Explanation recruits comparison in a category-learning task

Highlights

• Prompts to explain category membership boost discovery of broad classification rules.

• Explanation prompts increase self-reported comparison of labelled exemplars.

• The most beneficial comparison strategy is comparing groups of exemplars.

• Group comparison partially mediates the effect of explanation prompts on discovery.

Abstract

Generating explanations can be highly effective in promoting category learning; however, the underlying mechanisms are not fully understood. We propose that engaging in explanation can recruit comparison processes, and that this in turn contributes to the effectiveness of explanation in supporting category learning. Three experiments evaluated the interplay between explanation and various comparison strategies in learning artificial categories. In Experiment 1, as expected, prompting participants to explain items’ category membership led to (a) higher ratings of self-reported comparison processing and (b) increased likelihood of discovering a rule underlying category membership. Indeed, prompts to explain led to more self-reported comparison than did direct prompts to compare pairs of items. Experiment 2 showed that prompts to compare all members of a particular category (“group comparison”) were more effective in supporting rule learning than were pairwise comparison prompts. Experiment 3 found that group comparison (as assessed by self-report) partially mediated the relationship between explanation and category learning. These results suggest that one way in which explanation benefits category learning is by inviting comparisons in the service of identifying broad patterns.

Introduction

Explanation and comparison are pervasive in our everyday lives, and they often appear to operate in tandem. For example, asking someone to explain why children prefer chocolate to broccoli will prompt a comparison between chocolate and broccoli. Considering why-questions such as these motivates a search for understanding, and can invite a comparison between two alternatives, even if the alternatives are not explicitly stated (Chin-Parker & Bradner, 2017). For example, if asked “Why do flames burn upward?” one might mentally convert the question into “Why do flames burn upward (rather than downward)?” and consider relevant factors (such as that hot air rises). Indeed, comparison may be a valuable cognitive strategy for producing richer, more accurate, and more satisfying explanations.

Despite these intuitive links between explanation and comparison, researchers have typically studied explanation and comparison separately (for reviews, see Gentner, 2010, on analogy and comparison; Lombrozo, 2012, Lombrozo, 2016, on explanation). In this paper, we take steps towards a more integrated approach (see also Chin-Parker and Bradner, 2017, Hummel et al., 2008). Broadly, we strive to improve our understanding of why and how engaging in explanation and comparison can enhance learning, and especially how these processes might work together to do so. More specifically, our aim is to explore whether generating explanations in the context of a category-learning task (i.e., explaining why a labelled exemplar belongs to a particular category) encourages learners to engage in comparison. If so, what comparison strategies result, and how do these strategies affect subsequent learning?

We focus on category learning because of its importance in mental life, as reflected by the vast amount of psychological research in this area (e.g., Ashby and Maddox, 2005, Murphy, 2002, Smith and Medin, 1981). Prior research and theory also suggest potentially powerful relationships between explanation and comparison in this domain. For example, comparison is essential for discovering the similarities and differences within and between categories that can form the basis for an explanation of category membership. Additionally, as noted above, the search for an explanation often creates a specific implicit contrast (e.g., why is a tomato a fruit and not a vegetable?) (e.g., Chin-Parker & Bradner, 2017), leading people to engage in spontaneous comparison. We are especially interested in understanding how engaging in explanation might influence the specific comparison strategies people use when engaged in a category-learning task.

We begin by reviewing the respective literatures on how explanation and comparison support learning. We then present three experiments that address these central questions in the context of category learning. Finally, we consider whether and how our findings shed light on broader questions about the relationship between explanation and comparison.

For present purposes, we define explaining as the process of answering a why-question to achieve understanding of what is being explained.¹ Prior work shows that explaining, either to others (Roscoe and Chi, 2007, Roscoe and Chi, 2008) or to oneself (Chi, de Leeuw, Chiu, & LaVancher, 1994; for reviews, see Bisra et al., 2018, Fonseca and Chi, 2011), can substantially boost learning. This “self-explanation” effect has been demonstrated across a range of cognitive domains and experimental protocols. For example, generating self-explanations has been shown to improve students’ understanding of physics (Chi, Bassok, Lewis, Reimann, & Glaser, 1989), biology (Chi et al., 1994), and math (Aleven and Koedinger, 2002, McEldoon et al., 2013, Wong et al., 2002; for a review, see Rittle-Johnson, Loehr, & Durkin, 2017). These findings suggest a number of ways in which generating explanations might promote learning (for reviews, see Fonseca and Chi, 2011, Lombrozo, 2006, Lombrozo, 2012, Lombrozo, 2016).

One way in which explaining can support learning is by increasing metacognitive awareness. Metacognitive processes are essential for enabling people to identify deficiencies in their own knowledge. Explanation can help people detect (Rozenblit & Keil, 2002) and fill gaps in their knowledge (Chi, 2000), as well as resolve inconsistencies (Johnson-Laird, Girotto, & Legrenzi, 2004). Relatedly, the process of generating explanations can increase attention and cognitive engagement (e.g., Siegler, 2002), promoting deeper cognitive processing and improving learning outcomes.

Recent work additionally suggests that engaging in explanation can influence learning by leading people to selectively seek and extend some types of patterns, particularly those with broader scope (i.e., that apply to more cases; Walker et al., 2017, Williams and Lombrozo, 2010, Williams and Lombrozo, 2013) or that exhibit other “explanatory virtues” (Lombrozo, 2012, Lombrozo, 2016, Wilkenfeld and Lombrozo, 2015), such as simplicity (Walker, Bonawitz, & Lombrozo, 2017). As a result, explaining can promote abstraction (Walker & Lombrozo, 2017) and point to inductively rich, causal properties (Legare and Lombrozo, 2014, Walker et al., 2014). Williams and Lombrozo (2010) proposed and tested the “Subsumptive Constraints” account, which predicted that asking people to generate explanations would lead them to focus preferentially on broad patterns that can account for a greater proportion of the observed evidence. The experimental paradigm used in our studies is based on that developed in Williams and Lombrozo (2010), so we review their studies in some detail.

Across three experiments (Williams & Lombrozo, 2010), adults learned how to categorize robots labeled as Glorp robots or Drent robots. Of the eight study examples, six robots (75%) could be categorized by the 75% body-shape rule that Glorp robots have rectangular bodies and Drent robots have round bodies, but the other two robots were anomalous with respect to this rule (i.e., one Glorp robot had a round body and one Drent robot had a rectangular body). There was also a more subtle 100% foot rule that could perfectly categorize all eight robots. While each of the eight robots had a unique foot shape, all four Glorp robots had feet with pointy bottoms and all four Drent robots had feet with flat bottoms.

Compared to participants in a variety of control conditions, participants who were asked to explain why each robot belonged to its particular category were more likely to discover the 100% foot rule, but less likely than control participants to report discovering the 75% body-shape rule. These results suggest that engaging in explanation has fairly selective effects: it leads people to discover rules that account for all study examples; it does not simply increase the discovery rate of all possible categorization rules (Rehder, 2007, Williams and Lombrozo, 2013). However, it should be noted that favoring broad, exceptionless rules is not always beneficial, and explaining therefore has the potential to hinder learning. When the only way to achieve perfect classification is to memorize the idiosyncratic properties of individuals, seeking explanations can impair learning by encouraging learners to overgeneralize (i.e., disregard exceptions) or perseverate in seeking patterns (Williams, Lombrozo, & Rehder, 2013).

There is also evidence that engaging in explanation can affect learning by recruiting prior knowledge. People often attempt to integrate the phenomenon being explained with their prior beliefs (Chi et al., 1994, Kuhn and Katz, 2009, Lombrozo, 2006), and in so doing to accommodate it within a larger framework (Wellman & Liu, 2007). In particular, there is evidence that people often recruit prior knowledge when trying to explain and understand category structure (Murphy and Medin, 1985, Rips, 1989, Spalding and Murphy, 1996).

In a study of the effects of explanation and prior knowledge on category learning, Williams and Lombrozo (2013) presented adults with a similar set of robots that could be classified by two 100% rules, one based on foot shape and one based on the relative length of the antennae. One group of participants was asked to explain why each robot belonged to its particular category and the other group of participants engaged in free study. Within each group, participants were further divided based on whether the robots were given category labels that were uninformative (Glorp robots vs. Drent robots) versus informative (Indoor robots vs. Outdoor robots). The informative labels were intended to cue prior knowledge relevant to whether the antenna or foot rule was relevant to category membership. For example, robots suited for indoor versus outdoor environments might need different types of feet, while relative antenna length would be less relevant. For participants who were prompted to explain, those receiving the informative category labels were more likely to discover the more subtle foot rule than the antenna rule, while the opposite was true for those presented with the uninformative category labels. In contrast, the type of category label did not affect which rules participants in the free-study condition discovered.

Williams and Lombrozo (2013) argued that explanation invokes prior knowledge in the search for broad patterns, with patterns being judged broader (i.e., more likely to generalize) to the extent that they conform not only to current evidence, but also to prior beliefs. These findings are also consistent with the proposal that categorization can be construed as inference to the best explanation (Murphy and Medin, 1985, Rips, 1989), where explanations that are consistent with prior beliefs provide “better” explanations—because they have a broader scope, supply a causal mechanism, support a more coherent set of beliefs, or exhibit other virtues (Lombrozo, 2012, Lombrozo, 2016).

While these findings help characterize the precise learning consequences of engaging in explanation, many questions remain about the mechanisms by which explanation generates these effects. Lombrozo (2012) hypothesized that engaging in explanation may recruit (or be recruited by) a variety of cognitive processes, including inductive reasoning, deductive reasoning, categorization, causal reasoning, and analogical reasoning. In the present work, we focus on one candidate mechanism: analogical comparison. The very act of explaining could stimulate comparison in the service of fostering the discovery and generalization of broad patterns. This fits with research that has identified abstraction and generalization as two of the principal benefits of comparison (Gentner, 2010). As previously suggested, seeking and evaluating explanations often involves an explicit or implicit contrast between two alternatives: Why is a tomato a fruit (as opposed to a vegetable)? Why is this robot a Glorp (as opposed to a Drent)? (see also Chin-Parker and Cantelon, 2017, McGill, 2002, van Fraassen, 1980). The search for explanations—particularly when learning categories from examples—may therefore initiate a process of comparison, which could in part underlie explanation’s effects on learning. In the following section, we provide a more detailed review of the evidence that comparison can promote the kind of learning observed in experiments involving explanation.

Comparison is the process of identifying similarities and differences between two cases. Like explanation, engaging in comparison can provide significant learning benefits (e.g., Christie and Gentner, 2010, Gentner, 2003, Gentner, 2010, Gentner and Namy, 1999, Kotovsky and Gentner, 1996, Loewenstein et al., 2003, Richland et al., 2007, Rittle-Johnson and Star, 2009, Rittle-Johnson and Star, 2011, Thompson and Opfer, 2010; for a review, see Alfieri, Nokes-Malach, & Schunn, 2013). One way in which making comparisons can enhance learning is by promoting structural alignment of the cases being compared. In our discussion we use Gentner, 1983, Gentner, 2010 structure-mapping theory, which describes how analogical comparison can be used to uncover a common relational structure. According to this theory, analogical comparison is geared towards finding a structurally consistent set of one-to-one correspondences that maximizes the common relational structure. The idea is that people implicitly prefer structurally consistent alignments in which lower-order matches are connected by higher-order relational matches (the systematicity principle) (Gentner, 1983, Gentner and Markman, 1997, Gentner et al., 1993). A computational model of the structure-mapping process, SME, uses a three-stage local-global matching process to arrive at a maximal or near-maximal alignment (Falkenhainer et al., 1989, Forbus et al., 2017). Although there are a number of other computational models of analogy (e.g., LISA: Hummel & Holyoak, 1997, DORA: Doumas, Hummel, & Sandhofer, 2008, DRAMA: Eliasmith & Thagard, 2001), most current models of analogy share structure-mapping theory’s core assumption that inferences are based on finding a structurally consistent alignment.

On this view, comparison is an especially powerful learning process because it helps people do more than merely notice feature-level similarities and differences between two items. By highlighting common systems of features, the mapping generated by structural alignment supports the formation of an abstract relational schema. Thus, comparison plays an important role in the acquisition of abstract knowledge (Gentner & Medina, 1998). This schema can in turn facilitate successful analogical transfer, including far transfer to problems with vastly different surface features or in different cognitive domains (e.g., Catrambone and Holyoak, 1989, Gentner et al., 2009, Gick and Holyoak, 1983, Loewenstein et al., 2003). Further, in addition to highlighting the common system, structural alignment also highlights differences that play corresponding roles in the two systems (alignable differences) (Markman and Gentner, 1993, Sagi et al., 2012). Both of these are relevant to category learning.

Notions of similarity have played a prominent role in theories of categorization (Posner and Keele, 1968, Reed, 1972, Rosch and Mervis, 1975; for reviews, see Goldstone, 1994, Sloman and Rips, 1998, Smith and Medin, 1981), and there is considerable evidence that comparison processes are important in category learning (Gentner and Medina, 1998, Markman and Wisniewski, 1997, Spalding and Ross, 1994). Indeed, performing comparisons can help adults learn to categorize birds (Higgins & Ross, 2011) or learn new relational categories (Goldwater and Gentner, 2015, Kurtz et al., 2013). There is also evidence that comparison processes help young children select taxonomic choices over perceptually similar distractors in a categorization task (Gentner and Namy, 1999, Namy and Gentner, 2002) and learn challenging relational categories (Christie and Gentner, 2010, Gentner et al., 2011, Kotovsky and Gentner, 1996). Interestingly, in some of the developmental studies, children were asked “Do you see why these are both jiggies?”—which could be seen as an invitation to explain why these exemplars belong to the “jiggy” category. That this prompt seems to promote both comparison and explanation suggests a close relationship between these processes. Indeed, we hypothesize that when learning a category, people often invoke comparison processes in the service of generating or evaluating explanations.

One way to examine a possible relationship between explanation and comparison is to explore their effects on the same experimental task. Few studies have done so, and when they have, the aim has often been to isolate the effect of each process (that is, to have participants explain only or compare only), rather than consider their potentially interactive effects (Gadgil et al., 2012, Nokes-Malach et al., 2013, Richey et al., 2015). For example, Nokes-Malach et al. (2013) evaluated the relative effectiveness of three cognitive strategies for helping college students learn to solve physics problems: reading solutions to worked examples and solving practice problems, explaining the solutions to the worked examples, or comparing and contrasting the worked examples. Participants in the reading and explanation conditions achieved greater near transfer than participants in the comparison condition, while participants in the explanation and comparison conditions achieved greater far transfer than participants in the reading condition. Similarly, Gadgil et al. (2012) investigated the roles of explanation and comparison in acquiring more accurate theories of the circulatory system. They found that comparing an incorrect model of the circulatory system (that was consistent with the participant’s prior beliefs) with an expert model of the circulatory system was more effective than explaining the expert model of the circulatory system. These findings suggest that explanation and comparison are both beneficial for learning, but also make it clear that they do not generate equivalent outcomes.

Three additional studies hint at whether and how explanation and comparison might interact. In one study, Kurtz, Miao, and Gentner (2001) presented college students with two superficially dissimilar examples of heat flow. Participants who compared the two scenarios by analyzing the scenarios jointly and listing correspondences between the scenarios later rated the two scenarios as more similar than did both participants who analyzed the two scenarios separately (and who did not list correspondences) and control participants who did not previously analyze the scenarios. Furthermore, in a difference-listing task, participants who had previously engaged in the comparison task (including stating correspondences) listed differences that were more causally relevant to the principle of heat flow than did control participants. This provides evidence that intensive comparison supported the discovery of a common causal system, and that engaging in comparison can help participants identify principles that can serve as a basis for causal explanations.

In another study, Sidney, Hattikudur, and Alibali (2015) gave college students math problems and analyzed the roles of explanation and comparison in students’ learning. Most relevant for our purposes, participants who received explanation prompts noticed more similarities and differences between the problems than those who did not—suggesting that the explanation task facilitated comparison processing.

Finally, Hoyos and Gentner (2017) asked whether children’s explanations would be influenced by the kinds of comparisons that were readily available. Six-year-old children were asked to explain why a building with a diagonal brace is strong (more precisely, why it is stable, such that its shape cannot be changed without breaking a piece or a joint). They compared the effectiveness of three study-example conditions: (a) a single model building with diagonal braces (single-model condition), (b) a perceptually similar pair of model buildings, one with diagonal braces and one without such braces (high-alignability condition), or (c) a perceptually dissimilar pair (low-alignability condition). Children were asked “Which building is stronger?” (or in the single model case, “Is this building strong?”). Then they were asked to explain why that building was strong(er). Children in the high-alignability condition were most likely to produce brace-based explanations for the strength of the model with diagonal braces, and were also more likely to succeed on a far-transfer task than children in the low-alignability and single-model conditions. These results show that children can use information acquired through comparison to inform their causal explanations and support transfer to a novel problem.

While these findings reveal that explanation and comparison can work in tandem to support learning, they do not target the central question we explore here: namely whether engaging in explanation recruits comparison, and, if so, which comparison strategies are deployed and how they affect learning. In the next section, we develop a proposal for how explanation and comparison might work together to promote learning in a categorization task.

In a basic category-learning task like that in Williams and Lombrozo (2010), participants must learn a classification rule that allows them to successfully classify items into one of two novel categories, and they must do so on the basis of a small number of labelled examples. In this situation, explaining involves answering the question: why does this example belong to this category (as opposed to another)? An answer could identify a classification procedure (e.g., “I know it is an even number, rather than an odd number, because it ends in a ‘2’”), or it could invoke a deeper basis for category membership (e.g., “it is an even number because it is divisible by 2”). Often, people treat superficial bases for classification as indicative of deeper, category-defining properties (Gelman, 2003), so what look like fairly superficial explanations (e.g., “it is a Glorp because of its feet”) could reflect much deeper explanatory commitments. Bearing this in mind, how might explanation recruit comparison under these conditions?

We propose that when trying to explain why an item belongs to a particular category, people initially invoke comparison through an implicit or explicit contrast: people are likely to think about the problem as a question about why the item belongs to one category and not to another (Chin-Parker and Cantelon, 2017, Williams and Lombrozo, 2013). Given that comparison can be essential for explaining an item’s category membership, a deeper question than whether explanation recruits comparison is which of several comparison strategies is engaged. One strategy is to compare single pairs of items, either within the same category or across two categories. For example, the person might first carry out pairwise comparisons of individual items within a category to identify similarities, and then between the categories to identify differences. Another strategy is to carry out comparisons of all members of a single category, what we refer to as a group-level comparison. For example, a participant might carry out a series of comparisons within each category to identify features that are common (if not universal), and that form the basis for a prototype or some other, more abstract representation.

We hypothesize that such group-level comparisons are likely to be especially helpful in promoting the re-representation of features and exemplars to identify a subtle rule that underlies category membership. For example, a pairwise comparison between Robot A and Robot B in Fig. 1 is likely to support the conclusion that Glorp robots differ in their foot shape, and that this is not a basis for categorization. However, a group-level comparison of all four Glorp robots invites a re-representation of foot shape at a more abstract level—that despite surface-level differences, all these robots have feet with pointy bottoms. A comparison with the four Drent robots, all of which have feet with flat bottoms, suggests that foot shape is indeed diagnostic of category membership. (See Forbus et al., 2017, Kuehne et al., 2000; for a computational model of iterative alignment and abstraction.)

If this proposal is correct, then we should expect that prompting learners to explain will lead them to engage in more comparison processing, and that the strategy they pursue (i.e., pairwise or group-level comparisons) might affect what they ultimately learn. Our experiments are correspondingly designed to address the following questions. (1) Does explanation increase the extent to which participants engage in comparison? (2) If so, what comparison strategies does explanation recruit? (3) Do these comparison strategies contribute to the effectiveness of explanation in this task?

To answer these questions, we adapted the category-learning task from Williams and Lombrozo, 2010, Williams and Lombrozo, 2013. In the present experiments, some participants received prompts to explain and some received prompts to compare. We varied the nature of these prompts to consider both within- and between-category comparisons, as well as pairwise versus group-level comparisons. In order to assess whether participants used comparison when generating explanations, we asked participants to report the extent to which they engaged in comparison, as well as the extent to which they engaged in explanation. Across experiments, these self-reports² enabled us to gain insight into both the extent and nature of the specific comparison strategies (i.e., within-category, between-category, and group comparisons) that participants in each condition were performing, including how these different comparison strategies relate to learning.

In each experiment, we examined the effects of our experimental manipulations on category learning, as well as (1) whether instructions to generate explanations would lead participants to engage in comparison and (2) whether comparison (either directly prompted or as assessed by self-report) would promote category learning. Across experiments we varied the nature of the comparisons that were prompted and assessed, with Experiment 1 focusing on comparisons of pairs of robots within the same category, and Experiments 2 and 3 additionally focusing on group-level comparisons. We predicted that prompts to explain or to compare would be beneficial (replicating prior research), that they would lead to more self-reported comparison, and that comparison would in turn be associated with positive learning outcomes. To foreshadow our results, we found that our predictions were confirmed, but only for group-level comparisons. Pairwise comparisons of individual pairs of robots (as we explored in Experiment 1) were not associated with positive learning outcomes.