title: In how many ways is the approximate number system associated with exact calculation?
abstract: The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.
authors.affiliation: Cognitive Neuroimaging Unit, Institut National de la Santé et de la Recherche Médicale (INSERM) U992, Gif/Yvette, France; NeuroSpin Center, Institute of BioImaging Commissariat à l'Energie Atomique (CEA), Gif/Yvette, France; Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil.
authors.forename: Pedro
authors.initials: P
authors.lastname: Pinheiro-Chagas
authors.affiliation: Department of Neuropsychology, Institute of Psychology, Karl-Franzens University of Graz, Graz, Austria.
authors.forename: Guilherme
authors.initials: G
authors.lastname: Wood
authors.affiliation: Faculty of Life Sciences, Humboldt Universität zu Berlin, Berlin, Germany.
authors.forename: André
authors.initials: A
authors.lastname: Knops
authors.affiliation: Section Child Neuropsychology, Department of Child and Adolescent Psychiatry, University Hospital of the RWTH, Aachen, Germany.
authors.forename: Helga
authors.initials: H
authors.lastname: Krinzinger
authors.affiliation: German Institute for International Educational Research, Frankfurt, Germany; Center for Individual Development and Adaptive Education of Children at Risk (IDeA), Frankfurt, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Lonnemann
authors.affiliation: Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil.
authors.forename: Isabella
authors.initials: I
authors.lastname: Starling-Alves
authors.affiliation: Section Neuropsychology, Department of Neurology, University Hospital of the RWTH, Aachen, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Willmes
authors.affiliation: Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil; Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Faculdade de Medicina, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil.
authors.forename: Vitor Geraldi
authors.initials: VG
authors.lastname: Haase
mesh_terms: D001938:Brazil; D002648:Child; D003430:Cross-Sectional Studies; D004521:Educational Measurement / Q000379:methods*; D004522:Educational Status; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics / Q000193:education*