Do Individual Differences in Students’ Working Memory Moderate the Effects of Fraction Intervention?

• In Event: Math Learning Among At-Risk Students From Preschool Through Fourth Grade: Implications for Educational Policy and Practice

Abstract

Paper/presentation summary
Purposes: To (a) investigate whether individual differences in working memory (WM) moderate the effects of 2 variations of intervention designed to improve at-risk (AR) 4th graders’ fraction knowledge; (b) examine effects of each intervention against a business-as-usual control group; and (c) assess whether children’s measurement interpretation of fractions mediated effects.

Theoretical framework: Geary et al. (2008) hypothesized that building automaticity with skills or strategies central to a new domain of learning enhances outcomes by compensating for limitations in children’s cognitive abilities. This hypothesis predicts that the benefits of fluency practice should be stronger for students with weaker than stronger cognitive abilities. Few studies have examined whether or how children’s cognitive abilities moderate (i.e., interact with) the effects of intervention. Identifying such interactions may provide the basis for expanding the efficacy of intervention for a more diverse group of students.

Methods: We defined AR as scoring <35th% on a mathematics assessment and sampled half from <15th% and half from 15th - 34th%. The sample comprised 277 AR students from 49 classrooms in 14 schools. We randomly assigned students to fluency activities, conceptual activities, and the control condition. Additionally, 281 low-risk classmates were randomly sampled to serve as a comparison group. Each intervention condition focused mainly on measurement interpretation of fractions and incorporated the same instructional design. Supplementary activities, conducted for 5 min of each session, differed between the 2 conditions. One provided strategic activities to build fluency on 4 measurement interpretation topics. In the other, students explained their reasoning about the same 4 topics to consolidate understanding. Before intervention, we assessed children’s WM, processing speed, attentive behavior, and language. Before and after, we assessed fraction knowledge.

Data sources: measures of accuracy of number line placements; fraction calculation skill; released NAEP fraction items; commercial measures of WM, processing speed, attentive behavior, and language.

Results, conclusions, and scientific importance: The 2 interventions outperformed the control group. Effect sizes, compared to control, were 0.60 - 1.12 for fluency practice; 0.63 - 1.13 for conceptual practice. The achievement gap with respect to low-risk classmates was reduced by ~50% on NAEP and was closed for calculations. Improvement in measurement understanding partially mediated these effects. NMAP (2008) hypothesized that improvement in measurement interpretation is a key mechanism explaining fraction learning and recommended that fraction instruction be reoriented in this direction. Our findings support this recommendation. Findings also revealed an aptitude-treatment interaction, in which WM moderated effects between the fluency vs. conceptual condition on the number line measure. Conceptual work was superior to the fluency condition for students with weak WM, but supplementary fluency work promoted better learning for students with stronger WM. This indicates the need for a certain WM capacity to benefit from the strategic, speeded fraction strategies in fluency practice. For students lacking WM capacity, instructional time is better spent consolidating fraction understanding

Authors

• Lynn Fuchs, Vanderbilt University

• Robin Schumacher, Vanderbilt Peabody College

• Jessica Min Namkung, Vanderbilt University - Peabody College

• Amelia Schneider Malone, Vanderbilt University - Peabody College

• Douglas Fuchs, Vanderbilt University