Relational Reasoning Predicts Fraction Knowledge in Elementary School-Aged Children

• In Event: 1-082 - Beyond Magnitude: Multiple Interpretations of Rational Numbers

Integrative Statement

Fractions knowledge plays a critical role in establishing mathematical competence (e.g., Booth, Newton, & Twiss-Garrity, 2014). Despite the clear importance of fraction knowledge, children and adults often experience considerable difficulties understanding fractions (Ni & Zhou, 2005; Stigler, Givvin & Thompson, 2010). One source of these difficulties may be the inherently relational nature of fractions – the size of a fraction a/b is defined based on the relative magnitudes of components a and b rather than by the magnitudes of either component considered in isolation. Given the importance of these relational properties of fractions, we hypothesized that individual differences in relational reasoning ability might be predictive of fraction understanding.

We recruited typically developing 2nd graders (N = 82, Mage = 8.32 years, SD = 0.58 years) and 52 5th graders (N = 52, Mage = 11.16 years, SD = .86 years) as part of an ongoing longitudinal study on developing fractions skills. Participants completed computer administered number line estimation and fraction magnitude comparison tasks and paper-and-pencil test Fractions Knowledge Assessments (FKA) developed by our lab (separate grade-appropriate versions of the FKA was developed for 2nd and 5th graders). We measured relational reasoning ability with subtests of the Test of Relational Reasoning Jr. (TORR jr, Dumas & Alexander, 2016). The TORR jr. is a domain-general test of relational reasoning including tests of analogy and antithesis (opposites) using non-symbolic visual stimuli.

Relational reasoning ability was correlated with FKA scores for both 2nd (r(81) = .46, p < .001) and 5th graders (r(52) = .54, p < .001). We conducted a linear regression to test whether this relationship held, even when accounting for working memory and non-verbal intelligence (measured by the WJ-III spatial relations subtest; all regression coefficients are standardized). TORR jr. scores were still highly predictive of fractions knowledge for both 2nd graders (β = .311, p = .007) and 5th graders (β = .34, p = .013), even when controlling for these domain-general abilities. To verify that relational reasoning was not redundant with measures of fraction magnitude, we separately regressed FKA score against the TORR jr., symbolic fraction comparison accuracy, and percent absolute error on the fraction number line task. TORR jr. scores were still robustly predictive of FKA scores for both 2nd (β = .29, p = .002) and 5th graders (β = .26, p = .023).

We found that relational reasoning was an important predictor of fraction knowledge among school-age children. It held predictive power independent of domain-general reasoning abilities or fraction magnitude knowledge. Our longitudinal study will continue to examine how the strength of these relations varies over developmental time for children at different levels of math expertise. Future research is needed to examine the extent to which relational reasoning is malleable and the extent to which improving it can help promote fractions knowledge.

Authors

• Priya Kalra, University of Wisconsin-Madison
  Non-Presenting Author

• Edward Hubbard, University of Wisconsin-Madison
  Non-Presenting Author

• Percival Matthews, University of Wisconsin-Madison
  Presenting Author