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This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students’ proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem-solving and metacognitive strategy instruction, and focuses on the flexible use of multiple solution strategies. Eighty-two teachers/classrooms, with a total of 1,999 7th-grade students across 50 school districts, were randomly assigned to a treatment (SBI) or control (business-as-usual) condition. An observational measure provided evidence that the SBI intervention was implemented with fidelity. Results of multilevel modeling indicated that the SBI group scored, on average, significantly higher than the control group on the posttest and retention test (9 weeks later) and also showed significantly more growth in proportional problem solving. There were no treatment effects on the Process and Applications subtest of the Group Mathematics Assessment and Diagnostic Evaluation. These results demonstrate that SBI can be more effective than the control approach in improving students’ proportional problem solving.

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Bistrategic resource control entails using both coercive and prosocial strategies in competition for resources. The present study sought to clarify whether bistrategic involves more than simply using both strategies some of the time. Examining 88 preschoolers' coercion and prosociality over an entire school year, results showed that coercive resource control was used most frequently at the start of the school year, presumably to access resources and establish social dominance. Rates of prosocial resource control increased over the school year, and socially dominant preschoolers showed higher rates compared with peers, presumably to maintain resource control while keeping peers as allies. Socially dominant preschoolers also used reconciliation more often than peers, resulting in higher rates of affiliation between former competitors and more positive peer regard from fall to spring. Findings are discussed in terms of resource control theory and the importance of situating social behaviors within the behavioral and relationship context in which they are embedded.

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...

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This longitudinal, naturalistic study addressed behavioral and social cognitive processes implicated in preschool children's social dominance. In the first objective, we examined the degree to which peer aggression, affiliation, and postaggression reconciliation predicted social dominance across a school year. Consistent with predictions, all three predicted dominance early in the year while only affiliation predicted dominance later in the year, suggesting that aggression, affiliation, and reconciliation were used to establish social dominance where affiliation was used to maintain it. In the second, exploratory, objective we tested the relative importance of social dominance and reconciliation (the Machiavellian and Vygotskian intelligence hypotheses, respectively) in predicting theory of mind/false belief. Results indicated that social dominance accounted for significant variance, beyond that related to reconciliation and affiliation, in predicting theory of mind/false belief status. Results are discussed in terms of specific behavioral and social cognitive processes employed in establishing and maintaining social dominance.

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest ( g = 0.40) and again 6 weeks later ( g = 0.42). The interaction between treatment group and students’ difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students’ performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas.