Teaching fractions to middle-school students struggling in mathematics : an exploratory study
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Fractions are an essential skill for students to master, and one students struggling in mathematics face particular difficulty with (National Mathematics Advisory Panel, 2008; Mazzocco & Devlin, 2008). This study employed the multi-probe multiple baseline design to examine the effectiveness of the concrete-representational-abstract (CRA) approach and explicit teaching practices to teach fraction equivalence to students struggling in mathematics. The study was conducted across four students, and replicated simultaneously across four more. The CRA approach included concrete aids such as fraction circles and fraction strips, representations such as pictures of fraction circles and polygons, and algorithms. Explicit teaching involved following a model-lead-test sequence and included an advanced organizer, corrective feedback and cumulative reviews. Results of this study indicated that the intervention program was effective to improve students‟ performances in fraction equivalence tasks. In particular, the use of vii representations was seen to impact performance and concrete aids alone may not be sufficient to improve performance. With regards types of representational and concrete aids employed, results of this study tended to favor the use of linear versus circular aids. Results indicated that students whose performances tend to vary may not benefit to the same extent as those who have stable profiles. Students who demonstrate variable profiles may require additional practice to master skills being taught. This study also examined transfer of skills to word problems and, results demonstrated that the CRA and explicit teaching approaches were beneficial in helping aiding transfer. Several aspects of the program may have contributed to aiding transfer including, minimal exposure to word problems during intervention, drawing connections between representations and abstract information, and incorporating the fair sharing understanding or quotient interpretation of fractions. This program concluded that students were able to maintain performances over time, and that representations in particular appeared to aid conceptual understanding and promote maintenance of skills.