Introduction
One product of cognitive science research are principles of learning - teaching and study strategies that have been shown to enhance learning in a range of settings and ages in both classroom and lab tests. One such principle is interleaved practice, which involves mixing problems of different types during study rather than blocking them by category, and distributing problems of the same type over time. Interleaved practice has been found to improve both discrimination learning and long-term retention and a recent cluster randomized trial indicated substantial learning gains for interleaved practice over blocked practice in middle school mathematics (Rohrer et al. 2020). Still, interleaved practice remains relatively uncommon in mainstream mathematics curricula (Rohrer et al. 2020).
In the present study (ongoing), we are testing the efficacy of interleaved practice relative to blocked practice in a large, cluster randomized study. The study is designed to both replicate and extend the study conducted by Rohrer and colleagues (2020). Specifically, like Rohrer et al, the present study tests the efficacy of interleaving in middle school mathematics classrooms, randomly assigning classrooms within teachers to either an interleaved or blocked control group. However, unlike Rohrer et al, the study expands the sample beyond a single district and state to multiple districts and states in a U.S. nationally representative sample. The study also expands the intervention from a half year to a full year and implements interleaved practice on a digital platform - ASSISTments - which increases the intervention’s ability to be implemented at scale in authentic contexts.
Learning principles like interleaving are typically framed as straightforward strategies, but the implementation of such strategies can be challenging as they require many contextual decisions that are not directly informed by past research (e.g., how many items are optimal within an interleaved assignment? Can students work in pairs? etc.). To instantiate the intervention in the present work we engaged in a structured design process guided by a logic model. The logic model is a structured description of the intervention informed by existing research, theory, and practical constraints of the use context, that can be revised and iterated upon in formative tests. Table 1 displays this working model.
Table 1. Logic Model of Interleaved Practice in the present study The logic model of interleaved practice includes intervention components informed by prior research, materials and implementation features that define fidelity, and their connection to the interleaving intervention that this study is designed to replicate. | |||
Intervention Component | Study Materials | Instantiation in Practice | Relation to past efficacy study |
Interleaving problems of different types within assignments to support discrimination learning | Assignments created in ASSISTments that each consist of grade level appropriate problems that are interleaved | Students complete assignments that contain topics they’ve had prior instruction. | Core feature, held constant |
Students attempt each problem independently, writing out the corresponding solution steps | Core feature, held constant | ||
Students complete problems in ASSISTments | Design feature, varied | ||
Students complete assignments in class | Design feature, held constant | ||
Revision of incorrect solutions after each assignment to support comprehension | Visual tool for showing problems and corresponding solutions, such as a whiteboard or screen | Teachers discuss problems with solutions available visually | Core feature, held constant |
Students instructed to correct both their work and answers | Core feature, held constant | ||
Teachers collect and verify students corrected their errors | Design feature, varied | ||
Spaced practice of problems of same type to support long-term retention | Ordered assignments that consist of problems of the same type spaced across the assignments | Assignments are completed in the order of the study procedure, which are distributed over time so that long-term retention benefits from the spacing effect | Core feature, held constant |
One value of this logic model-based approach for replication is that it makes explicit the relationship between implementation features that are considered “core” to the intervention and therefore held constant between this and the prior study, and design features that are not theoretically critical and that can therefore differ from past work to best align with the context. Early formative testing identified several design features that were varied to maximize feasibility and fidelity for this sample and context. This logic model-based approach to learning design shares many similarities to other learning engineering approaches such as the Nested Learning Engineering cycle (e.g., Craig et al, 2025) that involve understanding the problem in context, developing, testing, and revising the working solution.
This work reports on preliminary results of the ongoing study. The present sample (representing two of three planned cohorts) includes 813 sixth and seventh grade students across 51 classes, 29 teachers, 15 schools, and 8 districts. Random assignment occurred at the classroom level, with classes blocked within teachers. The post-assessment, developed collaboratively with the original efficacy study author, consisted of 12 isomorphic items to those in the review assignments, administered four weeks after the final intervention to measure robust learning. Hierarchical linear models accounting for students nested within classes revealed that students receiving interleaved practice (M = 0.09, SD = 1.03) outperformed blocked practice students (M = -0.08, SD = 0.96) on the delayed post-assessment, but this difference was just shy of statistical significance at p < .05, F(1, 41.81) = 3.75, p = .05, Hedges' g = 0.18. This work shows promise for the potential of interleaving to be effectively applied in authentic education contexts at a broad scale.
This research is funded by the U.S. Dept of Education through grant R305R220012 to WestEd and does not reflect the views of the Dept. I thank the many WestEd colleagues, University collaborators, education professionals and students who have supported this work.
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