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The Use of Traditional Algorithmic Versus Instruction with Multiple Representations: Impact on Pre-Algebra Students' Achievement with Fractions, Decimals, and Percent

Han, Sunyoung (Sungkyunkwan University)
Flores, Raymond (Texas Tech University)
Inan, Fethi A. (Texas Tech University)
Koontz, Esther (Horace Mann Dual Language Magnet School)

Publication Information

School Mathematics / v.18, no.2, 2016 , pp. 257-275 More about this Journal

Abstract

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

Keywords

multiple representation; traditional algorithmic instruction; mathematical error; fraction; decimal; percent;

Citations & Related Records

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