Improving student learning of ratio, proportion, and percent: A replication study of schema-based instruction.

Abstract

The purpose of this replication study was to provide replication evidence not currently available of the effects of a research-based mathematics program, schema-based instruction, on the mathematical problem-solving performance of 7th-grade students. The replication was implemented in 36 schools in 5 districts; 59 mathematics teachers and their students (N ϭ 1,492) participated in the study. Multilevel hierarchical linear analyses revealed statistically significant differences between conditions on proximal and distal measures of mathematics problem solving, with effects sizes similar to those reported in Jitendra et al. (2015). Educational Impact and Implications StatementThe present study provides support for classroom practices linked to an educational program (schema-based instruction [SBI]) that is designed to improve middle school students' understanding of solving problems involving proportional relationships, which is critical for mastering the higherlevel mathematics students encounter later. The results of a large study of SBI's impact showed that students generally benefitted from SBI although there were differences favoring White students versus Black, Hispanic, and multiracial students, whereas Asian students outperformed White students. The latter results highlight the need to identify ways to eliminate differences among racial subgroups to ensure all students have the opportunity to benefit from SBI.

Using Regression Discontinuity to Estimate the Effects of a Tier-1 Research-Based Mathematics Program in Seventh Grade

“…A review of research on proportional reasoning for middle school students that included comprehensive coverage of topics (e.g., ratios and proportions, scale drawings, percent, and percent of change) found only a few randomized controlled Tier-1 studies (Jitendra, Harwell, Dupuis, Karl, Lein, Simonson, & Slater, 2015; Jitendra, Harwell, Im, Karl, & Slater, 2018; Jitendra, Harwell, Karl, Simonson, & Slater, 2017; Jitendra, Star, Dupuis, & Rodriguez, 2013; Jitendra, Star, Rodriguez, Lindell, & Someki, 2011). These studies were conducted in one upper Midwest state (Jitendra et al, 2011, 2013, 2015) and two states in the Southeastern and Western regions of the United States (Jitendra et al, 2018; Jitendra, Harwell, Karl, et al, 2017) and tested the efficacy of SBI, an instructional program designed to help seventh-grade students make sense of their reasoning related to proportions in word problem contexts. SBI is an instructional approach that has its roots in schema theory and research on expert problem solvers and is guided by cognitive models of mathematical problem solving (see Marshall, 1995; Mayer, 1999).…”

“…Subsequent studies of SBI improved the research design by increasing the sample size to include more classrooms ( j = 42 in Jitendra et al, 2013; j = 82 in Jitendra et al, 2015; j = 59 in Jitendra et al, 2018) across more schools ( k = 6 in Jitendra et al, 2013; k = 58 in Jitendra et al, 2015; k = 36 in Jitendra et al, 2018), reducing the direct involvement of the research staff in SBI implementation (Jitendra et al, 2013, 2015, 2018; Jitendra, Harwell, Karl, et al, 2017), and randomly assigning teachers to SBI or control and then randomly selecting one of their classrooms to participate in the study (i.e., Jitendra et al, 2015, 2018; Jitendra, Harwell, Karl, et al, 2017), meaning that each teacher taught in a SBI or control classroom but not both. The two recent studies of SBI (Jitendra et al, 2018; Jitendra, Harwell, Karl, et al, 2017) used similar conditions, materials, and methods in different geographic locations and schools more demographically diverse than in Jitendra et al (2015), which involved a rigorous replication of earlier studies of SBI and included a sample of students ( N = 1,981) larger than samples ( N s = 436 and 1,163) in Jitendra et al (2011, 2013).…”

“…In the recent replication study (Jitendra et al, 2018), which is an extension of the rigorous large-scale, randomized controlled efficacy study conducted by Jitendra et al (2015), the authors examined whether the impact of SBI would replicate in different geographical regions of the country and schools more demographically diverse than in Jitendra et al (2015). Results revealed statistically significant differences between conditions on proximal (effect sizes of 0.47 and 0.29 on the PPS posttest and delayed posttest) and distal measures (effect size of 0.31 on the GMADE) of mathematics problem solving, with effect sizes for proximal measures similar to those reported in Jitendra et al (2015).…”

Teaching Rate of Change and Problem Solving to High School Students With High Incidence Disabilities at Tier 3

“…There is a continued need for research on mathematics concepts that are foundational for success for learning higher-level mathematics, particularly for students with high incidence disabilities (Marita & Hord, 2017; Watt et al, 2016). For example, a growing evidence base has examined the effects of interventions on students’ proportional reasoning and problem solving using Schema-Based Instruction (SBI), a strategy to help students recognize and utilize underlying problem structures, paired with a metacognitive strategy to guide students in the problem-solving process (Jitendra, Harwell, Im, & Karl, 2019). However, research on SBI has not yet been extended to concepts of ROC, in particular in the context of linear equations on a coordinate plane.…”

“…However, research on SBI has not yet been extended to concepts of ROC, in particular in the context of linear equations on a coordinate plane. While there is a research base on interventions specifically targeting students’ understanding of proportional reasoning, a concept closely related to ROC (see Jitendra, Harwell, Dupuis, & Karl, 2017; Jitendra et al, 2019), no published studies to date have investigated ROC with students with disabilities (based on the authors’ thorough search of the literature).…”