Using Different Representational Tools to Develop Fraction Sense in Struggling Learners

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

Integrative Statement

Fractions are foundational for learning algebra, thus representing a crucial component of middle school mathematics (NMAP, 2008). Unfortunately, many students struggle to develop a basic understanding of fractions (Jordan et al., 2017). Students who leave 6th grade with weak fraction knowledge experience cascading mathematics difficulties. Understanding fractions as magnitudes that can be represented on a number line provides an underlying structure for learning a range of fraction concepts (e.g., Siegler et al, 2011). Unfortunately, many intervention approaches designed for students with mathematics difficulties do not use linear models (Gersten et al. 2016). As a result, many low-achieving students show little or no growth in fraction magnitude knowledge in the intermediate grades (Resnick et al., 2016). In this study, we present the third iteration of our fraction sense intervention for struggling sixth graders. The intervention is centered on linear representations of fractions (e.g., number lines, rulers, and fraction bars) and explicitly incorporates instructional principles from the science of learning. Simultaneously, we explored the effectiveness of two types of independent practice: one where students solved arithmetic problems using area models and the other using the number line models emphasized in the lessons. We expected that practice with area models would map more easily onto arithmetic problems than number lines.

A validated fraction screener was administered to all sixth-graders in general classes in two schools, which serve under-resourced, diverse communities. Consenting participants who fell below our cutoff (N = 81) were randomly assigned to the experimental or BAU control. Students in the experimental group were randomly assigned to an intervention class of about 14 students. Students in each intervention class were then randomly assigned to one of the two practice conditions (i.e., half of the class to each condition), which occurred at the end of every lesson. There was a total of 27 lessons delivered by researchers. The control group received the school assigned computer assisted intervention. Students were assessed on measures of general fraction concepts (with various fraction model representations), number line estimation, fraction magnitude comparisons, and fraction arithmetic. The study used a pretest, posttest, and delayed posttest design.

To assess whether there are differential improvements RMANOVAs were conducted on all outcome measures. Simple effects tests followed to determine sources of observed differences. Figure 1 shows the means broken down by practice condition and time. Intervention students, overall, performed significantly better than controls on all measures except arithmetic. Effects were observed both at posttest and delayed posttest, showing durable gains over time (Table 1). There was no difference between the two practice conditions except on the measure of fraction concepts, where students in the area model group performed significantly better than those in the number line model group. These differences were observed at both time points with large effect sizes (p <.001, g=.81 and delayed posttest, p<.005, g=.75).

Although our intervention, which focused on number line representations, led to meaningful gains on all measures, additional practice with fraction area model representations helped children consolidate learning of fraction concepts but not arithmetic skill.

Authors

• Nancy Jordan, University of Delaware
  Presenting Author

• Nancy Dyson, University of Delaware
  Non-Presenting Author

• Christina Barbieri, Temple University
  Non-Presenting Author

• Kelly-Ann Gesuelli, University of Delaware
  Non-Presenting Author