group, the ratio of meet criteria for MLD (non-MLD); (3) dren with MLD both perform more MLD in fragile X syndrome is 2.5–1 children from the general population poorly than children from the general [Mazzocco, 2001]. who meet criteria for MLD (children population on applied counting items with MLD); and (4) girls with Turner [Murphy et al., 2006]. Girls with fragile Persistence of MLD syndrome, another relatively common X syndrome and children with MLD The persistence of MLD during genetic syndrome. These types of com- perform at about the same level on early elementary school among girls parisons may inform which characteristics applied counting items, except on items with fragile X syndrome has been of poor performance can be associated measuring understanding of one-to-one documented in a single study [Murphy with fragile X syndrome specifically or correspondence. On these items, the et al., 2006]. In this study, persistence mathematics learning disability more gen- performance of girls with fragile X syn- of MLD did not distinguish girls with erally [Murphy et al., in press]. drome lags behind even that of children fragile X syndrome from children in the Recent and comprehensive with MLD [Murphy et al., 2006]. This general population. Approximately 77% reviews of mathematics skills among profile of relative strength in rote of girls with fragile X syndrome (who females with fragile X syndrome are counting and weakness in applied had MLD) continued to meet criteria available elsewhere [see Mazzocco and counting further distinguishes girls with for MLD more than once between kin- McCloskey, 2005; Mazzocco et al., fragile X syndrome from girls with dergarten and 3rd grade compared to 2007; Murphy et al., in press]. This Turner syndrome, whose performance 70% of children from the general popu- review focuses on selected findings is in the average range relative to the lation [Murphy et al., 2006]. related to number sense, rational num- general population on both rote and Although the MLD persistence ber knowledge, and the developmental applied counting knowledge. rate does not distinguish fragile X syn- trajectory of mathematics skills that may The rote-applied ability distinc- drome from the general population dur- best exemplify fragile X syndrome as a tion is documented during the elemen- ing early elementary school, poor math- model of pathways to MLD. tary school years [Murphy et al., 2006]. ematics performance among female However, little is known about how individuals with fragile X syndrome is Number sense this distinction might change over de- evident through elementary school Broadly defined number sense velopment as a function of maturation [Murphy and Mazzocco, 2008a,b, under refers to knowledge of numbers and or changing curricular demands across review] and into adulthood [Cronister their properties including reading and grades. In a study of rational number et al., 1991; Mazzocco, 1998; Bennetto writing numbers, counting, judging knowledge in middle school, we et al., 2001]. Moreover, during the which of two quantities is larger (mag- [Murphy and Mazzocco, 2008b] found early school-age years, girls with fragile nitude judgments), and the ability to a similar pattern of strengths and weak- X syndrome meet stricter criteria manipulate numbers along a mental nesses on rote versus applied knowl- for MLD (score consistently in the bot- number line [Berch, 2005]. As early as edge. Results from this study are dis- tom 10th percentile on a standardized kindergarten, girls with fragile X syn- cussed subsequently followed by find- measure of formal and informal math drome have difficulty with number ings from a study on the developmental skills) than children from the general sense relative to their age, grade, and trajectory of mathematics development population [Murphy et al., 2006]. IQ-matched peers from the general from 1st through 6th grades. population [Mazzocco, 2001]. Mathematics skills Despite generally poor perfor- Rational number knowledge Mathematics is an area of diffi- mance, not all aspects of number sense Rational numbers are numbers culty for individuals with fragile X syn- are impaired [Murphy et al., 2006]. Of that can be represented as a fraction or drome [Grigsby et al., 1990; Brainard the multiple aspects of number sense, ratio of integers (e.g., 1/2, 2/3). Mas- et al., 1991; Mazzocco, 1998; Bennetto girls with fragile X syndrome demon- tery of rational numbers knowledge

Dev Disabil Res Rev MATHEMATICAL LEARNING DISABILITIES IN FRAGILE X MURPHY 23 encompasses tasks that can be learned Bennetto et al., 2001], a developmental ness for boys with fragile X syndrome by rote, such as accurate reading of dec- perspective is required to understand relative to children with Down syn- imal amounts (e.g., using correct place how poor mathematics performance drome or nonspecific IADD, and men- value labels like ‘‘tenths’’ or ‘‘hun- emerges or resolves during the school tal age-matched peers [Dykens et al., dredths’’). Tasks that reflect a conceptual years as well as the possible contribu- 1987; Kemper et al., 1988; Hodapp understanding of rational numbers are tions of related cognitive skills to the et al., 1991, 1992]. Roberts et al. also important, such as recognizing that prediction of mathematics growth and [2005] found that early mathematical the same amount can be represented in outcomes. skills of boys with fragile X syndrome different ways; for example, the number were on par with early reading skills words ‘‘one-half’’ can be represented as Growth in mathematics skills during the (i.e., letter–word identification), and a fraction (1/2), as a decimal (0.5), or elementary and middle school years both areas were strengths relative to dic- pictorially ( ). In the only study to date to focus tation. However, early mathematical Middle school age girls with frag- on the growth of mathematical skills skills still represents an area of difficulty ile X syndrome do struggle with among girls with fragile X syndrome relative to chronological age-level rational numbers, but not on all aspects [Murphy and Mazzocco, under review], expectations [Roberts et al., 2005]. [Murphy and Mazzocco, 2008b]. In a we examined the trajectory of mathe- Although deficits in mathematics recent study, we [Murphy and Maz- matical skills between 1st and 6th grade. achievement are apparent, little work zocco, 2008b] compared the perform- Raw scores on the Woodcock Johnson- has been done to characterize the pro- ance of girls with fragile X syndrome to Revised (WJ-R) calculations subtest file of specific formal and informal children with and without MLD from were compared between girls with frag- mathematics skills among boys with the general population on the Ranking ile X syndrome and a comparison fragile X syndrome. Daniel et al. Proportions Task [RPT, Mazzocco and group from the general population. By [unpublished data] examined counting Devlin, 2008]. This task includes two 6th grade, girls with fragile X syndrome and sequential responding in children subtests that require the participant to had lower raw scores on the WJ-R with fragile X syndrome relative to rank order amounts that are represented: Calculations subtest and a slower growth children with Down syndrome and pictorially (e.g., , l) or as decimals mental age-matched children with typi- (e.g., 0.5, 0.25). Participants are also cal achievement. Sequential processing asked to read decimal amounts aloud. Much less is known was measured using a computer task in A distinct profile of strengths and which the child had to complete a se- challenges emerges across these RPT about mathematics ability ries of responses (point to a sequence of subtests for girls with fragile X syn- and disability in males stepping-stones) to meet a goal drome when compared to children from (opening a treasure chest). Variations in the general population with and with- with fragile X syndrome the displays included whether the step- out MLD [Murphy and Mazzocco, than females with fragile ping-stones were presented sequentially 2008b]. Girls with fragile X syndrome or simultaneously, spaced regularly or do not differ from children in the gen- X syndrome. irregularly, and whether the stones van- eral population on reading decimals and ished once touched. A similar sort of ranking pictured amounts, and their counting task was also used. On these performance on these tasks exceeds that rate than children in a comparison tasks, boys with fragile X syndrome had of children with MLD. Despite these group from the general population. This difficulty applying basic counting prin- strengths, girls with fragile X syndrome is consistent with cross-sectional reports ciples and inhibiting incorrect responses have difficulty ranking decimals; and during the elementary school years relative to their peers with Down syn- their performance on this subtest is [Mazzocco, 2001; Kirk et al., 2005; drome and typically achieving peers, comparable to that of children with Murphy et al., 2006; Murphy and Maz- whose performance did not differ from MLD. Thus, a pattern of relative zocco, 2008a]. However, group differ- one another. Thus, the authors suggest strength on rote skills (e.g., reading dec- ences in both 6th grade math perfor- that sequential processing may contrib- imals, ranking pictorial representations mance and growth rate in math skills ute to counting ability among boys with of fractions) coupled with poor concep- disappeared after controlling for FSIQ fragile X syndrome and to a syndrome- tual skills is observed among girls with and working memory performance at specific profile of basic mathematics fragile X syndrome. Further, this rote- 3rd grade. Such findings support the ability [Daniel et al., unpublished data]. conceptual performance distinction is stability of poor math performance as a consistent with performance on number characteristic of girls with fragile X syn- COGNITIVE CORRELATES sense tasks; and is of particular note drome and highlight the potential con- OF MATHEMATICS given that strong rote skills may mask tribution of working memory ability to PERFORMANCE underlying conceptual deficits, thereby mathematics achievement over time. Recent and comprehensive hindering mathematics achievement if reviews of cognitive correlates of math- instructors interpret rote skills as reflect- Male Individuals with ematics skills, such as executive func- ing conceptual mastery [Murphy and Fragile X Syndrome tion, visual spatial ability, and reading- Mazzocco, 2008b]. Much less is known about mathe- related skills, among females with fragile Although findings from this study matics ability and disability in male X syndrome are available elsewhere and others confirm that poor mathe- individuals with fragile X syndrome rel- [e.g., Mazzocco and McCloskey, 2005; matics performance persist through ele- ative to what is known about female Mazzocco et al., 2007; Murphy et al., mentary school and into middle school individuals (see Table 1). Findings from in press]. There is evidence of specific [e.g., Murphy and Mazzocco, 2008a] standardized achievement measures sug- visual spatial and language deficits and beyond [e.g. Grigsby et al., 1990; gest that arithmetic is an area of weak- among female individuals with fragile X

24 Dev Disabil Res Rev MATHEMATICAL LEARNING DISABILITIES IN FRAGILE X MURPHY syndrome, but these deficits may be sec- that tasks that are not generally consid- group differences in working memory ondary to deficits in executive function ered working memory tasks, such as at 3rd grade and their prediction of 6th [Bennetto et al., 2001; Murphy et al., naming stimuli by color or shape, are grade mathematics performance high- 2006]. Thus, the present review focuses more effortful for girls with fragile X light the importance of early interven- on the possible contributions of execu- syndrome than their peers. On these tion for girls with fragile X syndrome tive function to mathematics perform- naming tasks, 3rd grade girls with frag- [Murphy and Mazzocco, under review]. ance in fragile X syndrome. ile X syndrome had longer response Second, depending on the extent to Executive function encompasses a times than their peers, but their per- which growth in working memory is myriad of skills and abilities, including formance was just as accurate. Naming directly related to mathematics, these working memory. The ability to access, performance contrasted with perfor- findings also draw attention to the pos- hold, and manipulate information in mance on working memory tasks where sibility that improvements in working working memory is important for com- girls with fragile X syndrome were just memory observed by 7th grade may pleting a variety of tasks, including as fast, but less accurate than their peers. contribute to improvements in mathe- those related to mathematics (e.g., We hypothesize that the pattern of trad- matics performance during the middle counting, calculation). For example, ing accuracy for speed observed among school years rather than plateaus in per- successful counting may depend both girls with fragile X syndrome reflects formance [Murphy and Mazzocco, on knowledge of counting principles, the difficulty of the working memory under review]. Additional studies are such as one-to-one correspondence, tasks. Such speed/accuracy trade-offs needed to examine the association and the ability to keep track of the are also observed on select mathematics between working memory and mathe- items counted to avoid counting the tasks, such as tasks that require verifying matics, especially during the middle same item more than once. Indeed, the the accuracy of arithmetic problems school years. contribution of working memory to [Murphy and Mazzocco, 2008a]. mathematics performance is well docu- POTENTIAL PATHWAYS mented [as reviewed by Geary et al., TO MLD 2007] and working memory deficits Working memory Throughout this review perfor- have been associated with MLD performance at 3rd grade mance and characteristics of individuals [Swanson and Beebe-Frankenberger, th with fragile X syndrome as a group are 2004]. predicted 6 grade considered rather than drawing atten- As discussed previously, deficits in mathematics achievement tion to individual variability in per- executive function, including working formance. As evident among other syn- memory, are documented in fragile X and growth rate in dromes, such as Williams syndrome (this syndrome [Bennetto et al., 2001; Kwon mathematics between 1st issue), 22q11.2 deletion (this issue), and et al., 2001; Kirk et al., 2005; Tamm th Turner syndromes (this issue), individual et al., 2002; Murphy and Mazzocco, and 6 grades. variability among persons with a given under review]. Female individuals with syndrome is evident despite all individ- fragile X syndrome fail to show uals with a given syndrome sharing a increases in brain activation as task diffi- Lower working memory thresh- common known etiology. Thus, this culty increases on visual spatial [Kwon olds among girls with fragile X syn- relatively homogeneous group of indi- et al., 2001] or number-processing tasks drome does not reflect the absence of viduals can inform the study of path- [Rivera et al., 2002]. For example, growth in working memory ability ways to MLD [Murphy et al., in press]. females with fragile X syndrome [Murphy and Mazzocco, under review]. For example, the co-occurring deficits showed no changes in brain activation Over time from 1st to 7th grades, we in executive function and mathematics and were less accurate than their peers found gains in working memory per- associated with fragile X syndrome may at verifying the accuracy of equations formance among girls with fragile X provide insight into the contribution of when the equations involved three syndrome, albeit at a slower rate than executive function to MLD in fragile X operands (e.g., 2 þ 3 þ 1 5 5), but that of their peers. Improvements in syndrome and in the general population not when they involved two operands working memory are especially evident [Murphy et al., in press]. (e.g., 2 þ 3 5 4). Such findings may be between 5th and 7th grades among girls There is clear evidence of poor suggestive of difficulty recruiting the with fragile X syndrome. Moreover, math performance in fragile X syn- necessary cognitive resources to com- working memory performance at 3rd drome and difficulty with mathematics pensate for increasing task demands grade predicted 6th grade mathematics related cognitive skills. These findings [Rivera et al., 2002], or may reflect a achievement and growth rate in mathe- are consistent with the theoretical model lower threshold for working memory matics between 1st and 6th grades. To- of MLD proposed by Geary [1993, tasks relative to the general population gether, these findings suggest that select 2004]. Figure 1 presents a modified ver- [Kwon et al., 2001; Murphy and Maz- tasks that are not traditionally consid- sion of Geary’s model, which continues zocco, under review; Rivera et al., ered to be working memory tasks for to be tested and refined [e.g., Murphy 2002]. children in the general population may and Mazzocco, 2008b, under review]. Findings from our recent longitu- indeed be working memory tasks for According to this model, behavioral dinal study of mathematics and working girls with fragile X syndrome [Murphy characteristics associated with fragile X memory in girls with fragile X syn- and Mazzocco, under review]. syndrome (e.g., attention, arousal) may drome support the notion of a lowered The trajectory of working mem- influence performance, including the threshold for working memory among ory and its association with mathematics ability to acquire math skills. girls with fragile X syndrome relative to performance have two important educa- Continued investigation of these their peers [Murphy and Mazzocco, tional implications for girls with fragile relationships among both male and under review]. For example, we found X syndrome. First, the emergence of female individuals with fragile X syn-

Dev Disabil Res Rev MATHEMATICAL LEARNING DISABILITIES IN FRAGILE X MURPHY 25 REFERENCES

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