Abstract
In mathematics, learners often spontaneously draw on prior knowledge when learning new ideas. In this study, we examined whether the specific diagrams used to represent more familiar (i.e., whole number division) and less familiar ideas (i.e., fraction division) shape successful transfer. Undergraduates (N = 177) were randomly assigned to demonstrate fraction division in a 3 (Diagram: Number Line, Circle, None) × 3 (“Warm-up” Example: Whole Number Division, Fraction Addition, None) between-subjects design. We hypothesized that transfer from whole number division would be greatest in the number line condition. When using number lines and warming up with whole number division, students generated more accurate conceptual models of fraction division. However, both number lines and circles supported transfer from whole number concepts to fraction concepts, whereas having no diagrams did not. Diagrams may play a critical role in helping learners make use of their vast prior knowledge.
| Original language | English |
|---|---|
| Article number | 102066 |
| Journal | Contemporary Educational Psychology |
| Volume | 69 |
| DOIs | |
| State | Published - Apr 2022 |
Bibliographical note
Publisher Copyright:© 2022 Elsevier Inc.
Funding
The authors would like to thank Alexandria McDonald and Andrea MacDonald for their hard work coding participants’ work. We also thank Gabrielle Eismann, Jessica Blake, Deanna Chesser, and Andrea MacDonald for aiding in data collection. This research was supported in part by the U.S. Department of Education Institute of Education Sciences Grant R305U200004 to C.A. Thompson at Kent State University.
| Funders | Funder number |
|---|---|
| U.S. Department of Education Institute of Education Sciences | R305U200004 |
| Kent State University |
Keywords
- Analogical transfer
- Conceptual understanding
- Diagram
- Fraction learning
- Number line
ASJC Scopus subject areas
- Education
- Developmental and Educational Psychology