Analogical Reasoning in the Classroom: Insights from Cognitive Science Michael S

MIND, BRAIN, AND EDUCATION Analogical Reasoning in the Classroom: Insights From Cognitive Science Michael S. Vendetti1, Bryan J. Matlen2, Lindsey E. Richland3, and Silvia A. Bunge1 ABSTRACT— Applying knowledge from one context to Appreciating and learning from this analogy requires the another is a notoriously difficult problem, both for children student to look past surface-level differences between the and adults, but lies at the heart of educational endeavors. source and target and instead notice the underlying, shared Analogical reasoning is a cognitive underpinning of the abil- relational structure between domains—in this case, the fact ity to notice and draw similarities across contexts. Reasoning thattheplanetsorbitthesuninananalogousfashionasthe by analogy is especially challenging for students, who must electrons orbit the atom’s nucleus (Gentner, 1983). transfer in the context-rich and often high-pressure settings This ability, termed analogical reasoning, is critical for of classrooms. In this brief article, we explore how best to success in education. Nevertheless, research from cogni- facilitate children’s analogical reasoning, with the aim of tive science has consistently found that spontaneous trans- providing practical suggestions for classroom instruction. feracrossanalogicalcontextsisrareinlaboratorysettings We first discuss what is known about the development and (Gick & Holyoak, 1980, 1983). How do humans develop the neurological underpinnings of analogical reasoning, and capacity to reason by analogy? And how can educators sup- then review research directly relevant to supporting ana- port the analogical reasoning process? In this brief article, logical reasoning in classroom contexts. We conclude with we explore ways of supporting students’ analogical reason- concrete suggestions for educators that may foster their ing with the aim of providing teachers with research-based students’ spontaneous analogical reasoning and thereby strategies for supporting analogical thinking. We begin by enhance scholastic achievement. defining what it means to reason by analogy, and then exam- ine the neurocognitive development of analogical reasoning to provide educators with insight into their students’ think- A key challenge for students is learning to recognize and ing and reasoning development. Finally, we review findings learn from opportunities to apply previously learned infor- from cognitive science that bear directly on ways that educa- mation to new situations. For example, when teaching stu- tors can support students’ ability to generate and appreciate dents about the atom in school, one approach could be to analogies in the service of learning. present an analogy between the solar system and the atom (see Figure 1a). In this example, the solar system represents a Analogical Reasoning as Relational Comparison domain that is already familiar to students (the source), and What does it mean to reason analogically? Several steps are presumed to take place in analogical reasoning, includ- the atom represents the domain that students are learning ing paying attention to relevant information, extracting about (the target). relationships within and across items, and making the appropriate mappings across domains to either generate inferences and/or derive their common principles (Holyoak, 2012). The key component underlying each of these steps is 1 Department of Psychology, University of California, Berkeley attending to shared relationships that are common to both 2WestEd Program in Science, Technology, Engineering, and Mathematics domains (Gentner, 1983, 2010). When comparing the atom 3Department of Comparative Human Development, University of to the solar system, one must attend to the key common Chicago relationships that guide both domains—for example, the Address correspondence to Michael S. Vendetti, University of Califor- larger object in both domains causes the smaller object to nia at Berkeley, Berkeley, CA; e-mail: [email protected] rotate around it—and place entities into correspondence 100 © 2015 International Mind, Brain, and Education Society and Wiley Periodicals, Inc. Volume 9—Number 2 Michael S. Vendetti et al. (a) (b) (c) (d) Fig. 1. (a) Example analogy between models of the solar system and the atom. In this example, the atom is the target because this is the domain that children are going to be learning more about. The solar system would be the source, and this would provide information that would be transferred to the atom once an analogical comparison had been made. (b) Brain activation patterns demonstrating greater activation while solving analogies versus looking at a fixation cross, for correct trials only. Average activation for 6- to 9-year-olds (N = 34) and 14- to 18-year-olds (N = 29), with the left and right hemispheres shown to the left and right, respectively. A remarkably similar network of regions are involved while solving analogies across these two age ranges, even though the older participants performed the task more accurately. This image is based on analyses by Dr. Kirstie Whitaker of data from an NIH-supported project led by S.Bunge and E. Ferrer, titled “Neurodevelopment of Reasoning Ability.” (c) A visual analogy comparing the Earth’s convection (the target domain) to a boiling pot of water (the source domain). The visual analogy is designed to direct attention to relationally corresponding parts. For instance, the Earth’s Core and the Stove are both physically aligned at the bottom of the images to emphasize their common relational roles (i.e., they both act as the heat source). Similarly, the convection currents are made to be perceptually similar (in both color and shape) to emphasize their common relational roles. (d) Correct (left) and incorrect (right) examples of controlled experiments that are designed to test whether the color of the ramp’s surface affects how far a ball will roll. The design of the experiments differ in only one way: the ramp lengths are set to be equal in the correct example, but they are set to be varied in the incorrect example. Side-by-side comparison helps students to recognize the key difference connected to the common structure: namely, that two variables are set as varied in the incorrect example and only one variable is set to be varied in the correct example (the variable that is the target of the experiment). Volume 9—Number 2 101 Analogical Reasoning in the Classroom that share common relational roles (e.g., the sun and the to understand better the timing and nature of change in nucleus are similar because they are both the larger object). the neural mechanisms underlying children’s analogical This relational mapping process is critical for analogical rea- reasoning growth. soning. However, novices in a domain often notice and map Given the observed changes in analogical reasoning over correspondences based on perceptual features of the analogs elementary school, one possibility is that younger chil- instead of the underlying relationships (Chi, Feltovich, & dren rely on different underlying neural mechanisms when Glaser, 1981). For instance, one could attend to visual sim- attempting to solve analogies. Another possibility is that ilarities between the analogs, noting similarities between younger children recruit the same network of brain regions the sun and the electrons (e.g., both are depicted as round as older children when solving analogies, but do not yet objects suspended in space), which could lead to misconcep- engage the network in an efficient manner. This distinction tions or conceptual misalignments. As we will outline below, is helpful for understanding whether young children already a key challenge in analogical reasoning is learning to attend have the necessary “hardware” to engage in analogical rea- to the deeper structural relationships between domains in soning, or whether significant brain maturation must first the face of these irrelevant perceptual similarities. take place. Research to date on analogical reasoning across typi- Development of Analogical Reasoning cal development has demonstrated that children engage When do children begin to make analogical comparisons, the same set of brain regions as adults during analogical and how does this ability develop? Though the rudiments reasoning by the age of 6 (and perhaps earlier, although of analogy are in place at an early age, children’s reasoning this is not yet known; see Figure 1b; Wendelken, O’Hare, is not adult-like until late adolescence, meaning that they Whitaker, Ferrer, & Bunge, 2011; Wright, Matlen, Baym, Fer- will need additional support to notice and successfully use rer, & Bunge, 2008). Thus, by the time children enter into analogical thinking in learning contexts (e.g., Gentner & early elementary school, they already engage the appropri- Ratterman, 1991; Halford, 1992; Richland, Morrison, & ate neural network for processing analogies. However, two Holyoak, 2006). Children’s reasoning is more fragile than key developmental differences have been observed. First, adults’ in two primary ways. First, children exhibit more as children get older, they exhibit reduced activation of difficulty ignoring irrelevant perceptual distractors than key brain regions when making easier relational compar- adults, though this improves with age. For instance, work by isons (Wendelken et al., 2011). Second, older children and Richland et al. (2006) demonstrated that, although children adolescents show stronger functional connectivity—that is, as young as 3 could notice and use

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