Explore the vast range of titles available.

In most mathematics textbooks, each set of practice problems is comprised almost entirely of problems corresponding to the immediately previous lesson. By contrast, in a small number of textbooks, the practice problems are systematically shuffled so that each practice set includes a variety of problems drawn from many previous lessons. The standard and shuffled formats differ in two critical ways, and each was the focus of an experiment reported here. In Experiment 1, college students learned to solve one kind of problem, and subsequent practice problems were either massed in a single session (as in the standard format) or spaced across multiple sessions (as in the shuffled format). When tested 1 week later, performance was much greater after spaced practice. In Experiment 2, students first learned to solve multiple types of problems, and practice problems were either blocked by type (as in the standard format) or randomly mixed (as in the shuffled format). When tested 1 week later, performance was vastly superior after mixed practice. Thus, the results of both experiments favored the shuffled format over the standard format.

Bargh et al. (2001) reported two experiments in which people were exposed to words related to achievement (e.g., strive, attain) or to neutral words, and then performed a demanding cognitive task. Performance on the task was enhanced after exposure to the achievement related words. Bargh and colleagues concluded that better performance was due to the achievement words having activated a \"high-performance goal\". Because the paper has been cited well over 1100 times, an attempt to replicate its findings would seem warranted. Two direct replication attempts were performed. Results from the first experiment (n = 98) found no effect of priming, and the means were in the opposite direction from those reported by Bargh and colleagues. The second experiment followed up on the observation by Bargh et al. (2001) that high-performance-goal priming was enhanced by a 5-minute delay between priming and test. Adding such a delay, we still found no evidence for high-performance-goal priming (n = 66). These failures to replicate, along with other recent results, suggest that the literature on goal priming requires some skeptical scrutiny.

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.

Every day, students and instructors are faced with the decision of when to study information. The timing of study, and how it affects memory retention, has been explored for many years in research on human learning. This research has shown that performance on final tests of learning is improved if multiple study sessions are separated—i.e., \"spaced\" apart—in time rather than massed in immediate succession. In this article, we review research findings of the types of learning that benefit from spaced study, demonstrations of these benefits in educational settings, and recent research on the time intervals during which spaced study should occur in order to maximize memory retention. We conclude with a list of recommendations on how spacing might be incorporated into everyday instruction.

Because people forget much of what they learn, students could benefit from learning strategies that yield long-lasting knowledge. Yet surprisingly little is known about how long-term retention is most efficiently achieved. Here we examine how retention is affected by two variables: the duration of a study session and the temporal distribution of study time across multiple sessions. Our results suggest that a single session devoted to the study of some material should continue long enough to ensure that mastery is achieved but that immediate further study of the same material is an inefficient use of time. Our data also show that the benefit of distributing a fixed amount of study time across two study sessions--the spacing effect--depends jointly on the interval between study sessions and the interval between study and test. We discuss the practical implications of both findings, especially in regard to mathematics learning.

Two highly effective math learning strategies are spaced practice (in which problems of the same kind are distributed across many sessions) and interleaved practice (in which problems of different kinds are mixed rather than blocked). Though these strategies are supported by data, students may be reluctant to use them if they perceive the strategies as ineffective or unpleasant. In Study 1, we surveyed 174 grade 7 math students about the efficacy and likability of spaced and interleaved practice. Spaced practice was often judged likable, but nearly half of students failed to recognize its efficacy. Interleaved practice was judged both unlikable and inefficacious by most students. In Study 2, we further explored perceptions of interleaving in a survey of 233 grade 7 math students. Again, students erroneously judged interleaved practice to have low efficacy. Compared to blocked practice, interleaved practice was judged less effective, less preferable, more time-consuming, and more difficult. This work identifies perceptions that may discourage students from using effective learning strategies and also shows that specific perceptions differ by strategy. Helping students overcome their negative perceptions of spacing and interleaving is an important future direction.

In many academic courses, students encounter a particular fact or concept many times over a period of a few weeks and then do not see it again during the remainder of the course. Are these brief instructional periods sufficient, or should the same amount of instruction be distributed over longer periods of time? This question was the focus of several recent studies in which a fixed amount of instruction was distributed over time periods of varying duration and followed by a delayed posttest. With few exceptions, the results showed that longer instructional periods produced greater posttest scores if the posttest was delayed by at least a month or so. Notably, the search criteria for this review excluded several oft-cited studies favoring short foreign language courses over longer ones, but a closer look at these studies reveals limitations (e.g., no delayed posttest or confounding variables). In brief, the best reading of the data is that long-term learning is best achieved when the exposures to a concept are distributed over time periods that are longer rather than shorter.

Our research on learning enhancement has been focusing on the consequences for learning and forgetting of some of the more obvious and concrete choices that arise in instruction, including questions such as these: How does spacing of practice affect retention of information over significant retention intervals (up to 1 year)? Do spacing effects generalize beyond recall of verbal materials? Is feedback needed to promote learning, and must it be immediate? Although retrieval practice has been found to enhance learning in comparison with additional study, does it actually reduce the rate of forgetting? Can retrieval practice effects be extended to nonverbal materials? We suggest that as we begin to find answers to these questions, it should become possible for cognitive psychology to offer nonobvious advice that can be applied in a variety of instructional contexts to facilitate learning and reduce forgetting.

There has been a recent upsurge of interest in exploring how choices of methods and timing of instruction affect the rate and persistence of learning. The authors review three lines of experimentation—all conducted using educationally relevant materials and time intervals—that call into question important aspects of common instructional practices. First, research reveals that testing, although typically used merely as an assessment device, directly potentiates learning and does so more effectively than other modes of study. Second, recent analysis of the temporal dynamics of learning show that learning is most durable when study time is distributed over much greater periods of time than is customary in educational settings. Third, the interleaving of different types of practice problems (which is quite rare in math and science texts) markedly improves learning. The authors conclude by discussing the frequently observed dissociation between people's perceptions of which learning procedures are most effective and which procedures actually promote durable learning.

When students encounter a set of concepts (or terms or principles) that are similar in some way, they often confuse one with another. For instance, they might mistake one word for another word with a similar spelling (e.g., allusion instead of illusion) or choose the wrong strategy for a mathematics problem because it resembles a different kind of problem. By one proposition explored in this review, these kinds of errors occur more frequently when all exposures to one of the concepts are grouped together. For instance, in most middle school science texts, the questions in each assignment are devoted to the same concept, and this blocking of exposures ensures that students need not learn to distinguish between two similar concepts. In an alternative approach described in this review, exposures to each concept are interleaved with exposures to other concepts, so that a question on one concept is followed by a question on a different concept. In a number of experiments that have compared interleaving and blocking, interleaving produced better scores on final tests of learning. The evidence is limited, though, and ecologically valid studies are needed. Still, a prudent reading of the data suggests that at least a portion of the exposures should be interleaved.