Title: An Efficacy Study of Interleaved Mathematics Practice

Psychology in the Schools, 2000

High school students in remedial mathematics classes were exposed to three pairs of mathematics computation assignments. Three of the assignments served as control assignments and contained 15 target problems (i.e., three-digit by two-digit multiplication problems). Students were also exposed to three paired experimental assignments that contained either 15 (0% more), 18 (20% more), or 21 (40% more) equivalent target problems. Each experimental assignment was also lengthened by interspersing additional one-digit by one-digit problems following every third target problem. After exposure to each pair of assignments, students reported which of the two assignments (control or experimental) would require the most time and effort to finish, which was most difficult, and which assignment they would prefer to do for homework. Across all three assignment pairs, significantly more students rated the experimental assignment more favorably for time, effort, and difficulty and chose the experimental assignment for homework. These results extend previous research on interspersing additional brief tasks by showing that this procedure has sufficient strength to get students to prefer homework assignments with 20% and 40% more target problems.

Journal of Behavioral Education, 2005

Explicit timing and interspersal interventions were investigated using a withinsubjects design with 45 third-grade students. A control assignment consisted of subtraction of a two digit number from a two digit number (i.e., target problem) and served as a baseline. An explicit timing assignment consisted of similar problems as those for the control assignment. The interspersal assignment consisted of similar problems as those for the control and explicit timing assignments with the addition of subtraction of a one digit number from a one digit number interspersed following every third target problem. Total problem completion rates, target problem completion rates, accuracy on target problems and students' rating regarding difficulty, time, effort, and preference between assignments for class work were collected. Student preference choices were analyzed for fit with the discrete task completion hypothesis. Three trials were administered. Results indicated that: (a) students completed more total problems during interspersal, (b) target problem completion rates were higher during explicit timing, (c) accuracy rates remained constant, (d) students rated the explicit timing assignment as requiring more time and being more difficult for all trials and as requiring more effort for trial 2 and 3, (e) students selected the interspersal assignment to do in class as compared to the explicit timing assignment for all trials, and (f) the data fit the discrete task completion hypothesis relatively well for all trials. Discussion

Cognitive Science, 2017

Typical mathematics instruction involves blocked practice across a set of conceptually similar problems. Interleaving, or practice across a set of conceptually dissimilar problems, improves learning and transfer by repeatedly reloading information and increasing discrimination of problem features. Similarly, comparing problems across different contexts highlights relevant and irrelevant knowledge. Our experiment is the first to investigate the relative effects of interleaving geometry problems and interleaving contexts. Thirty-three fourth-grade students received the same practice problems but were randomly assigned to one of three conditions: interleaved by math skill, interleaved by context, and interleaved by math skill and by context (i.e., hyperinterleaved). Afterward, each participant was exposed to tests assessing declarative and procedural knowledge. The results suggest that interleaving math skill within varying contexts enhances the acquisition of mathematical procedures.

The purpose of this study was to replicate and extend research on task intersper-sal. The authors investigated whether changes in on-task behavior of two middle school students were functionally related to changes in the relative percentages of easy and difficult items on math worksheets. They found that the participants remained on task longer while completing worksheets with 33 and 67% interspersed easy problems than while completing worksheets without the interspersed easy problems. Participants' accuracy in answering the target problems was not affected, however, by the interspersal procedure. The authors concluded that interspersing easy items on independent math seatwork assignments can increase on-task behavior. Academic demands in both general and special education settings require task engagement from learners. During arithmetic classes, in particular, when students learn basic algorithms, they need to remain on task long enough to grasp the skill being taught and to practice it independently. Once students become fluent in performing a skill, their levels of achievement will decrease over time unless they receive opportunities to practice the skill at regular intervals. If students do not remain on task during this independent practice, they could forfeit their chances of maintaining sufficient skill fluency to be able to take more advanced math courses. The importance of participation in those courses is increasing as

2021

How does interleaving the mathematics curriculum while promoting productive struggle, improve student understanding in and between mathematical concepts? To clarify, I mean to say that 'understanding' is more about knowing 'why' and knowing 'when' to apply specific concepts and strategies, and not just knowing 'what' the mathematical concepts are. Interleaving is a multilayered approach, varying the curriculum to allow students to discriminate between strategies they already know and apply them to new information. It is a way of deepening their understanding, allowing them to productively struggle (Warshauer, 2015), think critically and problem solve to come to their own conclusions. Research shows there is benefit to interleaving practice and intermixing different kinds of practice problems and spacing out the same types of problems across different assignments (Rohrer, Dedrick & Stershic, 2014; Rohrer, Dedrick & Burgess, 2014). Spaced practice interrupts forgetting (Brown et al., 2014). This allows for the creation of a variety of mental models of information and transforms it from short term memory into long term memory and allows for better recall. Experiencing different conditions and circumstances to create our information model broadens mastery, fosters conceptual learning, improves versatility and primes the mind for learning (Brown et al., 2014).

Journal of Behavioral Education, 1996

Journal of Behavioral Education, 2007

Educational Psychology Review, 2020

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems-a format known as interleaved practice. Interleaving prevents students from safely assuming that each practice problem relates to the same skill or concept as the previous problem, thus forcing them to choose an appropriate strategy on the basis of the problem itself. Yet despite the efficacy of interleaved practice, blocked practice predominates most mathematics textbooks. As an illustration, we examined 13,505 practice problems in six representative mathematics texts and found that only 9.7% of the problems were interleaved. This translates to only one or two interleaved problems per school day. In brief, strong evidence suggests that students benefit from heavy doses of interleaved practice, yet most mathematics texts provide scarcely any.

Journal of Experimental Education, 1999