Space It, Mix It: Spaced Practice and Interleaving for Learning
The following is an excerpt of the journal article “Teaching the science of learning,” written by Yana Weinstein, Christopher R. Madan and Megan A. Sumeracki and published in Cognitive Research: Principles and Implications. It has been licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. This excerpt includes sections on spaced practice and interleaving. Text and links have been reproduced as they are in the original article, although some graphics have been added.
Spaced practice
The benefits of spaced (or distributed) practice to learning are arguably one of the strongest contributions that cognitive psychology has made to education (Kang, 2016). The effect is simple: the same amount of repeated studying of the same information spaced out over time will lead to greater retention of that information in the long run, compared with repeated studying of the same information for the same amount of time in one study session. The benefits of distributed practice were first empirically demonstrated in the 19th century. As part of his extensive investigation into his own memory, Ebbinghaus (1885/1913) found that when he spaced out repetitions across 3 days, he could almost halve the number of repetitions necessary to relearn a series of 12 syllables in one day (Chapter 8). He thus concluded that “a suitable distribution of [repetitions] over a space of time is decidedly more advantageous than the massing of them at a single time” (Section 34). For those who want to read more about Ebbinghaus’s contribution to memory research, Roediger (1985) provides an excellent summary.
Since then, hundreds of studies have examined spacing effects both in the laboratory and in the classroom (Kang, 2016). Spaced practice appears to be particularly useful at large retention intervals: in the meta-analysis by Cepeda, Pashler, Vul, Wixted, and Rohrer (2006), all studies with a retention interval longer than a month showed a clear benefit of distributed practice. The “new theory of disuse” (Bjork & Bjork, 1992) provides a helpful mechanistic explanation for the benefits of spacing to learning. This theory posits that memories have both retrieval strength and storage strength. Whereas retrieval strength is thought to measure the ease with which a memory can be recalled at a given moment, storage strength (which cannot be measured directly) represents the extent to which a memory is truly embedded in the mind. When studying is taking place, both retrieval strength and storage strength receive a boost. However, the extent to which storage strength is boosted depends upon retrieval strength, and the relationship is negative: the greater the current retrieval strength, the smaller the gains in storage strength. Thus, the information learned through “cramming” will be rapidly forgotten due to high retrieval strength and low storage strength (Bjork & Bjork, 2011), whereas spacing out learning increases storage strength by allowing retrieval strength to wane before restudy.
Teachers can introduce spacing to their students in two broad ways. One involves creating opportunities to revisit information throughout the semester, or even in future semesters. This does involve some up-front planning, and can be difficult to achieve, given time constraints and the need to cover a set curriculum. However, spacing can be achieved with no great costs if teachers set aside a few minutes per class to review information from previous lessons. The second method involves putting the onus to space on the students themselves. Of course, this would work best with older students — high school and above. Because spacing requires advance planning, it is crucial that the teacher helps students plan their studying. For example, teachers could suggest that students schedule study sessions on days that alternate with the days on which a particular class meets (e.g., schedule review sessions for Tuesday and Thursday when the class meets Monday and Wednesday; see Fig. 1 for a more complete weekly spaced practice schedule). It important to note that the spacing effect refers to information that is repeated multiple times, rather than the idea of studying different material in one long session versus spaced out in small study sessions over time. However, for teachers and particularly for students planning a study schedule, the subtle difference between the two situations (spacing out restudy opportunities, versus spacing out studying of different information over time) may be lost. Future research should address the effects of spacing out studying of different information over time, whether the same considerations apply in this situation as compared to spacing out restudy opportunities, and how important it is for teachers and students to understand the difference between these two types of spaced practice.
It is important to note that students may feel less confident when they space their learning (Bjork, 1999) than when they cram. This is because spaced learning is harder — but it is this “desirable difficulty” that helps learning in the long term (Bjork, 1994). Students tend to cram for exams rather than space out their learning. One explanation for this is that cramming does “work”, if the goal is only to pass an exam. In order to change students’ minds about how they schedule their studying, it might be important to emphasize the value of retaining information beyond a final exam in one course.
Ideas for how to apply spaced practice in teaching have appeared in numerous teacher blogs (e.g., Fawcett, 2013; Kraft, 2015; Picciotto, 2009). In England in particular, as of 2013, high-school students need to be able to remember content from up to 3 years back on cumulative exams (General Certificate of Secondary Education (GCSE) and A-level exams; see CIFE, 2012). A-levels in particular determine what subject students study in university and which programs they are accepted into, and thus shape the path of their academic career. A common approach for dealing with these exams has been to include a “revision” (i.e., studying or cramming) period of a few weeks leading up to the high-stakes cumulative exams. Now, teachers who follow cognitive psychology are advocating a shift of priorities to spacing learning over time across the 3 years, rather than teaching a topic once and then intensely reviewing it weeks before the exam (Cox, 2016a; Wood, 2017). For example, some teachers have suggested using homework assignments as an opportunity for spaced practice by giving students homework on previous topics (Rose, 2014). However, questions remain, such as whether spaced practice can ever be effective enough to completely alleviate the need or utility of a cramming period (Cox, 2016b), and how one can possibly figure out the optimal lag for spacing (Benney, 2016; Firth, 2016).
There has been considerable research on the question of optimal lag, and much of it is quite complex; two sessions neither too close together (i.e., cramming) nor too far apart are ideal for retention. In a large-scale study, Cepeda, Vul, Rohrer, Wixted, and Pashler (2008) examined the effects of the gap between study sessions and the interval between study and test across long periods, and found that the optimal gap between study sessions was contingent on the retention interval. Thus, it is not clear how teachers can apply the complex findings on lag to their own classrooms.
A useful avenue of research would be to simplify the research paradigms that are used to study optimal lag, with the goal of creating a flexible, spaced-practice framework that teachers could apply and tailor to their own teaching needs. For example, an Excel macro spreadsheet was recently produced to help teachers plan for lagged lessons (Weinstein-Jones & Weinstein, 2017; see Weinstein & Weinstein-Jones (2017) for a description of the algorithm used in the spreadsheet), and has been used by teachers to plan their lessons (Penfound, 2017). However, one teacher who found this tool helpful also wondered whether the more sophisticated plan was any better than his own method of manually selecting poorly understood material from previous classes for later review (Lovell, 2017). This direction is being actively explored within personalized online learning environments (Kornell & Finn, 2016; Lindsey, Shroyer, Pashler, & Mozer, 2014), but teachers in physical classrooms might need less technologically-driven solutions to teach cohorts of students.
It seems teachers would greatly appreciate a set of guidelines for how to implement spacing in the curriculum in the most effective, but also the most efficient manner. While the cognitive field has made great advances in terms of understanding the mechanisms behind spacing, what teachers need more of are concrete evidence-based tools and guidelines for direct implementation in the classroom. These could include more sophisticated and experimentally tested versions of the software described above (Weinstein-Jones & Weinstein, 2017), or adaptable templates of spaced curricula. Moreover, researchers need to evaluate the effectiveness of these tools in a real classroom environment, over a semester or academic year, in order to give pedagogically relevant evidence-based recommendations to teachers.
Interleaving
Another scheduling technique that has been shown to increase learning is interleaving. Interleaving occurs when different ideas or problem types are tackled in a sequence, as opposed to the more common method of attempting multiple versions of the same problem in a given study session (known as blocking). Interleaving as a principle can be applied in many different ways. One such way involves interleaving different types of problems during learning, which is particularly applicable to subjects such as math and physics (see Fig. 2a for an example with fractions, based on a study by Patel, Liu, & Koedinger, 2016). For example, in a study with college students, Rohrer and Taylor (2007) found that shuffling math problems that involved calculating the volume of different shapes resulted in better test performance 1 week later than when students answered multiple problems about the same type of shape in a row. This pattern of results has also been replicated with younger students, for example 7th grade students learning to solve graph and slope problems (Rohrer, Dedrick, & Stershic, 2015). The proposed explanation for the benefit of interleaving is that switching between different problem types allows students to acquire the ability to choose the right method for solving different types of problems rather than learning only the method itself, and not when to apply it.
Do the benefits of interleaving extend beyond problem solving? The answer appears to be yes. Interleaving can be helpful in other situations that require discrimination, such as inductive learning. Kornell and Bjork (2008) examined the effects of interleaving in a task that might be pertinent to a student of the history of art: the ability to match paintings to their respective painters. Students who studied different painters’ paintings interleaved at study were more successful on a later identification test than were participants who studied the paintings blocked by painter. Birnbaum, Kornell, Bjork, and Bjork (2013) proposed the discriminative-contrast hypothesis to explain that interleaving enhances learning by allowing the comparison between exemplars of different categories. They found support for this hypothesis in a set of experiments with bird categorization: participants benefited from interleaving and also from spacing, but not when the spacing interrupted side-by-side comparisons of birds from different categories.
Another type of interleaving involves the interleaving of study and test opportunities. This type of interleaving has been applied, once again, to problem solving, whereby students alternate between attempting a problem and viewing a worked example (Trafton & Reiser, 1993); this pattern appears to be superior to answering a string of problems in a row, at least with respect to the amount of time it takes to achieve mastery of a procedure (Corbett, Reed, Hoffmann, MacLaren, & Wagner, 2010). The benefits of interleaving study and test opportunities — rather than blocking study followed by attempting to answer problems or questions — might arise due to a process known as “test-potentiated learning”. That is, a study opportunity that immediately follows a retrieval attempt may be more fruitful than when that same studying was not preceded by retrieval (Arnold & McDermott, 2013).
For problem-based subjects, the interleaving technique is straightforward: simply mix questions on homework and quizzes with previous materials (which takes care of spacing as well); for languages, mix vocabulary themes rather than blocking by theme (Thomson & Mehring, 2016). But interleaving as an educational strategy ought to be presented to teachers with some caveats. Research has focused on interleaving material that is somewhat related (e.g., solving different mathematical equations, Rohrer et al., 2015), whereas students sometimes ask whether they should interleave material from different subjects — a practice that has not received empirical support (Hausman & Kornell, 2014). When advising students how to study independently, teachers should thus proceed with caution. Since it is easy for younger students to confuse this type of unhelpful interleaving with the more helpful interleaving of related information, it may be best for teachers of younger grades to create opportunities for interleaving in homework and quiz assignments rather than putting the onus on the students themselves to make use of the technique. Technology can be very helpful here, with apps such as Quizlet, Memrise, Anki, Synap, Quiz Champ, and many others (see also “Learning Scientists”, 2017) that not only allow instructor-created quizzes to be taken by students, but also provide built-in interleaving algorithms so that the burden does not fall on the teacher or the student to carefully plan which items are interleaved when.
An important point to consider is that in educational practice, the distinction between spacing and interleaving can be difficult to delineate. The gap between the scientific and classroom definitions of interleaving is demonstrated by teachers’ own writings about this technique. When they write about interleaving, teachers often extend the term to connote a curriculum that involves returning to topics multiple times throughout the year (e.g., Kirby, 2014; see “Learning Scientists” (2016a) for a collection of similar blog posts by several other teachers). The “interleaving” of topics throughout the curriculum produces an effect that is more akin to what cognitive psychologists call “spacing” (see Fig. 2b for a visual representation of the difference between interleaving and spacing). However, cognitive psychologists have not examined the effects of structuring the curriculum in this way, and open questions remain: does repeatedly circling back to previous topics throughout the semester interrupt the learning of new information? What are some effective techniques for interleaving old and new information within one class? And how does one determine the balance between old and new information?
