Strategies Students With and Without Mathematics Disabilities Use When Estimating Fractions on Number Lines

Abstract

We examined faulty strategies with possible underlying misconceptions, as well as execution mistakes, among middle schoolers with and without mathematics disabilities when estimating fractions on number lines. Fifty-one middle schoolers participated in this study, including 27 students with mathematics disabilities. Participants were asked to estimate 10 fractions on a 0-1 number line and 11 fractions on a 0-5 number line and explain their procedures. We identified two incorrect strategies (i.e., not-on-the-line and ruler-tick-mark counting strategy) and two execution mistakes (i.e., unequal segmentation based on denominator and inaccurate numerical transformation) on both number-line estimation tasks. We also identified one additional faulty strategy (i.e., treating 0-5 as the 0-1 number line) with the 0-5 number-line estimation tasks. Students with mathematics disabilities were significantly more likely to use the faulty strategies than students without mathematics disabilities. The faulty strategies, rather than execution mistakes, were consistent across two number-line tasks and predicted students’ performance in other fraction problem-solving tasks. Results illustrated specific problems that students with and without mathematics disabilities encountered when using number lines to illustrate fractions. We discussed possible negative influences of using rulers to teach fractions and how to help students to construct the concept of units.