Using Interleaving to Promote Inductive Learning in Educational Contexts
Promises and Challenges
Abstract
Abstract. Inductive learning, that is, abstracting conceptual knowledge, rules, or principles from exemplars, plays a major role in educational settings, from literacy acquisition to mathematics and science learning. Interleaving exemplars of different categories rather than presenting blocks might be a simple but powerful way to improve inductive learning by supporting discriminative contrast. Although a consistent advantage of interleaving has been demonstrated for visual materials, relatively few studies have examined educationally relevant materials, such as mathematical tasks, science problems, and verbal materials, and their results are mixed. We discuss how interleaving could be made fruitful for school learning of mathematics, science, and literacy acquisition. We conclude that interleaving should be tailored to the specific learning content and combined with supportive instructional measures that assist students in comparing exemplars for discriminating features. Finally, we sketch research gaps that revolve around the use of interleaved learning in the classroom.
Zusammenfassung. Induktives Lernen, d. h. die Abstraktion von konzeptuellem Wissen, Regeln oder Prinzipien aus Beispielen, ist zentral für das schulische Lernen– vom Schriftspracherwerb bis hin zur Mathematik und den Naturwissenschaften. Das Verschachteln von Beispielen verschiedener Kategorien ist verglichen mit einer geblockten Präsentation eine wirkungsvolle Methode zur Optimierung induktiver Lernprozesse, indem es Vergleichsprozesse zwischen den Beispielen evoziert. Empirisch hat sich konsistent ein Vorteil des verschachtelten Lernens für visuelle Materialien gezeigt, es gibt allerdings nur wenige und uneinheitliche Befunde zur Wirksamkeit des Verschachtelns schulisch relevanter Materialien. Wir gehen der Frage nach, wie verschachteltes Lernen im unterrichtlichen Kontext – beispielhaft anhand der Domänen Mathematik, Naturwissenschaften und dem Schriftspracherwerb – nutzbar gemacht werden kann. Neben der Wahl geeigneter Inhalte scheint die Implementation weiterer instruktionaler Maßnahmen, mit denen Schülerinnen und Schüler beim Vergleichen unterstützt werden, dessen Wirksamkeit zu begünstigen. Abschließend werden Forschungslücken skizziert, die im Hinblick auf die Nutzung des verschachtelten Lernens im Unterricht bestehen.
Students encounter different content in a certain sequence when learning. Much research in instructional psychology and subject didactics has addressed how topics should be arranged when learning to optimize the learning process. For example, one core element of adaptive instruction is creating individualized content sequences tailored to the individual learner’s needs and abilities (e. g., Skinner, 1986). If we approach the issue from a different perspective, we learn that direct instruction embraces the principle that teachers should present subtopics in a factually based and logically structured sequence (Huitt et al., 2009). Similarly, a major issue in subject-matter education is arranging the topics specified in curricula to enhance learning. The merits of these approaches notwithstanding, they usually focus on the arrangement of learning content on a macrolevel, telling us little about how learning content should be arranged in inductive learning settings on a microlevel, for example, different tasks, procedures, or subskills.
Inductive learning refers to abstracting and consolidating conceptual knowledge (e. g., generic facts, rules, principles, or categories) from studying exemplars. It is a major form of human learning in many formal and informal learning settings, from babies learning new words to doctors learning to interpret X-rays (Kornell & Bjork, 2008). Inductive learning also plays a vital role in school learning, although the term is seldom addressed explicitly in educational-psychology textbooks. When students practice solving math problems (e. g., Rohrer & Taylor, 2007), when they derive scientific principles from a set of observations (e. g., Prince & Felder, 2007), when they practice reading to grasp a grapheme-phoneme correspondence rule (e. g., Müller et al., 2020), or when they work through examples to understand a grammatical rule in learning a foreign language (e. g., DeKeyser, 1995), they perform inductive learning. In most classroom applications, inductive learning is not used in its pure form but is combined with deductive elements. Thus, introducing the rule or concept to be learned first in a more or less explicit and comprehensive fashion before students practice it using examples is commonplace. Herron and Tomasello (1992) coined the term “guided induction” for this procedure, where the inductive phase may not be misunderstood as a mere application and consolidation of the concept taught in the beginning. Instead, the bulk of learning takes place in the inductive learning phase, which also takes up most of the class time.
The question is then how to design inductive learning settings at school to make them most effective, in particular for lasting learning. One possible and simple way to improve inductive learning might be to change the sequence in which exemplars are presented. Research suggests that interleaving exemplars from different categories (e. g., A – B – C – A – C – A – C – B – C) might support the acquisition of the underlying concepts under certain circumstances compared to “blocking” the same exemplars (e. g., A – A – A – B – B – B – C – C – C), that is, presenting all items of one category or concept before presenting those of another category or concept (e. g., Kang & Pashler, 2012; Kornell & Bjork, 2008; Rohrer & Taylor, 2007).
This article discusses the principle of interleaved learning, focusing on its suitability for school-based learning. We start by reviewing theories to explain why and when interleaving is effective for learning and discuss empirical studies that shed light on this approach to learning. Based on the discussion of existing theoretical and empirical work, we propose that, to unfold its full potential for school-based learning, interleaving should be tailored to the specific learning content and combined with supportive instructional measures that assist students in cognitive processes conducive to inductive learning. We substantiate and illustrate this proposition by sketching possible interleaving applications in three central school learning areas: mathematics, science, and literacy acquisition. The discussion of these applications reveals open questions that revolve around interleaved learning in the classroom which deserve increased research efforts in psychology and the educational sciences.
When and Why Is Interleaving Effective for Learning?
Kornell and Bjork (2008) popularized interleaved learning and showed that students learned the painting styles of various impressionistic painters considerably better when presented with different painters’ works interleaved rather than blocked (interleaving effect), although the participants in the experiment reported that they learned better in the blocked compared to the interleaved condition. Accordingly, interleaving is a desirable difficulty that makes learning subjectively more difficult while objectively improving learning outcomes (Bjork & Bjork, 2011). The effect has been replicated with the original materials (e. g., Metcalfe & Xu, 2016; Kang & Pashler, 2012), and other experiments have demonstrated interleaving effects with mathematical tasks, photographs, pictures of artificial objects, and physics problems (e. g., Birnbaum et al., 2013; Rohrer & Taylor, 2007; Samani & Pan, 2021Wahlheim et al., 2011). Still, other studies with various materials reported no interleaving effect (e. g., Carpenter & Mueller, 2013; Sorensen & Woltz, 2016). Brunmair and Richter (2019) conducted a meta-analysis of all published studies (cut-off date June 2018) and found a medium-sized positive overall effect of interleaved learning (Hedges’ g = 0.42). However, they also found substantial heterogeneity of effect sizes between studies, suggesting that the advantage of interleaving over blocking occurs in only some learning situations, depending on certain conditions.
Theoretical accounts of interleaved learning provide the key to better understanding the divergent results. The extant theories explain the potential benefits of interleaving by assuming that the interleaved presentation facilitates the detection of differences between exemplars. The discriminative-contrast hypothesis (Kang & Pashler, 2012) posits that presenting exemplars from different categories in temporal proximity facilitates discriminative contrasts, which augments category learning. Discriminative contrasts refer to comparisons directed at distinguishing features of exemplars, such as features of paintings that distinguish the styles of different painters in the experiments by Kang and Pashler (2012). Evidence for the hypothesis comes from experiments showing that temporal spacing between items hinders inductive learning in an interleaved presentation but not in a blocked presentation. The sequential attention theory (Carvalho & Goldstone, 2017; also called the attentional bias framework, Carvalho & Goldstone, 2015) adopts the idea of discrimination as the mechanism of interleaved learning and additionally specifies the conditions that render discriminative contrasts effective. According to this theory, an interleaved presentation of exemplars facilitates the detection of differences, whereas a blocked presentation facilitates the detection of similarities. Thus, the effect of interleaving emerges when the to-be-learned categories are difficult to discriminate. In contrast, the acquisition of clearly distinguishable categories, which are defined more by similarities of category members, works well – or even better – with a blocked presentation of exemplars. Carvalho and Goldstone (2017) provided evidence for these assumptions in experiments in which participants learned to distinguish between species of aliens by looking at sequentially presented pictures. An interleaved presentation directed the attentional focus to features discriminating between species and to a better encoding of such features. In contrast, a blocked study led to better encoding of features common to one category (for a presentation and discussion of further evidence, see also Carvalho & Goldstone, 2014, 2015).
In their meta-analysis, Brunmair and Richter (2019) found support for the basic predictions of the sequential theory of attention. In a metaregression, a positive effect emerged for the similarity of exemplars between categories and a negative effect of the similarity of exemplars within categories on the size of the interleaving effect. The second finding of particular importance was that the type of learning material moderated the effects. The positive interleaving effect was strongest (Hedges’ g = 0.67) for visual materials, such as naturalistic paintings (such as those used by Kornell & Bjork, 2008; or Kang & Pashler, 2012) and pictures of artificial objects (g = 0.36) typically used as stimuli in category learning experiments (e. g., Carvalho & Goldstone, 2014). In comparison, the interleaving effect was still positive but smaller for mathematical tasks (g = 0.34), not significantly different from zero when texts were used as learning materials, and even negative when words were used as learning materials (g = –0.39).
These findings suggest that, for learning materials typically used in inductive learning in school contexts, interleaving might not be sufficient to induce the comparison processes that enable learners to successfully discriminate between different concepts. Possible causes lie in the higher complexity and dependence on prior knowledge that characterize such learning materials. These features are likely to make comparison processes not only more cognitively demanding but also give them the character of cognitive learning strategies that students may not be expected to apply routinely, either because they lack the relevant declarative or procedural knowledge, or because they lack the relevant conditional knowledge of when the strategies are useful (Schneider et al., 2022). With instructional interventions that specifically support students in using comparison strategies tailored to the students’ abilities, the learning materials, and the learning objectives, interleaving could exhibit its full potential for school learning. In the following sections, we elaborate on these assumptions for inductive learning in three areas: mathematics, the natural sciences, and literacy acquisition.
The Potential Benefits of Interleaved Learning in Mathematics
A central goal of mathematics instructions is to enable students to switch flexibly between different solution methods, strategies, or formulas, and thus to choose an appropriate solution approach leading to faster and more accurate problem-solving (Baroody & Dowker, 2003; Heinze et al., 2009). Therefore, learners need to know not only about different strategies (declarative knowledge) and how to use them (procedural knowledge) but also when and why to use which strategy for which type of task (conditional knowledge; Paris et al., 1983). Choosing appropriate methods for solving mathematical tasks is often very challenging for students, especially when the tasks are superficially similar (Rohrer et al., 2015). For example, subtraction tasks, such as 514 – 199 and 342 – 338, are superficially similar but differ in the most appropriate solution method. Adding one to both integers is more efficient for the first task (i. e., 515 – 200), and subtracting by adding (i. e., 338 + _ = 342) is more efficient for the second task. When solving algebra problems, such as x + 2x – 1, students also must choose a useful strategy (e. g., factoring, quadrating, adding; Rohrer et al., 2015). In such situations, interleaved learning can be an appropriate instructional strategy.
Studies on Interleaving inMathematics Learning
When introducing new solution methods, strategies, or formulas for a specific mathematical topic, teachers usually teach them and their application conditions in a blocked fashion (Rohrer et al., 2020). Thus, students often practice different solution methods separately from each other. However, students need to learn to recognize and discriminate the differences between superficially similar mathematical tasks to match the problems to an appropriate strategy.
Interleaving mathematical tasks should directly evoke these discrimination processes (Birnbaum et al., 2013) and help students to abstract rules and principles about when to use which strategy for which kind of task. However, the meta-analysis by Brunmair and Richter (2019) revealed only a small effect of interleaving mathematical tasks, with primary studies ranging from strongly negative to positive effects. Still, several studies have shown the advantage of interleaving over blocking mathematical tasks for different topics such as graph and slope problems (Rohrer et al., 2015), equations and terms (Rohrer, Dedrick et al., 2020), algebraic addition and multiplication (Ziegler & Stern, 2014, 2016), surface and volume calculations of solids (Rohrer & Taylor, 2007), and subtraction strategies (Nemeth et al., 2019, 2021).
How to Implement Interleaving in Mathematics Learning
Some studies on interleaving mathematical tasks present the mathematical tasks in an interleaved fashion but also implement further instructional guidance, such as explicit prompts to contrast and compare or to self-explain – or they present the tasks simultaneously instead of successively (e. g., Nemeth et al., 2019, 2021; Ziegler & Stern, 2014, 2016). These studies observed longer-lasting effects up to ten weeks of interleaving mathematical tasks, whereas studies investigating a pure form of interleaved practice in mathematics predominantly focused on shorter time intervals with a maximum of about 30 days (e. g., Rohrer et al., 2020). Therefore, additional instructional support might be necessary or at least helpful for lasting positive effects of interleaving in mathematics.
Providing indirect support for this assumption, Ziegler et al. (2018) compared the effectiveness of interleaving algebraic multiplication and addition problems in an implicit and explicit learning condition. In their study, interleaving mathematical tasks were more effective when different forms of additional instructional guidance (i. e., self-explanation prompts and comparison prompts) were included, and the effects persisted even after ten weeks. However, systematic research disentangling the effects of these different forms of instructional support on interleaving mathematical tasks is lacking. We discuss three types of instructional support, self-explanation prompts, comparison prompts, and simultaneous presentation as well as how they might be combined with interleaved learning to boost its effectiveness in mathematics learning.
Generating self-explanations is a learning technique that promotes deep processing and transfer (Chi et al., 1994). Several studies have shown positive effects when including prompts for self-explaining in mathematics (Rittle-Johnson et al., 2017). Chi (2000) proposed two main mechanisms explaining the positive impact of self-explaining: (1) Self-explaining promotes knowledge integration by either connecting different pieces of new information or integrating them into existing knowledge structures. (2) Self-explaining facilitates the recognition of central structural features, promoting knowledge transfer of the learned content. We presume that prompting students to self-explain why they use a specific solution method for a specific mathematical task can support students in abstracting rules and principles and in acquiring conditional knowledge about when and why specific solution methods should be used. Therefore, combining interleaved practice, which augments students’ ability to choose appropriate solution methods, with self-explanation might strengthen the interleaving effect.
Comparison processes are expected to be underlying learning mechanisms that explain the advantage of interleaved over blocked practice (Birnbaum et al., 2013; Carvalho & Goldstone, 2015, 2017). However, individuals often neglect to compare different categories unless explicitly prompted (Durkin et al., 2017). Previous research on learning by comparison has shown that supporting learners’ comparison processes with explicit comparison prompts results in higher learning gains than offering only opportunities to compare (e. g., Catrambone & Holyoak, 1989). Studies demonstrate that prompting students to compare different problem types or solution methods for solving mathematical tasks can promote their flexible strategy use (e. g., Rittle-Johnson & Star, 2007, 2009). Therefore, augmenting interleaved practice with explicit comparison prompts could support students when comparing and discriminating interleaved categories.
Most studies presented interleaved exemplars sequentially (Brunmair & Richter, 2019). According to the sequential attention theory, interleaved practice facilitates the identification of differences between categories (Carvalho & Goldstone, 2017). Research on comparison learning in mathematics has shown that a simultaneous presentation is often superior to a sequential presentation (Begolli & Richland, 2016; Rittle-Johnson & Star, 2007). Hence, we presume that detecting differences when presenting the interleaved examples or tasks simultaneously instead of sequentially makes comparisons easier for students because recalling previous tasks from working memory is not required to draw comparisons. However, whether simultaneous presentation can augment comparison processes is an open question. Previous research regarding the role of a simultaneous vs. sequential presentation in interleaved learning is inconsistent (Brunmair & Richter, 2019) and largely lacking in the domain of mathematics learning.
Interleaved Learning in theNatural Sciences
The natural sciences of physics, chemistry, and biology are typically regarded as important domains in education. Moreover, inductive learning plays a large role in science education (Prince & Felder, 2007). Despite this importance, the number of studies on interleaved learning in the science classroom is small. For example, a search in the PsycInfo database using the keywords “interleav*” and “physics” or “interleav*” and “chemistry” each yielded only one and “interleav*” and “biology” yielded no relevant hits (as of 9 November 2022). Given the scarcity of studies on interleaving in science learning, we focus our discussion on three exemplary studies and discuss them and their implications in the broader context of the meta-analysis by Brunmair and Richter (2019).
Studies on Interleaving in Science Learning
In a study by Sana and Yan (2022), 155 students in eight classrooms (physics, biology, chemistry, and integrated science) were taught for four weeks with different materials. At the end of each week, nine multiple-choice quiz tasks in the respective subject were administered blocked by concept (A1A2A3 B1B2B3 C1C2C3) or interleaved with different concepts (A1B1C1 A2B2C2 A3B3C3). One month after the final quiz, students were finally tested on the concepts covered in the four weeks. The results revealed that the scores on the interleaved quizzes were significantly lower than those on the blocked quizzes, albeit with a small effect size (Cohen’s d = 0.21). However, the interleaved-quiz condition led to significantly better final test performance than the blocked-quiz condition, with a small-to-medium effect size (d = 0.35). Despite the use of very different scientific content, the results by Sana and Yan (2022) correspond to findings showing that interleaving is initially less favorable than blocking in the short term but more effective for lasting learning (e. g., Ziegler & Stern, 2014). Accordingly, interleaved learning in this study would qualify as a desirable difficulty (Bjork & Bjork, 2011).
Another important study was conducted by Samani and Pan (2021) in introductory physics courses at the university level. These authors investigated the interleaving of physics problems that were given as homework to 576 students in 20 lectures over eight weeks. After each lecture, students received blocked and interleaved homework assignments to foster factual knowledge and problem-solving ability. In one condition, the problems were blocked with three practice problems each, for example, on the electric capacitor (1) with different filling materials (P1P2P3), (2) with different sizes (Q1Q2Q3), and (3) their stored energy (R1R2R3). In the second condition, the problems were interleaved, for example, P1Q1R1 M2N2O2 J3K3 L3. Two unannounced criterial tests examined content from the first ten and last ten lectures, respectively. Both tests showed a significant positive interleaving effect with medium-to-large effect sizes (d = 0.40 and d = 0.91). These results are remarkable in several respects: First, like the study by Sana and Yan (2022), students performed slightly worse in the interleaved assignments and found the interleaved homework assignments more difficult than the blocked assignments, which is in line with a classification of interleaved learning as a desirable difficulty. Second, the criterial tests were administered after four-week learning phases, implying that at least some of the questions referred to materials learned and practiced several weeks before, which underscores the potential of interleaving augmenting lasting learning. Third, the bandwidth of tested physics concepts is relatively large (20 lectures in electrodynamics, atomic, and quantum physics), suggesting that the effect generalizes across different content. Fourth, the physics problems used by Samani and Pan were relatively complex, meaning that the kind of inductive learning instigated by the homework assignments and the to-be-learned conceptual knowledge were quite different from the relatively simple tasks and concepts used, for example, in the category learning experiments based on visual materials.
A study by Eglington and Kang (2017) is a third instructive example of a study examining interleaved learning in science learning. The authors found advantages of interleaving over blocking in learning chemical compounds in three consecutive experiments with undergraduate students. In Experiment 1, simple chemical structural diagrams of five categories of hydrocarbons of similar structure (e. g., alcohol and alkynes) were presented as visual material. Unique visual critical features defined the categories (e. g., alcohols have an oxygen atom; alkynes have a carbon-carbon triple bond). In the posttest, students in the interleaving condition outperformed students in the blocked condition with a medium effect size (d = 0.61). In Experiment 2, the materials included four new, more complex chemical categories, leading to more irrelevant features than in the materials used in Experiment 1. This change of materials allowed manipulating within-category similarity. The benefit of interleaving persisted despite increasing the complexity of the chemical categories with a medium effect size (d = 0.61). However, no main effect of within-category similarity or interaction of similarity and presentation condition on test performance emerged. Experiment 3 used the same materials, but the critical features of each chemical category were highlighted in red. Similar to the previous results, participants in the interleaved condition outperformed those in the blocked condition, again with a medium effect size (d = 0.57). The advantage of interleaving over blocking found by Eglington and Kang fits the meta-analytical results reported by Brunmair and Richter (2019), who found a small-to-medium effect size for pictures of artificial objects. At first glance, this might seem surprising and at odds with the sequential theory of attention (Carvalho & Goldstone, 2014). That is, despite an increase in intracategory similarity, interleaving again had an advantage over blocking. However, as Eglington and Kang argued, this finding may be traced back to the specific manipulation of the within-category similarity (limited by the complexity of real-world chemical categories) that was not strong enough for an effect to emerge. The highlighting of distinctive features in Experiment 3 can be regarded as a kind of instructional support that helped students to focus on differentiating features between categories.
How to Implement Interleaving in the Science Classroom
Content taught in science classes is usually quite complex and requires prior knowledge to be properly understood, which indicates the need to support students in interleaving tasks. Moreover, learning in the natural sciences often includes categorizing materials based on visual or other features. The categorization of structural diagrams in Eglington and Kang’s (2017) study is a case in point. Further examples from physics and biology are the differentiation of states of matter (solid, liquid, or gas) or the categorization of animals or plants in biology. However, prototypical scientific knowledge is characterized by a complex interplay of observations, its generalization into laws, and the principle-based interpretation within theoretical frames (Chalmers, 1999; Lederman, 2007), with the overarching goal of fostering students’ scientific reasoning. For example, consider the movement of charge carriers in electric and magnetic fields. On the surface, the two categories are similar, for example, because of their vectorial character. Probably, this similarity is why students have difficulty discriminating between electric and magnetic fields (Maloney et al., 2001). However, the different motions of charge carriers in these two fields can be easily observed by students (e. g., by using simulations), which also makes the two categories of fields easily distinguishable. However, one key aspect of physics, even in physics education at school, is predicting the future behavior of objects based on a theoretical frame. Consequently, students’ acquisition of complex scientific concepts requires comprehending the underlying principles. To master this complexity, students must acquire adequate principle-based cognitive skills (Renkl, 2015). The underlying principles and laws of scientific concepts are often complex and thus difficult to learn.
How should interleaved learning in the science classroom accommodate the complexity of science concepts? Teachers might be prudent to teach these concepts, such as the motion of charge carriers in electric and magnetic fields, or the law of equilibrium of forces and Newton’s third law, in blocks. In the next step, contrasted comparisons of concepts can be triggered by the interleaved presentation of corresponding tasks. Following the sequential attention theory (Carvalho & Goldstone, 2017), students can first be supported in recognizing the commonalities within each category to acquire fundamental knowledge about the concepts (e. g., the law of equilibrium of forces and Newton’s third law) before the subsequent interleaved learning phase prompts students’ attention to the differences of the two concepts. Thus, difficulty increases as students’ proficiency increases (Nakata & Suzuki, 2019). This combination of blocking and subsequent interleaving might be fruitful (Kang, 2017). Further instructional guidance, such as comparison and self-explanation prompts and simultaneous instead of sequential presentation, may further support interleaved learning in science. Moreover, computer-based simulations of physical phenomena offer a straightforward way to point students toward crucial differences between exemplars. Similarly, phases of direct instruction that convey the relevant principles before they are deepened and consolidated by solving interleaved science problems may be useful. The studies by Samani and Pan (2021) and by Sana and Yan (2022) followed this principle, using quizzes or homework assignments that referred to previously learned content and combining interleaving with retrieval practice, which is a different desirable difficulty that benefits learning independently of interleaving (see Roelle et al., 2022). Hence, teaching scientific concepts requires the combination of various learning phases (Koedinger et al., 2012, 2013; Oser & Baeriswyl, 2001) to master complexity and secure the acquisition of adequate principle-based cognitive skills to achieve lasting learning.
Interleaved Learning WithVerbal Materials
Learning in school is often based on written verbal materials of varying complexity, from single words to texts of varying length. One central objective of elementary education is for children to learn how to read and write. This learning process involves extensive reading and writing practice, which is essentially inductive learning (in addition to routinization of reading and writing processes), or it contains strong inductive elements. Moreover, according to the sequential theory of attention, the learning materials may easily be designed to exhibit the conditions that make interleaving effective (Carvalho & Goldstone, 2015, 2017). Many learning tasks and verbal stimuli children encounter during literacy acquisition are characterized by high similarities between categories, which makes discriminative contrasts useful. This raises the question of whether interleaving is also useful for improving literacy acquisition.
Studies on Using Interleaving With Verbal Learning Materials
As noted above, the meta-analysis by Brunmair and Richter (2019) suggests that interleaving with verbal materials works poorly, with a medium-sized negative interleaving effect estimated for words as learning materials. However, scrutinizing the studies included in the meta-analysis reveals that this conclusion may be premature. First, the effect sizes for words as learning materials were based on only three studies. Second, the studies that yielded negative or null effects of interleaving were based on materials characterized by high within-category similarity and low between-category similarity – or inductive learning was not studied at all (only retention of information). For example, in the study by Carpenter and Mueller (2013), which yielded a clear advantage of blocking (g = –0.85 in Experiment 1), non-French speakers learned grapheme-phoneme correspondences in French. The words used as learning materials exemplified pronunciation rules for words ending with -eau, -er, -e, -eux, and -t. Thus, the graphemes and phonemes relevant to each pronunciation rule were clearly distinguishable but identical within each category, which should be ideal conditions for blocking to be effective. In sum, the available studies leave open the possibility that interleaving is beneficial for inductive learning when used with verbal materials.
How to Implement Interleaving inLiteracy Instruction
When children learn how to read and write in elementary school, the acquisition of the relevant skills invariably involves a large amount of reading and writing practice, which is essentially inductive learning and therefore a domain in which interleaved learning could be fruitfully applied. Numerous approaches to reading and spelling instruction exist in German and other alphabetic languages (Müller & Richter, 2017). Critical for literacy acquisition in such languages is a developmental phase in which children learn to decode words by applying grapheme-to-phoneme conversion rules (Ehri, 2005; Frith, 1986).
In line with this development, the most prevalent and most effective approach for teaching reading to beginning readers is phonics instruction, which focuses on systematically teaching and practicing grapheme-phoneme correspondence rules (for meta-analytic results, see Ehri et al., 2001; Galuschka et al., 2014). In German, didactic approaches for reading instruction exist that contain systematic, well-reasoned, and partly research-based guidelines on the order in which letters (and letter combinations) and the corresponding phonological structures should be introduced (e. g., see Dummer-Smoch & Hackethal, 2007). However, no systematic research and evidence-based guidelines exist on the best way to design the “microsequencing” of words practiced within units. This lack is precisely where interleaved learning, that is, interleaving words exemplifying different (but similar) grapheme-phoneme correspondence rules, could offer a distinct advantage over a blocked presentation, which is often implemented in practice materials.
However, many children may not spontaneously engage in comparisons and may thus profit from instructional support to carry out the processes of comparing and distinguishing between grapheme-phoneme correspondence rules, which should underly the effectiveness of interleaved learning (Birnbaum, 2013). Like in mathematics learning, comparison and self-explanation prompts seem to be an easy and straightforward way to foster such processes, especially for weaker readers. Comparison prompts can remind learners to look for distinguishing features between words, letters, or syllables, exemplifying different grapheme-phoneme correspondence rules. To our knowledge, comparison prompts have been applied and evaluated only in reading instruction for children with special needs (e. g., Bird et al., 2000). Nevertheless, there is good reason to assume they would also be effective in other groups of beginning readers. Self-explanation prompts are cognitively more demanding; they invite children to explain why a certain grapheme-phoneme correspondence rule applies to a written stimulus or groups of written stimuli (e. g., how self-explanations have been implemented in category learning, Edwards et al., 2019). With increasing skill level, these prompts could be adaptively abated during a learning session to facilitate the routinization of phonological recoding.
Similarly, spelling instruction could profit from an interleaved presentation of words during practice phases. Spelling and reading draw on the same cognitive resources, and the development of the associated abilities is closely intertwined (e. g., Frith, 1986; Houghton & Zorzi, 2003). Parallel to learning how to read, learning how to spell also starts with associations of phonemes and graphemes (phoneme-grapheme associations), but even for languages with a highly transparent orthography (e. g., German), not all words can be spelled correctly based on their phonology. Therefore, children need to learn spelling rules in addition to phoneme-grapheme associations; they need to understand that words are composed of morphemes that partly govern regularities of spelling; and they need to acquire representations of orthographic word forms through reading and writing practice (Treiman, 2018; Treiman & Kessler, 2014). Interleaved learning is a promising approach for improving the effectiveness and efficiency of the intensive spelling exercises that accompany this learning process on all levels of spelling development. Instead of repeatedly practicing a single phoneme-grapheme correspondence rule, for example, exercises could involve sequences of words that exemplify different but easy-to-confuse rules, such as words ending with -er and -a, which are difficult to distinguish phonologically in German. Likewise, easily-confused spelling rules could be practiced in an interleaved fashion. Again, comparison prompts and self-explanation prompts could be used to support the comparison processes that supposedly underlie the effectiveness of interleaving. To the best of our knowledge, no studies to date have systematically examined the use of interleaving or comparison and self-explanation prompts in spelling instruction.
Conclusion and Open Questions
This review and discussion of existing research underscores the potential of interleaving exemplars for school learning in subject areas as diverse as mathematics, science, and literacy instruction. Interleaving is an instructional measure that can be applied easily in all kinds of inductive learning settings in which students acquire conceptual knowledge by studying exemplars, case studies, single observations, or by working on tasks exemplifying general principles. Compared to blocked content presentation, interleaving incurs no extra costs on teachers or students, because it requires no additional learning time or materials. However, the discussion of existing studies also suggests that important research questions are still open. To date, the evidence supporting the efficacy of interleaved learning is strongest (but far from exhaustive) for mathematics learning, emerging (but still weak) for science learning, and almost nonexistent for learning with verbal materials. Therefore, at this point, interleaving should be applied in educational contexts with several caveats in mind.
First, an important limitation to note is that the benefits of interleaving seem to be confined to learning settings that involve an inductive element, or at least where the benefits of interleaving are limited to learning situations in which comparisons between tasks or examples are informative and consequently add value to learning. Learning is not enhanced when simply mixing unrelated topics (e. g., Hausman & Kornell, 2014).
Second, according to relevant theories of interleaving (Birnbaum et al., 2013; Carvalho & Goldstone, 2015, 2017), the effectiveness of interleaved learning is based on the execution of comparison processes between exemplars belonging to different categories or exemplifying different principles. Therefore, an interleaved presentation can only be expected to promote learning if between-category comparisons of exemplars are informative and contribute to abstracting conceptual knowledge. If categories are defined through commonalities of exemplars and concepts can be better understood by grasping such commonalities, a blocked presentation may be more effective.
Third, given the complex and demanding nature of learning content presented in educational contexts, students may not always be expected to perform the comparison processes necessary to abstract the underlying concepts (see also Richter et al., 2022). For example, Gentner’s structure mapping theory of analogical learning states that comparison processes required to learn a concept from studying exemplars vary in complexity (Gentner & Markman, 1997). If the underlying conceptual structure is based on surface features (such as a single feature or object present), as is the case in many studies on interleaved learning with visual stimuli (see Brunmair & Richter, 2019, for an overview), interleaving is likely to be effective without further instructional support. In contrast, if the underlying conceptual structure is based on commonalities in the relational structure of features, learners need to draw an analogy to learn the underlying concept. In that case, instructional support that guides students’ analogical reasoning may be necessary for the advantages of interleaving to emerge. Consider, for example, the similarities of the two arithmetic expressions 1:3 and 3:9 (see Gentner & Markman, 1997, p. 47). If the underlying concept was “Contains the number 3,” focusing on whether an expression contains the number 3 would be sufficient during inductive learning. In that case, interleaving expressions that contain the number 3 and those that do not contain the number 3 may be sufficient to foster inductive learning. However, if the underlying category is “The ratio 1:3,” students should receive instructional support that guides their attention to the relation of the two numbers. The same holds for other concepts characterized by their relational structure, including causal relations that are often constitutive of scientific concepts.
In sum, targeted instructional measures that facilitate comparisons and specific instructional measures, such as comparison or self-explanation prompts, seem promising to assist students in comparison processes with more complex concepts that require analogical reasoning. The acquisition of such concepts is characteristic for mathematics and science learning as well as learning from text. On a related note, the application of interleaving in science, abstracting concepts from exemplars, or solving problems often presupposes extensive prior knowledge, implying that instruction should be designed such that relevant prior knowledge is provided before inductive learning phases are implemented.
We emphasize that, to date, all recommendations of how to best implement interleaving in the classroom stand on shaky empirical grounds. Research on interleaving in educational contexts and with curriculum-based materials is scarce. Among other factors, the role of learner motivation in the effectiveness of interleaving is still largely unresolved – clearly a research gap that stands in the way of implementing interleaving in the classroom. Several studies have shown that learners judge blocking to be more effective than interleaving and would rather choose a blocked schedule when they have to decide between learning scenarios, although this judgment is at odds with their actual learning gains (e. g., Kornell & Bjork, 2008; McCabe, 2011; Yan et al., 2016, 2017). This metacognitive illusion of blocking being superior to interleaving is difficult to mend, even if learners are informed about the benefits of interleaved practice (Yan et al., 2016). Thus, the question arises of how students can be motivated to interleave their practice schedule when being informed about its effectiveness is insufficient. In contrast to these studies, Kornell and Vaughn (2018) showed that learners block as well as interleave categories when they can determine the order of the categories during the study phase by themselves. Lu et al. (2021) provided a deeper insight into the conditions under which learners are more likely to block or interleave in self-regulated learning. In their study, participants were allowed to choose the next exemplar to be presented during real-time studying. The results show that students studying high-similarity categories switch more often between categories than students learning low-similarity categories. These findings provide evidence that learners do not actually plan their practice schedule beforehand but flexibly adapt their schedule during learning depending on the similarity of the categories. However, it is unclear whether these findings generalize across learning situations, materials, and contexts. Still, it is plausible to assume that interleaving requires more cognitive effort, implying that interleaving categories in self-regulated learning can be positively influenced by motivating learners to invest this effort during learning.
With few exceptions in the areas of mathematics and science learning (e. g., Nemeth et al., 2019, 2021; Sana & Yan, 2022; Ziegler & Stern, 2014, 2016), the extant studies have not fully addressed the extent to which interleaving can be used to foster lasting learning (Richter et al., 2022). There are hints, though, that interleaving may qualify as a desirable difficulty (Bjork & Bjork, 2011) and may contribute to lasting knowledge that prepares students for future learning. Future research should address this issue by focusing on experimental classroom studies with assessments of both short-term and long-term outcomes.
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