Do Children Understand Fraction Magnitudes? Sometimes Yes, and Sometimes No.

• In Event: From Proportions to Symbolic Rational Numbers

Abstract

Understanding fractions imposes major challenges for many children and even adults (Kloosterman, 2010; Stigler, Givvin, & Thompson, 2010). More disturbingly, many children do not consistently employ their (limited) fraction knowledge. On pairs of virtually identical fraction arithmetic problems (e.g., 3/5 * 1/5 and 3/5 * 4/5), many students used the correct strategy on one but not on the other problem (Siegler & Pyke, 2013). In the current study, we extended prior research on children’s inconsistent use of fraction knowledge to the area of fraction magnitude. In particular, we examined whether children demonstrate a similar understanding across different tasks assessing fraction magnitude knowledge.

In Experiment 1, 148 2nd and 3rd graders estimated fractions on number lines, estimated fractions on area models, and compared pairs of fractions (Figure 1; data reanalyzed from pretest of Gunderson et al., 2019). Correlations among the three tasks were quite small (Table 1, .03 < |r| < .18). We used Bayesian comparisons to categorize children’s strategies on the number line and the area model estimation (Liang, Paulo, Molina, Clyde, & Berger, 2008). A child’s strategy was categorized as a fraction magnitude strategy if the child’s estimates were best predicted by fraction magnitude, a componential strategy if the child’s estimates were best predicted by fraction components (i.e., numerators and denominators) or by the combination of fraction components and magnitudes, or a null strategy if there was no substantial evidence for either the fraction magnitude or the componential strategy. Among the 128 children with sufficient data on both tasks, 14% and 37% used the fraction magnitude strategy on number line estimation and on area model estimation, respectively. Critically, among the 54 children who used the fraction magnitude strategy on either task, only 21% used the magnitude strategy on both tasks.

In Experiment 2, we extended these findings to an older age group (i.e., fourth and fifth graders; N = 133) and improper fractions. Children completed the same three tasks as in Experiment 1 (except for with both proper and improper fractions) and another task that requires comparing fractions symbolically: a comparison to one task (Figure 1). On the comparison to one task, children judged whether a fraction was less than, equal to, or greater than one. Children’s performance on the four tasks only weakly correlated with each other (Table 1; .06 < |r| < .27). The accuracy of the comparison to one task did not correlate with the accuracy of comparing proper versus improper fractions on the magnitude comparison task (r(124) = 0.15, p = .085). Moreover, among the 18 children who used the fraction magnitude strategy on either the number line or the area model estimation task, only 28% used that strategy on both tasks.

In sum, 2nd through 5th graders did not consistently use their fraction magnitude knowledge across tasks, in sharp contrast to substantial consistency across tasks in prior studies of whole number magnitude knowledge (Laski & Siegler, 2007). These findings call for more attention to the process of transfer to improve children’s fraction magnitude knowledge.

Authors

• Jing Tian, Temple University
  Presenting Author

• Maya Rahman, Temple University
  Non-Presenting Author

• Elizabeth A Gunderson, Temple University
  Non-Presenting Author