Fraction Estimation Predicts Later Calculation, but not Fluency: A Cross-Sequential Study of Primary School Children

• In Event: Poster Session 09
  In Poster Session: PS 09 Topic - Cognitive Processes

Abstract

Children’s fraction number line estimation (NLE) skill is more strongly correlated with their overall math achievement than are other foundational math skills (e.g., Fazio et al., 2014; Torbeyns et al., 2015). However, most studies of this correlation have measured NLE and achievement concurrently, included few control measures, and examined the relation in late elementary or middle school. A single longitudinal study showed that 4th-graders’ fraction NLE predicted math achievement over 2 years, even with robust controls (Hansen et al., 2017). We sought to replicate and extend this finding with two different age groups and two subdomains of math achievement.

We hypothesized that fraction NLE would predict later math achievement even with strong controls, but that this relationship would be stronger for 2nd graders than for 5th graders, because students who start with a stronger understanding of fractions as magnitudes may learn more from early fraction instruction (e.g., Siegler et al., 2011). We also hypothesized that fraction NLE would more strongly support later problem solving and multi-step computations than retrieval of simple facts.

This study followed 160 second graders and 128 fifth graders for three years. In Year 1, they completed fraction NLE tasks on 0-1, 0-2, and 0-5 lines and whole number NLE tasks on 0-100 and 0-1000 lines. Estimation performance was measured by mean percent absolute error (|estimated value – given value| / range). In Year 2, they completed two subtests of math achievement, Woodcock-Johnson Calculation (operations with multi-digit numbers, geometry, etc.) and Fluency (rapid, single-digit math facts). In Year 3, they completed both math achievement subtests again, and measures of domain-general cognitive skills (Matrix Reasoning, Block Design, and Spatial Reasoning).

We tested whether fraction NLE in 2nd and 5th grade prospectively explained unique variance in math calculation and math fluency 2 years later. For each age group, we regressed Year 3 calculation on fraction NLE, including Year 2 calculation, domain-general skills, and whole number NLE as controls. We repeated these tests with Fluency as the outcome.

As shown in Table 1, fraction NLE was a unique predictor of Calculation scores two years later for both 2nd (β = -.31, p < .001) and 5th (β = -.25, p = .039) grade students, over and above the effect of domain-general controls, prior achievement autoregressor, and whole number NLE. Whole number NLE was also a significant predictor of calculation in year 3 for 2nd graders (β = -.24, p = .004), but not for 5th graders (p = .87). However, fraction NLE did not longitudinally predict Fluency scores in either age group after adding controls (p2nd = .53 and p5th = .14).

In conclusion, we found that fraction estimation longitudinally predicted calculation skill, but not math fluency, in two separate age cohorts. Whereas whole number estimation only predicted calculation skill for the youngest participants, fraction estimation was a significant predictor for both. Future studies should investigate mechanisms underlying the relations between fraction NLE and formal math achievement and how they vary across a broader range of age cohorts.

Authors

• Alexandria A Viegut, University of Delaware
  Presenting Author

• Yunji Park, University of Wisconsin-Madison
  Non-Presenting Author

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

• Percival G Matthews, University of Wisconsin - Madison
  Non-Presenting Author