title: Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement.
abstract: Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to one-half, fraction pairs with common denominators) differentiates those with mathematics learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics and whether long-term learning trajectories of this knowledge also differentiate these groups. We confirmed that although fourth graders with TA (n=93) were more accurate in evaluating "one-half" fractions than in evaluating "non-half" fractions (until they reached ceiling performance levels on both types of fractions), children with MLD (n=11) did not show a one-half advantage until Grade 7 and did not reach ceiling performance even by Grade 8. Both the MLD and LA groups had early difficulties with fractions, but by Grade 5 the LA group approached performance levels of the TA group and deviated from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short-lived for the TA group (because ceiling level was achieved across formats), whereas it was slightly more persistent for the LA group and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties vary across children with math difficulties (MLD or LA).
authors.affiliation: Institute of Child Development, University of Minnesota, Minneapolis, MN 55455, USA. mazzocco@umn.edu
authors.forename: Michèle M M
authors.initials: MM
authors.lastname: Mazzocco
authors.forename: Gwen F
authors.initials: GF
authors.lastname: Myers
authors.forename: Katherine E
authors.initials: KE
authors.lastname: Lewis
authors.forename: Laurie B
authors.initials: LB
authors.lastname: Hanich
authors.forename: Melissa M
authors.initials: MM
authors.lastname: Murphy
mesh_terms: D000293:Adolescent; D002648:Child; D003210:Concept Formation; D004522:Educational Status; D005260:Female; D006801:Humans; D007859:Learning Disabilities / Q000523:psychology*; D008137:Longitudinal Studies; D008297:Male; D008433:Mathematics / Q000193:education