From Proportions to Symbolic Rational Numbers

Session Type: Paper Symposium

Abstract

The long-lasting difficulty with rational numbers contrasts with the relatively rapid development of whole number knowledge (Siegler et al., 2009) and the strong early intuitions about proportions (Boyer et al., 2008), a skill closely related to fraction knowledge. This symposium aims at contributing to our understanding of the development of rational number knowledge with recent data from young children's proportional reasoning to older children's and adults' magnitude knowledge of fractions and decimals.

The first paper revealed that 6-year-olds using more gestures highlighting continuous amounts rather than whole number parts of proportions were more accurate at reasoning with proportions. The second paper showed that playing a game that involved partitioning area models to represent fractions improved 1st and 2nd graders' fraction knowledge. The third paper documented that 2nd through 5th graders did not consistently apply their (limited) fraction magnitude knowledge across tasks. The last paper showed that when comparing decimals, whole number components interfered with performance of both adults and children, but adults were more sensitive to decimal magnitudes than children.

These talks reveal complementary ways in which children’s difficulty with rational numbers can be mitigated, via non-symbolic proportional reasoning and symbolic reasoning with fractions and decimals. In particular, by 1) leveraging children's own gestures on proportions, 2) learning the meaning of numerator and denominator through partitioning area models, 3) focusing on the process of transfer to apply fraction magnitude knowledge to a broader range of tasks, and 4) overcoming inference of whole number components in comparing decimals.

Sub Unit

• Cognitive Processes

Chair

• Jing Tian, Temple University

Individual Presentations

• Children’s Gesture use Provides Insight into Proportional Reasoning Strategies - Presenting Author: Michelle A Hurst, University of Chicago; Non-Presenting Author: Alyson Wong, Boston College; Non-Presenting Author: Raychel Barkin, University of Maryland - College Park; Non-Presenting Author: Aziza Alam, Boston College; Non-Presenting Author: Sara Cordes, Boston College

• Connecting Symbolic Fractions to Continuous Proportion Using a Fraction Card Game - Presenting Author: Jacob Butts, University of Chicago; Non-Presenting Author: Michelle A Hurst, University of Chicago; Non-Presenting Author: Susan Cohen Levine, University of Chicago

• Do Children Understand Fraction Magnitudes? Sometimes Yes, and Sometimes No. - Presenting Author: Jing Tian, Temple University; Non-Presenting Author: Maya Rahman, Temple University; Non-Presenting Author: Elizabeth A Gunderson, Temple University

• Tracking the Development of Whole Number Bias and Rational Magnitude Representation in Decimal Comparison - Presenting Author: Miriam Rosenberg-Lee, Rutgers University - Newark; Non-Presenting Author: Roberto Abreu-Mendoza, Rutgers University - Newark; Non-Presenting Author: Shannon Cahalan, Rutgers University - Newark