Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…

This study explored the extent to which domain-specific knowledge predicted proportional word problem-solving performance. We tested 411 seventh-grade students on conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge, and proportional word problem solving. Multiple regression analyses indicated that all four…

This study examined the effect of schema-based instruction (SBI) on 7th-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…

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…

Background: During the middle school years, students frequently show significant declines in motivation toward school in general and mathematics in particular. One way in which researchers have sought to spark students' interests and build their sense of competence in mathematics and in STEM more generally is through the use of technology. Yet…

The concept of "implementation fidelity" is broadly used to capture the extent to which an intervention is executed as intended by the designers of the intervention (Century, Rudnick, & Freeman, 2010; Huntley, 2005, McNaught, Tarr, & Sears, 2010, Munter, 2010). Though implementation fidelity instruments are often used to assess…

This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents. The SBI program emphasized the underlying mathematical structure of problems via schematic diagrams, focused on a…

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing…

Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh- and eighth-grade students learned to solve equations (a)…