1-082 - Beyond Magnitude: Multiple Interpretations of Rational Numbers

Session Type: Paper Symposium

Integrative Statement

Competence with rational numbers (i.e., fractions, decimals, and percentages) is essential for further progress in mathematics and career development (Lortie-Forgues et al., 2015; Handel, 2016). Recent research on rational numbers has focused on knowledge of numerical magnitudes (e.g., Fazio et al., 2014; Kallai & Tzelgov, 2009; Iuculano & Butterworth, 2011; Siegler et al., 2011). However, earlier perspectives on rational numbers claim that rational numbers encompass multiple interpretations (Kieren, 1976; Behr et al., 1983). In this symposium, three papers present recent data that highlight the importance of understanding the different interpretations of rational numbers.

The first talk presents a longitudinal study that revealed relational reasoning to predict general fraction knowledge among school-age children, even after controlling for domain-general reasoning abilities and fraction magnitude knowledge. The second talk presents two experiments that focused on the proportional interpretation of percentages; the experiments showed that middle school children and pre-service teachers exhibited better understanding of percentage multiplication with an “of” expression (e.g., 35% of 78) than with the multiplication sign (e.g., 35% × 78). The third talk presents a fraction intervention with a focus on number line representation that led to meaningful gains on several fraction measures. Additional practice with fraction area models helped children consolidate learning of fraction concepts but not arithmetic skill. All three talks thus illustrate the importance of interpretations of fractions beyond magnitudes. Finally, the discussant will comment on the three talks from both theoretical and practical perspectives.

Sub Unit

• Education, Schooling

Chair

• Jing Tian, Teachers College, Columbia University

Discussant

• Robert Siegler, Professor

Individual Presentations

• Relational Reasoning Predicts Fraction Knowledge in Elementary School-Aged Children - Non-Presenting Author: Priya Kalra, University of Wisconsin-Madison; Non-Presenting Author: Edward Hubbard, University of Wisconsin-Madison; Presenting Author: Percival Matthews, University of Wisconsin-Madison

• Linguistic Facilitation of Understanding of Percentages - Presenting Author: Jing Tian, Teachers College, Columbia University; Non-Presenting Author: Robert Siegler, Professor

• Using Different Representational Tools to Develop Fraction Sense in Struggling Learners - Presenting Author: Nancy Jordan, University of Delaware; Non-Presenting Author: Nancy Dyson, University of Delaware; Non-Presenting Author: Christina Barbieri, Temple University; Non-Presenting Author: Kelly-Ann Gesuelli, University of Delaware