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...autistic children’s difficulties with regards to number. Autism Res 2015, 00: 000–000. VC 2015 International Society for Autism Research, Wiley Periodicals, Inc. Keywords: autism; mathematics; number; visual perception Introduction Individuals diagnosed with an autism spectrum condition (hereafter, “autism”) are often most well known for their difficulties in social communication. It is now well established, however, that they often show an uneven profile of abilities, including a pattern of typical or often superior performance in other domains, particularly in visuospatial processing [e.g., Frith, 1989; Mottron, Dawson, & Soulieres, 2009; see Simmons et al., 2009, for review]. Number skills are often reported anecdotally and in the mass media as a relative strength for autistic1 people. For example, Sacks [1985] reported the extraordinary behavior of two twins with autism, who could determine instantly the correct numbers of matches dispersed on the floor as 111, and subsequently qualify them as “equal to three times thirty-seven.” This striking ability, which provided the inspiration for the talents of the lead autistic character in the film, Rain Man, was in stark contrast to the twins’ ...

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... in arithmetic achievement in autism is striking. Yet as informative as these standardized tests are, they are unable to provide a detailed and comprehensive analysis of why such achievement is so variable. Here, we investigated autistic children’s numerical estimation skills to determine whether individual differences in these skills might be one potential source of the variability in formal arithmetic skills. Researchers typically distinguish between two number systems operating over different numerical ranges, both of which are believed to contribute to children’s mathematical achievement [Feigenson, Dehaene, & Spelke, 2004]. For relatively few items (<4) a “subitizing” system enables a rapid, exact representation of numerosity while an approximate system is utilized to estimate magnitudes when more items are present [see Burr & Ross, 2008]. To our knowledge, only three studies have investigated these numerical estimation skills in autism, both targeting the exact number system. Jarrold and Russell [1997] found that autistic children showed less benefit than comparison children in counting dot stimuli presented in canonical (dots on dice) than noncanonical (distributed randomly) form, and used a less efficient d...

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...roposed that such perceptual operations are generally enhanced in autism, rendering it possible that many autistic individuals might excel at numerosity. Furthermore, it is assumed that the ability to represent numerosity or nonsymbolic numerical magnitude (rather than subitizing) is a prerequisite for the later acquisition of symbolic representations of numerical magnitude [Feigenson et al., 2004]. Consistent with this view, the ability to estimate numerosity correlates strongly with mathematics achievement at different ages [Anobile, Stievano, & Burr, 2013; Gilmore, McCarthy & Spelke, 2010; Halberda, Mazzocco, & Feigenson, 2008; Piazza et al., 2010; although see Tibber et al., Figure 1. Nonsymbolic estimation: numerosity discrimination task. Children were introduced to two animated characters in a battle to see who can win the most marbles. Children were asked to help the friendly character, Zando (left). They were told they would see two sets of “marbles” briefly and to touch the side of the screen that contains more “marbles.” 2 Aagten-Murphy et al./Numerical estimation in children with autism INSAR 2013]. Individual differences in nonsymbolic estimation (numerosity) could, therefore, provide one explanation for t...

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...ildren to indicate the position of a symbolic digit or a cloud of dots on a “numberline” [Booth & Siegler, 2006]. Younger children tend to overestimate smaller numbers and compress larger numbers at the end of the line, producing estimates that are better fit by a logarithmic than a linear function. Older children and adults tend to produce more accurate, more nearly linear estimates. Importantly, individual differences in children’s symbolic estimation, their ability to map numbers onto space is also linked to variation in mathematical achievement [Booth & Siegler, 2006; Piazza et al., 2010; Siegler & Booth, 2004]. The Present Study The aim of this research was to investigate number estimation in children with autism. First, we assessed cognitively able 8- to 13-year-old children with and without autism on an engaging and developmentally sensitive nonsymbolic estimation (numerosity) task. Second, we determined their symbolic estimation by measuring their ability to map symbolic representations onto space with two numberline tasks. Finally, we also sought to establish the extent to which individual differences in these skills related to differences in mathematical achievement. Method Participants Thirt...

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...nonautistic adolescents, although the groups were not compared statistically [see O’Hearn, Franceroni, Wright, Minshew, & Luna, 2013, for replication and extension]. Although all three studies assess precise enumeration using different methods, none is suggestive of superiorities in the exact system in autism. It remains possible, however, that estimation of approximate number might be enhanced in autism. This skill is typically assessed using psychophysical paradigms whereby participants are briefly shown two patches of dots and asked to report which patch contains more dots [see Fig. 1, and Ansari, 2008, for review]. Some researchers [Mottron, Dawson, Soulieres, Hubert, & Burack, 2006; Plaisted, 2001] have proposed that such perceptual operations are generally enhanced in autism, rendering it possible that many autistic individuals might excel at numerosity. Furthermore, it is assumed that the ability to represent numerosity or nonsymbolic numerical magnitude (rather than subitizing) is a prerequisite for the later acquisition of symbolic representations of numerical magnitude [Feigenson et al., 2004]. Consistent with this view, the ability to estimate numerosity correlates strongly with ma...

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...lp the friendly character, Zando (left). They were told they would see two sets of “marbles” briefly and to touch the side of the screen that contains more “marbles.” 2 Aagten-Murphy et al./Numerical estimation in children with autism INSAR 2013]. Individual differences in nonsymbolic estimation (numerosity) could, therefore, provide one explanation for the variability in arithmetic abilities in autism. Another potential source of individual differences in mathematics is mapping number to space, asking children to indicate the position of a symbolic digit or a cloud of dots on a “numberline” [Booth & Siegler, 2006]. Younger children tend to overestimate smaller numbers and compress larger numbers at the end of the line, producing estimates that are better fit by a logarithmic than a linear function. Older children and adults tend to produce more accurate, more nearly linear estimates. Importantly, individual differences in children’s symbolic estimation, their ability to map numbers onto space is also linked to variation in mathematical achievement [Booth & Siegler, 2006; Piazza et al., 2010; Siegler & Booth, 2004]. The Present Study The aim of this research was to investigate number estimation in chil...

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... are generally enhanced in autism, rendering it possible that many autistic individuals might excel at numerosity. Furthermore, it is assumed that the ability to represent numerosity or nonsymbolic numerical magnitude (rather than subitizing) is a prerequisite for the later acquisition of symbolic representations of numerical magnitude [Feigenson et al., 2004]. Consistent with this view, the ability to estimate numerosity correlates strongly with mathematics achievement at different ages [Anobile, Stievano, & Burr, 2013; Gilmore, McCarthy & Spelke, 2010; Halberda, Mazzocco, & Feigenson, 2008; Piazza et al., 2010; although see Tibber et al., Figure 1. Nonsymbolic estimation: numerosity discrimination task. Children were introduced to two animated characters in a battle to see who can win the most marbles. Children were asked to help the friendly character, Zando (left). They were told they would see two sets of “marbles” briefly and to touch the side of the screen that contains more “marbles.” 2 Aagten-Murphy et al./Numerical estimation in children with autism INSAR 2013]. Individual differences in nonsymbolic estimation (numerosity) could, therefore, provide one explanation for the variability in ari...

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... children’s numerical estimation skills to determine whether individual differences in these skills might be one potential source of the variability in formal arithmetic skills. Researchers typically distinguish between two number systems operating over different numerical ranges, both of which are believed to contribute to children’s mathematical achievement [Feigenson, Dehaene, & Spelke, 2004]. For relatively few items (<4) a “subitizing” system enables a rapid, exact representation of numerosity while an approximate system is utilized to estimate magnitudes when more items are present [see Burr & Ross, 2008]. To our knowledge, only three studies have investigated these numerical estimation skills in autism, both targeting the exact number system. Jarrold and Russell [1997] found that autistic children showed less benefit than comparison children in counting dot stimuli presented in canonical (dots on dice) than noncanonical (distributed randomly) form, and used a less efficient dot-by-dot counting strategy. Gagnon, Mottron, Bherer, and Joanette [2004] showed that, when asked to judge numerosities between 2 and 9 (e.g., “how many squares are on the screen?”), adolescents with autism seemed to sho...

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...oni, Wright, Minshew, & Luna, 2013, for replication and extension]. Although all three studies assess precise enumeration using different methods, none is suggestive of superiorities in the exact system in autism. It remains possible, however, that estimation of approximate number might be enhanced in autism. This skill is typically assessed using psychophysical paradigms whereby participants are briefly shown two patches of dots and asked to report which patch contains more dots [see Fig. 1, and Ansari, 2008, for review]. Some researchers [Mottron, Dawson, Soulieres, Hubert, & Burack, 2006; Plaisted, 2001] have proposed that such perceptual operations are generally enhanced in autism, rendering it possible that many autistic individuals might excel at numerosity. Furthermore, it is assumed that the ability to represent numerosity or nonsymbolic numerical magnitude (rather than subitizing) is a prerequisite for the later acquisition of symbolic representations of numerical magnitude [Feigenson et al., 2004]. Consistent with this view, the ability to estimate numerosity correlates strongly with mathematics achievement at different ages [Anobile, Stievano, & Burr, 2013; Gilmore, McCarthy & Spelke...

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...y Online Library (wileyonlinelibrary.com) DOI: 10.1002/aur.1482 VC 2015 International Society for Autism Research, Wiley Periodicals, Inc. INSAR Autism Research 00: 00–00, 2015 1 contrary to Baron-Cohen’s [2002] prediction, not all children with autism show strengths in mathematics. Consistent with anecdotal and single-case reports, studies have identified a sizeable proportion of young people with autism [up to 16% of n 5 100; Jones et al., 2009] with exceptional arithmetic processing relative to their intellectual functioning, or “hypercalculia.” Yet between 6% [Jones et al., 2009] and 22% [Mayes & Calhoun, 2003a] of children and adolescents with autism were reported to struggle with calculation and mental arithmetic to an extent that their maths difficulties were incommensurate with intellectual functioning, indicative of a specific disability in arithmetic, or developmental dyscalculia. The amount of variability in arithmetic achievement in autism is striking. Yet as informative as these standardized tests are, they are unable to provide a detailed and comprehensive analysis of why such achievement is so variable. Here, we investigated autistic children’s numerical estimation skills to determine wh...

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...r. Autism Res 2015, 00: 000–000. VC 2015 International Society for Autism Research, Wiley Periodicals, Inc. Keywords: autism; mathematics; number; visual perception Introduction Individuals diagnosed with an autism spectrum condition (hereafter, “autism”) are often most well known for their difficulties in social communication. It is now well established, however, that they often show an uneven profile of abilities, including a pattern of typical or often superior performance in other domains, particularly in visuospatial processing [e.g., Frith, 1989; Mottron, Dawson, & Soulieres, 2009; see Simmons et al., 2009, for review]. Number skills are often reported anecdotally and in the mass media as a relative strength for autistic1 people. For example, Sacks [1985] reported the extraordinary behavior of two twins with autism, who could determine instantly the correct numbers of matches dispersed on the floor as 111, and subsequently qualify them as “equal to three times thirty-seven.” This striking ability, which provided the inspiration for the talents of the lead autistic character in the film, Rain Man, was in stark contrast to the twins’ cognitive ability (IQ<70). This report echoes many reports of s...

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...y Online Library (wileyonlinelibrary.com) DOI: 10.1002/aur.1482 VC 2015 International Society for Autism Research, Wiley Periodicals, Inc. INSAR Autism Research 00: 00–00, 2015 1 contrary to Baron-Cohen’s [2002] prediction, not all children with autism show strengths in mathematics. Consistent with anecdotal and single-case reports, studies have identified a sizeable proportion of young people with autism [up to 16% of n 5 100; Jones et al., 2009] with exceptional arithmetic processing relative to their intellectual functioning, or “hypercalculia.” Yet between 6% [Jones et al., 2009] and 22% [Mayes & Calhoun, 2003a] of children and adolescents with autism were reported to struggle with calculation and mental arithmetic to an extent that their maths difficulties were incommensurate with intellectual functioning, indicative of a specific disability in arithmetic, or developmental dyscalculia. The amount of variability in arithmetic achievement in autism is striking. Yet as informative as these standardized tests are, they are unable to provide a detailed and comprehensive analysis of why such achievement is so variable. Here, we investigated autistic children’s numerical estimation skills to determine wh...

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...abilities in autistic savants [e.g., Cowan & Frith, 2009; Soulieres et al., 2010] but whether such superiorities are characteristic of autistic individuals who are not savants is unclear. One popular theoretical account of autism gives us reason to expect that individuals with autism might be generally talented at mathematics. Baron-Cohen’s [2002; Baron-Cohen, Ashwin, Aswin, Tavassoli, & Chakrabarti, 2009] theory proposes that males have an inherent drive to understand rule-based systems (i.e., to “systemize”), which he claims is linked to talent in the fields of mathematics and engineering [Baron-Cohen, Wheelwright, Stott, Bolton, & Goodyer, 1997; although see Jarrold & Routh, 1998]. On this account, autistic individuals are considered to have an “extreme form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skills are critical to educational achievement and for achieving independence post full-time education, there are only a handful of studies on this topic [see Chiang & Lin, 2007, for review]. However, with one exception [Iuculano et al., 2014], most st...

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...elds of mathematics and engineering [Baron-Cohen, Wheelwright, Stott, Bolton, & Goodyer, 1997; although see Jarrold & Routh, 1998]. On this account, autistic individuals are considered to have an “extreme form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skills are critical to educational achievement and for achieving independence post full-time education, there are only a handful of studies on this topic [see Chiang & Lin, 2007, for review]. However, with one exception [Iuculano et al., 2014], most studies demonstrate that, 1The term “autistic” is the preferred language of many people on the spectrum (e.g., Sinclair, 1999). In this article, we use this term as well as person-first language to respect the wishes of individuals on the spectrum. From the Department of Psychology, Ludwig-Maximilians-Universit€at M€unchen, Munich, Germany (D.A.M.); Department of Psychology, University of Florence, Florence, Italy (D.A.M., D.B.); School of Psychology, University of Western Australia, Perth, Australia (D.B., E.P.); Centre ...

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... Dawson, Soulieres, Hubert, & Burack, 2006; Plaisted, 2001] have proposed that such perceptual operations are generally enhanced in autism, rendering it possible that many autistic individuals might excel at numerosity. Furthermore, it is assumed that the ability to represent numerosity or nonsymbolic numerical magnitude (rather than subitizing) is a prerequisite for the later acquisition of symbolic representations of numerical magnitude [Feigenson et al., 2004]. Consistent with this view, the ability to estimate numerosity correlates strongly with mathematics achievement at different ages [Anobile, Stievano, & Burr, 2013; Gilmore, McCarthy & Spelke, 2010; Halberda, Mazzocco, & Feigenson, 2008; Piazza et al., 2010; although see Tibber et al., Figure 1. Nonsymbolic estimation: numerosity discrimination task. Children were introduced to two animated characters in a battle to see who can win the most marbles. Children were asked to help the friendly character, Zando (left). They were told they would see two sets of “marbles” briefly and to touch the side of the screen that contains more “marbles.” 2 Aagten-Murphy et al./Numerical estimation in children with autism INSAR 2013]. Individual differences in nonsymboli...

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...y and in the mass media as a relative strength for autistic1 people. For example, Sacks [1985] reported the extraordinary behavior of two twins with autism, who could determine instantly the correct numbers of matches dispersed on the floor as 111, and subsequently qualify them as “equal to three times thirty-seven.” This striking ability, which provided the inspiration for the talents of the lead autistic character in the film, Rain Man, was in stark contrast to the twins’ cognitive ability (IQ<70). This report echoes many reports of superior calculations abilities in autistic savants [e.g., Cowan & Frith, 2009; Soulieres et al., 2010] but whether such superiorities are characteristic of autistic individuals who are not savants is unclear. One popular theoretical account of autism gives us reason to expect that individuals with autism might be generally talented at mathematics. Baron-Cohen’s [2002; Baron-Cohen, Ashwin, Aswin, Tavassoli, & Chakrabarti, 2009] theory proposes that males have an inherent drive to understand rule-based systems (i.e., to “systemize”), which he claims is linked to talent in the fields of mathematics and engineering [Baron-Cohen, Wheelwright, Stott, Bolton, & Goodyer, 1997...

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... al., 2010] but whether such superiorities are characteristic of autistic individuals who are not savants is unclear. One popular theoretical account of autism gives us reason to expect that individuals with autism might be generally talented at mathematics. Baron-Cohen’s [2002; Baron-Cohen, Ashwin, Aswin, Tavassoli, & Chakrabarti, 2009] theory proposes that males have an inherent drive to understand rule-based systems (i.e., to “systemize”), which he claims is linked to talent in the fields of mathematics and engineering [Baron-Cohen, Wheelwright, Stott, Bolton, & Goodyer, 1997; although see Jarrold & Routh, 1998]. On this account, autistic individuals are considered to have an “extreme form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skills are critical to educational achievement and for achieving independence post full-time education, there are only a handful of studies on this topic [see Chiang & Lin, 2007, for review]. However, with one exception [Iuculano et al., 2014], most studies demonstrate that, 1The term “a...

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...me form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skills are critical to educational achievement and for achieving independence post full-time education, there are only a handful of studies on this topic [see Chiang & Lin, 2007, for review]. However, with one exception [Iuculano et al., 2014], most studies demonstrate that, 1The term “autistic” is the preferred language of many people on the spectrum (e.g., Sinclair, 1999). In this article, we use this term as well as person-first language to respect the wishes of individuals on the spectrum. From the Department of Psychology, Ludwig-Maximilians-Universit€at M€unchen, Munich, Germany (D.A.M.); Department of Psychology, University of Florence, Florence, Italy (D.A.M., D.B.); School of Psychology, University of Western Australia, Perth, Australia (D.B., E.P.); Centre for Research in Autism and Education (CRAE), UCL Institute of Education, University College London, UK (C.A., N.D., E.K., E.P.) Received July 23, 2014; accepted for publication February 28, 2015 Addr...

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...en.” This striking ability, which provided the inspiration for the talents of the lead autistic character in the film, Rain Man, was in stark contrast to the twins’ cognitive ability (IQ<70). This report echoes many reports of superior calculations abilities in autistic savants [e.g., Cowan & Frith, 2009; Soulieres et al., 2010] but whether such superiorities are characteristic of autistic individuals who are not savants is unclear. One popular theoretical account of autism gives us reason to expect that individuals with autism might be generally talented at mathematics. Baron-Cohen’s [2002; Baron-Cohen, Ashwin, Aswin, Tavassoli, & Chakrabarti, 2009] theory proposes that males have an inherent drive to understand rule-based systems (i.e., to “systemize”), which he claims is linked to talent in the fields of mathematics and engineering [Baron-Cohen, Wheelwright, Stott, Bolton, & Goodyer, 1997; although see Jarrold & Routh, 1998]. On this account, autistic individuals are considered to have an “extreme form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skill...

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... Stott, Bolton, & Goodyer, 1997; although see Jarrold & Routh, 1998]. On this account, autistic individuals are considered to have an “extreme form of the male brain” and, as such, show “hyper-systemizing.” One might, therefore, expect individuals with autism also to show enhanced underlying number and mathematical skills. Despite this widespread belief and the fact that such skills are critical to educational achievement and for achieving independence post full-time education, there are only a handful of studies on this topic [see Chiang & Lin, 2007, for review]. However, with one exception [Iuculano et al., 2014], most studies demonstrate that, 1The term “autistic” is the preferred language of many people on the spectrum (e.g., Sinclair, 1999). In this article, we use this term as well as person-first language to respect the wishes of individuals on the spectrum. From the Department of Psychology, Ludwig-Maximilians-Universit€at M€unchen, Munich, Germany (D.A.M.); Department of Psychology, University of Florence, Florence, Italy (D.A.M., D.B.); School of Psychology, University of Western Australia, Perth, Australia (D.B., E.P.); Centre for Research in Autism and Education (CRAE), UCL Institute of Edu...