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IES Grant

Title: An Efficacy Study of Interleaved Mathematics Practice
Center: NCER Year: 2016
Principal Investigator: Rohrer, Douglas Awardee: University of South Florida
Program: Cognition and Student Learning      [Program Details]
Award Period: 4 years (8/1/2016-7/31/2020) Award Amount: $1,521,294
Type: Efficacy and Replication Award Number: R305A160263

Co-Principal Investigator: Dedrick, Robert

Purpose: This project assessed the efficacy and feasibility of a mathematics learning intervention known as interleaved practice. In a typical mathematics practice assignment, students see a group of problems that can be solved by the same strategy (e.g., 10 parabola problems), and this format allows students to use nearly the same strategy for every problem. With interleaved practice, different kinds of practice problems are arranged so that no two consecutive problems can be solved by the same strategy (e.g., a problem about the median followed by a problem about the mean). This approach forces students to choose an appropriate strategy for each problem on the basis of the problem itself, just as they must do when they solve problems on cumulative exams and high stakes tests. In simplest terms, interleaved practice provides students with an opportunity to practice what they need to know. Interleaved practice can be implemented in any mathematics course, and it can be used at home or in the classroom, with or without computers.

Project Activities: The main study took place in 54 grade 7 mathematics classes in Florida public schools. By random assignment, each class received either mostly interleaved practice (intervention) or little interleaved practice (business-as-usual control). The two groups saw the same practice problems; only their order was manipulated. Students completed the assignments periodically over a period of four months before completing a review assignment, followed one month later by an unannounced final test.

Key Outcomes: The increased dose of interleaving sharply boosted scores on the unannounced test, 61 percent vs. 38 percent, d = 0.83 (Rohrer, Dedrick, Hartwig, & Cheung, 2020).

Structured Abstract

Setting: Data were collected in public middle schools in a suburban area of Florida.

Sample: The main study included 787 students from 54 classes taught by 14 teachers at 5 schools in a single school district. The student sample was 53 percent female, and 26 percent received free or reduced lunch. The school district reported that the sample was 64 percent White, 8 percent Black, 4 percent Asian, and 5 percent Other. The school district reported that 19 percent of the sample were Hispanic.

Intervention: The intervention group periodically completed practice assignments during a period of about 4 months. Most of the practice problems were arranged so that no two consecutive problems related to the same concept. Problems were drawn from basic algebra (e.g., simplification of algebraic expressions, solving of inequalities). All problems were aligned with the Common Core State Standards for grade 7 mathematics.

Research Design and Methods: The study was a cluster randomized controlled trial, with students nested within classes. The researchers randomly assigned each of 54 grade 7 math classes to either the intervention group or the business-as-usual control group. Students completed all practice problems and tests during class. All students completed practice assignments, a review, and a delayed final test.

Control Condition: The control condition was identical to the intervention with one exception: most of the practice problems were arranged so that problems of the same kind (e.g., simplifying an algebraic expression) were grouped together. The intervention and control conditions saw the same practice problems; only the scheduling varied.

Key Measures: The outcome measure was students' score on the researcher-created final test. The primary fidelity measure was based on students' completion and self-correction of the practice problems. The school district provided researchers with students' scores on a high-stakes mathematics test given in the prior school year (grade 6).

Data Analytic Strategy: Data were analyzed using a two-level model, with students nested within classrooms and schools as a fixed effect.

Related IES Projects: A Systematic Replication Study of Interleaved Mathematics Practice (R305R220012), Interleaved Mathematics Practice (R305A110517), Harnessing Retrieval Practice to Enhance Learning in Diverse Domains (R305B070537), Optimizing Resistance to Forgetting (R305H040108), Optimizing Resistance to Forgetting (R305H020061)

Publications and Products

ERIC Citations: Find available citations in ERIC for this award here.

Publicly Available Data: The dataset for the efficacy trial is available on the Open Science Framework as entry pfeg4as. Other available datasets include the following:
Emeny et al. (2021)
Hartwig et al. (2022)
Rohrer et al. (2020):

WWC Review:  Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C. N. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112, 40–52. [WWC Review]

Select Publications:

Journal articles

Emeny, W. G., Hartwig, M. K., & Rohrer, D. (2021). Spaced mathematics practice improves test scores and reduces overconfidence. Applied Cognitive Psychology, 35, 1082–1089.

Hartwig, M. K & Malain, E. D. (2022). Do students space their course study? Those who do earn higher grades. Learning and Instruction, 77, 101538.

Hartwig, M. K., Rohrer, D., & Dedrick, R. F. (2022). Scheduling math practice: Students' underappreciation of spacing and interleaving. Journal of Experimental Psychology: Applied. 8(1), 100–113.

Rohrer, D., Dedrick, R. F., & Hartwig, M. K. (2020). The scarcity of interleaved practice in mathematics textbooks. Educational Psychology Review, 32, 873–883.

Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C. N. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112, 40–52.

Rohrer, D., & Hartwig, M. K. (2020). Unanswered questions about spaced and interleaved mathematics practice. Journal of Applied Research in Memory and Cognition, 9, 433–438.