Number line unidimensionality is a critical feature for promoting fraction magnitude concepts

• Published in: Journal of experimental child psychology Vol. 187; p. 104657
• Main Authors: Gunderson, Elizabeth A., Hamdan, Noora, Hildebrand, Lindsey, Bartek, Victoria
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.11.2019
• Subjects: Area model; Fractions; Magnitude; Mathematical development; Number line; Numerical Cognition; Number line; Numerical Cognition; Mathematical development; Magnitude; Fractions; Area model
• ISSN: 0022-0965; 1096-0457
• DOI: 10.1016/j.jecp.2019.06.010

•Children completed fraction number line training in one of four conditions.•Training with unidimensional number lines led to transfer to magnitude comparisons.•Training using a square area model or 2-D square number line did not.•Unidimensionality is necessary for transfer to fraction magnitude concepts. Children’s ability to estimate fractions on a number line is strongly related to algebra and overall high school math achievement, and number line training leads to better fraction magnitude comparisons compared with area model training. Here, we asked whether unidimensionality is necessary for the number line to promote fraction magnitude concepts and whether left-to-right orientation and labeled endpoints are sufficient. We randomly assigned second- and third-graders (N = 148) to one of four 15-min one-on-one, experimenter-led trainings. Three number line trainings had identical scripts, where the experimenter taught children to segment and shade the number line along the horizontal dimension. The number line conditions varied only in the vertical dimension of the training number line: pure unidimensional number line (17.5 cm horizontal line), hybrid unidimensional number line (17.5 × 0.6 cm rectangle), and square number line (17.5 × 17.5 cm). In the area model condition, children were taught to segment and shade a square (17.5 × 17.5 cm) along both dimensions. The conditions significantly differed in posttest fraction magnitude comparison accuracy (a transfer task), controlling for pretest accuracy, reading achievement, and age. In preregistered analyses, the hybrid unidimensional number line condition significantly outperformed the square area model condition and the square number line condition. In exploratory analyses accounting for training protocol fidelity, these results held and the pure unidimensional number line also outperformed the area model condition on fraction magnitude comparisons. We argue that unidimensionality is a critical feature of the number line for promoting fraction magnitude concepts because it aligns with a key concept—that real numbers, including fractions, can be ordered along a single dimension.