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The sensitivity of number sense as cognitive phenotype for Mathematical Learning Disabilities (MLD) was assessed in siblings of children with MLD (n = 9) and age matched children without family members with MLD (n = 63). A number line estimation paradigm was used as a measure of childrens" early number sense. In line with the triple code model of Dehaene (1992), three different presentation formats were presented. The results of the study confirmed that number line estimation was related to early arithmetic achievement in kindergarten. In addition siblings were less proficient in number line placements compared to non-siblings, with a larger effect size for symbolic and especially number word estimation compared to the non-symbolic results. Siblings also differed from non siblings on procedural and conceptual counting skills and logical thinking in kindergarten. Moreover MLD had a familial aggregation, since about three out of five sibling girls had clinical scores on a early numeracy test in kindergarten, pointing to a risk to develop MLD themselves. Implications of the study to our understanding of MLD are discussed.Keywords: mathematical learning disability (MLD), cognitive phenotype, number line estimation, siblings, magnitudes, early literacy, early numeracy, kindergarten Highlights Number sense is a candidate for cognitive phenotype of MLD Number line estimation is related to early numeracy Children access an amodal representation of magnitudes in kindergarten There is a delay in counting, classification and seriation in siblings of children with MLD Familial aggregation of MLD IntroductionMathematical literacy is important in our society (e.g., Vanmeirhaeghe, 2012). Most practitioners and researchers currently report a prevalence of mathematical learning disabilities (MLD) between 3-14% of children (Barbaresi, Katuskic, Colligan, Weaver, & Jacobsen, 2005; Geary, Hoard, Nugent, & Bailey, 2011; Shalev, Manor, & Gross-Tsur, 2005).The prevalence of MLD in siblings even ranges from 40 to 64% (Shalev et al., 2001). The comorbidity between MLD and Reading disabilities is estimated between 30% and 50% (Shalev, Auerbach, Manor, & Gross-Tsur, 2000), Given that MLD is associated with cost to society, family and the individual person, it is important to better understand what causes MLD so that treatments can be developed and targeted at the underlying causes. In some disorders the study of the phenotypes helps to In reading learning disabilities the phonological deficit is often described as core deficit. In MLD there are several models trying to predict achievement or explain atypical development. A central role has also been awarded to counting and logical thinking skills in kindergarten (e.g., Lipton & Spelke, 2005; Nunes et al., 2006; Stock, Desoete, & Roeyers, 2010). However the above mentioned skills can be considered as "higher" order skills building further on core competencies such as "number sense". This number sense -"the ability to quickly understand, approximate, and manipulate numerical qua...

Extending previous research on the predictive value of large number discrimination, this study explored the role of infants' and toddlers' small number discrimination for numerical competencies in kindergarten (NCK). Although no significant relationship could be found between number discrimination in infancy (8 months, T1) and NCK (48 months, T3), the predictive value of toddlers' number discrimination (24 months, T2) for NCK could be demonstrated at least for some NCK. The finding that only toddlers' small number discrimination related to NCK raised thoughts about the task, age, set size, stability and development of number discrimination or other influencing factors. Future research should study all small set sizes (not only 1vs3) and a broader range of NCK in a larger sample. Nevertheless, whereas infants' small number discrimination might be too early to predict NCK, performance in toddlerhood might be addressed in the future to establish a measure to detect at-risk mathematical development. FACULTY OF PSYCHOLOGY AND EDUCATIONAL SCIENCES Department of Experimental Clinical and Health PsychologyFaculty of Psychology and Educational Sciences Department of Experimental Clinical and Health Psychology Henri Dunantlaan 2, 9000 Ghent, Belgium www.UGent.be We thank the reviewers for their constructive comments and think this has lead to an improved paper.My coauthors and I do not have any interests that might be interpreted as influencing the research, and APA ethical standards were followed in the conduct of the study. The work described has not been published previously and is not under consideration for publication elsewhere. I will be serving as the corresponding author for this manuscript. All of the authors listed in the byline have agreed to the byline order and to submission of the manuscript in this form. I have assumed responsibility for keeping my coauthors informed of our progress through the editorial review process, the content of the reviews and any revisions made. I understand that, if accepted for publication, a certification of authorship form will be required that all authors will sign. In the previous version of the manuscript we used number sense as a conceptual framework for studying number discrimination as an innate form of number sense which in its turn has frequently been studied as a predictor for later mathematical achievement, mostly in older children than toddlers or infants (e.g., Dowker, 2008; Mazocco & Thompson, 2005;). However, we understand the concern of reviewer #2 and acknowledge that a review of the literature indeed learns that the concept of 'number sense' is defined and conceptualized in many different ways. In order to meet the suggestion of this reviewer we aimed at building the 'Introduction-section' upon a framework starting from (large) 'number discrimination' as a predictor to later mathematical achievement as recently studied by . Changes in the 'Introduction-section' are shown in the 'track-changesversion' of the manuscript which is attached to this respo...

Studies comparing mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are hitherto scarce, inconclusive, and mainly focusing on elementary school children or adolescents. The present study wants to gain insight into the foundation of mathematics by looking at preschool performances. Five early numerical competencies known to be important for mathematical development were examined: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. These competencies were studied in 20 high-functioning children with ASD and 20 age-matched control children aged 4 and 5 years. Our data revealed similar early number processing in children with and without ASD at preschool age, meaning that both groups did not differ on the foundation of mathematics development. Given the pervasiveness and the family impact of the condition of ASD, this is an important positive message for parents and preschool teachers. Implications and several directions for future research are proposed.