Study Reviews: Instructional Practices in Middle School Math

Not all education research is equal—the What Works Clearinghouse (WWC) identifies high-quality studies and meaningful findings to inform educator decisions and improve student outcomes. This week, the WWC highlights three new study reviews of instructional practices for teaching middle school math, adding to the evidence from more than 11,000 citations about what works in education. The studies examined the effects of three instructional practices designed to help middle school students improve their problem-solving, algebra, and mathematical reasoning skills: Schema-based instruction, a set of lessons designed to help students solve problems by asking them to identify the structure of the problem, represent information in the problem visually, estimate the answer to the problem, plan how to solve it, solve the problem, and determine if their answer makes sense Interleaved practice that includes concepts from current and past lessons and requires multiple strategies learned at different points in the curriculum Worked examples, correctly or incorrectly solved math problems that show students how someone else solved the problems Study One: Jitendra et al. (2019) study of schema-based instruction In this IES-funded study, students received 21 daily lessons using schema-based instruction over 6 weeks during their regularly scheduled math classes. The lessons focused on proportional relationships, including ratios, rates, and percentages.  Study design: Jitendra and colleagues (2019) randomly assigned classrooms or schools to receive either schema-based instruction or typical math instruction for 6 weeks. Fifty-nine seventh-grade math classrooms in 36 middle schools across five districts in two states participated in the study. Of the 1,411 students included in the study, 56% identified as White, 26% identified as Hispanic, 8% identified as Black, and 5% identified as Asian. About one-quarter of students were eligible for free or reduced-price lunch. Study findings: Compared with students who received typical math instruction, students who received schema-based instruction performed higher on a standardized math problem-solving test. They also demonstrated better problem-solving skills on an assessment developed by the study authors.   WWC study rating: This study meets WWC standards without reservations. Access the full study review here, in the WWC’s review of individual studies database. Effectiveness tier: The study meets Department of Education standards for Strong Evidence (Tier 1) because the study has favorable, statistically significant findings, meets WWC standards, and satisfies other criteria. See the video titled Using the WWC to Identify ESSA Evidence Ratings to learn more about these criteria. Study Two: Rohrer et al. (2015) study of interleaved practice In this IES-funded study, students completed 10 interleaved or blocked practice assignments over 88 days, followed by a review session 5 days later. The assignments included graphing problems, where students were asked to graph a line, or slope problems, where students were asked to find the slope of a line between two points, as well as additional problems on other math topics. For the interleaved practice assignments, the problems were spread out over the assignments. For the blocked practice assignments, all problems were included in a single assignment. Study design: Rohrer and colleagues (2015) randomly assigned classrooms to use either interleaved or blocked practice assignments on graphing and slope problems. Nine seventh-grade math classrooms with 63 students taught by three teachers in a public middle school in Tampa, Florida, participated in the study. The classes included only students who passed the Florida state assessment in sixth grade, and two of the classes were classified as honors/gifted by the school. For the graphing problems, four classrooms with 30 students used interleaved practice assignments and five classrooms with 33 students used blocked practice assignments. For the slope problems, the five classrooms used interleaved practice assignments and the four classrooms used blocked practice assignments. Forty-seven percent of the students identified as White, 22% identified as Hispanic or Latino, 14% identified as Black, 10% identified as Asian, Approximately one-third of students were eligible for free or reduced-price lunch. Study findings: Compared with students who completed the blocked practice assignments, students who completed the interleaved practice assignments demonstrated stronger algebra skills on graphing and slope problems on two assessments developed by the study authors. WWC study rating: This study meets WWC standards without reservations. Access the full study review here, in the WWC’s review of individual studies database. Effectiveness tier: The study meets Department of Education standards for Promising Evidence (Tier 3) because the study has favorable, statistically significant findings and meets WWC standards but has a small sample size. See the video titled Using the WWC to Identify ESSA Evidence Ratings to learn more about these criteria. Study Three: Hallinen & Booth (2018) study of worked examples In this IES-funded study, teachers gave students worked examples of arithmetic problems. Students were given worked examples of arithmetic problems on 69 assignments and asked to explain why the worked examples were correct or incorrect, and then solve a similar problem on their own. Study design: Hallinen and Booth (2018) conducted a random assignment study that compared student use of worked examples of arithmetic problems with students who did not receive worked examples and solved the same problems on their own. The study  included 527 fifth-grade students from 32 classrooms in midwestern states. WWC study rating: This study does not meet WWC standards because it does not establish the reliability of the researcher-developed assessment used to measure the effectiveness of the worked examples. The reliability is one indicator that the assessment produces scores that are trustworthy. Access the full study review here, in the WWC’s review of individual studies database. Effectiveness tier: The study does not qualify for an evidence tier because it does not meet WWC standards.