## 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).

Original language | English (US) |
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Pages (from-to) | 371-387 |

Number of pages | 17 |

Journal | Journal of Experimental Child Psychology |

Volume | 115 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2013 |

Externally published | Yes |

## Keywords

- Arabic numerals
- Concrete symbols
- Dyscalculia
- Fractions
- Low math achievement
- Mathematics disability
- Middle school
- Visual models

## ASJC Scopus subject areas

- Experimental and Cognitive Psychology
- Developmental and Educational Psychology