Learning Improper Fractions with the Number Line and the Area Model

ABSTRACT

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We randomly assigned fourth and fifth graders to a number line training, an area model training, or a non-numerical control condition. The number line and area model trainings involved both proper and improper fractions and were closely modeled on the training procedures in prior studies. Fraction training with the area model produced improvements in children’s area model estimation of proper and improper fractions. However, contrary to our expectations, training with the number line did not improve number line estimation, and neither training led to improvements in transfer tasks assessing fraction magnitude knowledge. These findings suggest that children can develop the skill to represent improper fractions on area models with brief training. Nevertheless, it is unclear whether this skill enhances a comprehensive understanding of fraction magnitudes.

Acknowledgments

We thank the children and teachers who gave their time to this research and the research assistants who helped carry it out including Yiqiao Wang, Jorge Carvalho Pereira, Grace Bennett-Pierre, Nadia Tavassolie, Khushi Sibal, Paula Ueki, Dianna Wambach, Madyson Kolbes, Su Dam, Nadhia Marie Engle, and Brianna Stein.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data described in this article are openly available in the Open Science Framework at https://osf.io/c7a5q/.

Open scholarship

This article has earned the Center for Open Science badges for Open Data, Open Materials and Preregistered. The data and materials are openly accessible at https://osf.io/c7a5q/.

Additional information

Funding

This research was supported by NSF CAREER DRL-1452000, NSF ECR-1760144, and James S. McDonnell Foundation Award #220020546 to Elizabeth A. Gunderson.