Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

Abstract

This study examined the effect of schema-based instruction (SBI) on seventh-grade students' mathematical problem solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention-posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a six-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students' regular mathematics instruction.KEYWORDS: word problem solving, ratio, proportion, and percent, middle school students, schema-based instruction SCHEMA-BASED INSTRUCTION 3 Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students' Proportional Reasoning: A Randomized ExperimentReform efforts in U.S. mathematic education are motivated by the need to raise the mathematics performance of students. Although the mathematical achievement of U.S. students in relation to national standards and international comparisons has shown signs of improvement over the years, there is concern that a large proportion of U.S. middle-and higher-grade students are not performing at adequate levels (National Mathematics Advisory Panel, [NMAP], 2008).On the 2009 National Assessment of Education Progress mathematics, for example, only 32% and 12% of Grade 8 and Grade 12 students, respectively, performed at or above the "proficient" level in mathematics (National Center for Education Statistics, 2009). These findings have translated into the need for more remedial mathematics education courses for incoming students at U.S. colleges (NMAP, 2008).One explanation for this lackluster performance is students' difficulties with proportional reasoning (Fujimura, 2001;Lobato, Ellis, Charles, & Zbiek, 2010). Mathematics researchers agree that proportional thinking (reasoning with ratios, rates, and percentages) is critical to understanding advanced mathematics; it provides the bridge between the numerical, concrete mathematics of arithmetic and symbolic algebra (e.g., Fuson & Abrahamson, 2005;Lamon, 2007;Lesh, Post, & Behr, 1988). The centrality of proportional reasoning is emphasized in the Common Core State Mathematics Standards (2010), where "developing understanding of and applying proportional relationships" in Grade 7 is one of four critical areas of focused instructional time. Furthermore, proportionality is closely associated with real-world applications and for understanding many problems in science, and technology (Karplus, Pulos, & Stage, 1983;Lo & Watanabe, 1997; Tourniare & Pul...

A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

“…Additional controversy arose related to the use of universal heuristics. One study criticized Pólya's (2014) universal heuristics for being too broad when in relation with middle school mathematics word problems (Jitendra et al, 2013). However, another study used Pólya's (2014) heuristic and found that students using the method produced higher posttest scores than the contrast group (Koichu et al, 2007).…”

“…Several studies focused on acronym-related stepby-step methods such as DISC, SOLVED, and Solve it!. These studies concentrated on and the effectiveness of these methods within the mathematics classroom (Barak, 2013;Hohn & Frey, 2002;Jitendra et al, 2013;Schaefer Whitby, 2012). These studies are of particular interest because this routine procedure is essential to the implementation of SBI.…”

“…Universal heuristics, such as Pólya's, are just as controversial. While Koichu et al (2007) employs Pólya's method, Jitendra et al (2013) criticizes its use in tandem with SBI because it is too broad (p. 10; p. 117). Future research is necessary to determine whether or not problem-solving heuristics should be implemented.…”

“…The research of Jitendra, Star, Dupuis, and Rodriguez (2013) suggest positive results when SBI was tested in connection with students' word problemsolving skills (p. 131). This four-step instructional mathematics strategy is designed to help students solve word problems by (1) priming the mathematical structure of problems, (2) utilizing visual-spatial representations as mathematical tools, (3) explicitly instructing through problem-solving heuristics, and (4) employing procedural flexibility (Jitendra, Star, Dupuis, & Rodriguez, 2013, p. 115-117).…”

“…This four-step instructional mathematics strategy is designed to help students solve word problems by (1) priming the mathematical structure of problems, (2) utilizing visual-spatial representations as mathematical tools, (3) explicitly instructing through problem-solving heuristics, and (4) employing procedural flexibility (Jitendra, Star, Dupuis, & Rodriguez, 2013, p. 115-117). Jitendra et al (2013) define priming the mathematical structure as schema training that separates relevant structural features from irrelevant and surface information (p. 115-116). Visual-spatial representations encompass both pictorial and schematic illustrations which include some kind of written or drawn construction of an individual's ideas (Jitendra et al, 2013, p. 116;van Garderen, Scheuermann, & Jackson, 2012, p. 145).…”