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ERIC Number: EJ1366970
Record Type: Journal
Publication Date: 2022-Oct
Pages: 19
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0012-1649
EISSN: EISSN-1939-0599
From Integers to Fractions: The Role of Analogy in Developing a Coherent Understanding of Proportional Magnitude
Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one another. To address this, we asked 177 third, fourth, and fifth graders (M = 9.85 years, 87 girls, 69% White, 19% low income) to estimate the position of proportionally equivalent integers and fractions on number lines (e.g., 3 on a 0-8 number line vs. 3/8 on a 0-1 number line, Study 1). With increasing age, children's estimates of implicit and explicit proportions became more coherent, such that a child's estimates of fractions on a 0-1 number-line was a linear function of the same child's estimates of equivalent integers. To further investigate whether preexisting integer knowledge can facilitate fraction learning through analogy, we assigned 100 third to fifth graders (M = 10.04 years, 55 girls, 76% White) to an Alignment condition, where children estimated fractions and integers on aligned number lines, or to a No Alignment condition (Study 2). Results showed that aligning integers and fractions on number lines facilitated a better understanding of fractional magnitudes, and increased children's fraction estimation accuracy to the level of college students'. Together, findings suggest that analogies can play an important role in building a coherent understanding of proportions.
American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED)
Authoring Institution: N/A
IES Funded: Yes
Grant or Contract Numbers: R305A160295