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Abstract

The practice of learning from multiple instances seems to allow children to learn about relational structure. The experiments reported here focused on two issues regarding relational learning from multiple instances: (a) what kind of perceptual situations foster such learning and (b) how particular object properties, such as complexity and similarity, interact with relational learning. Two kinds of perceptual situations were of interest here: simultaneous view, where instances are viewed at once, and sequential view, where instances are viewed one at a time (one right after the other). We examined the influence of particular perceptual situations and object properties using two tests of relational reasoning: a common match-to-sample task, where new instances are compared with a common sample, and a variable match-to-sample task, where new instances are compared with a sample that varies on each trial. Experiments 1 and 2 indicate that simultaneous presentation of even highly dissimilar instances, one simple and one complex, effectively connects them together and improves relational generalization in both match-to-sample tasks. Experiment 3 shows that simple samples are more effective than complex ones in the common match-to-sample task. However, when one instance is not used a common sample and various pairs of instances are simply compared, as in Experiment 4, simple and rich instances are equally effective at promoting relational learning. These results bear on our understanding of how children connect instances and how those initial connections affect learning and generalization.

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... The four experiments reported here explored this issue by assessing the impact of sequential presentation of items (i.e., one-by-one) and simultaneous presentation of items (i.e., at the same time) on property projection. Sequential presentation and simultaneous presentation have been shown to yield distinct outcomes in a range of cognitive tasks with adults (e.g., Carvalho & Goldstone, 2014;Krueger, 1984;Lappin & Bell, 1972;Lupyan, Thompson-Schill, & Swingley, 2010;Shiffrin, Gardner, & Allmeyer, 1973), and children (e.g., Lipsitt, 1961;Oakes & Ribar, 2005;Son, Goldstone, & Smith, 2011;Quinn & Bhatt, 2010). Gentner and Namy (1999) showed that simultaneous presentation of two exemplars (e.g., apple and pear) supported generalization to a relational match (e.g., banana) rather than a perceptual match (e.g. ...
... balloon). In a direct comparison of these two presentation formats, Son et al. (2011) found that children as young as 3 years of age performed better on a relational sample-to-match task when sample items were presented simultaneously than when they were presented sequentially. Similar findings have been demonstrated in other domains. ...
... It is important to note that sequential presentation in the present studies followed a slightly different method than has been used in prior studies. In previous research sequential presentation was implemented in such a way that an item was presented and labeled and then removed prior to the presentation of the next item (e.g., Son et al., 2011;see also Spencer, Perone, Smith, & Samuelson, 2011). In the sequential conditions in Experiments 1 and 3 each evidence exemplar remained visible after it was presented. ...
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Young children are remarkably flexible reasoners insofar as they modify their inferences to accommodate the conceptual information or perceptual relations represented in an inductive problem. Children’s inductive reasoning is highly sensitive to what evidence is presented to them. Four experiments with 115 preschoolers (Mage = 4.69 years) and 119 adults (Mage = 21.73 years) examined whether induction is influenced by how evidence is presented. Specifically, these studies explored the extent to which presenting evidence exemplars at the same time (i.e., simultaneous presentation) or one-by-one (i.e., sequential presentation) would influence property projections to a range of targets. Experiment 1 revealed that simultaneous presentation yielded a higher rate, and a broader scope, of projections than sequential presentation. Experiment 2 confirmed that these effects were not due to how items were labeled. Experiments 3 and 4 explored the interplay between evidence presentation and specific task features that impact how participants compare evidence and target exemplars. In Experiment 3 there were no differences between the two presentation formats when evidence exemplars were removed prior to the projection phase thereby eliminating the opportunity to compare between evidence exemplars and targets. Finally, Experiment 4 showed that sequential presentation yielded a high rate of projections when participants were not afforded the opportunity to compare exemplars within the evidence sample. These results have implications for understanding the mechanisms that guide children’s inductive decisions.
... Other commonly used measures in this literature include relational match-to-sample tasks (used by 9.5 % of the 21 included studies) where participants are asked to identify a given pattern and then select its analog (Son et al. 2011), verbal four-term analogies in the form of A:B::C:D (14.3 %; e.g., Wendelken et al. 2008) and four-term pictorial analogies, also in the form A:B::C:D (23.8 %; e.g., Krawczyk et al. 2008). Each of these tasks is different from the RPM, but they all share the same focus on analogy as the form of relational reasoning being tested. ...
... However, although brain imaging was the most common methodology used in this body of literature, there were studies incorporating methodologies closer to the educational context. These include research conducted in schools (e.g., Son et al. 2011), in which relational reasoning ability was empirically connected to educational outcomes and inferences were made about the best way to promote learners' relational reasoning. Other methodologies present in this literature included cognitive tasks and measures given in a laboratory setting (e.g., Birney and Halford 2002b) and semistructured interviews (Stephens 2006). ...
... One apparent strength of the literature on generic relational reasoning is the many different populations that have been studied. The construct of relational reasoning has been examined in preschoolers (Son et al. 2011), elementary-school students (Crone et al. 2009), adolescents (Eslinger et al. 2009), students with intellectual disability (Scruggs et al. 1994), healthy adults (Krawczyk et al. 2011), men with Klinefelter's syndrome (Fales et al. 2003), patients with brain injuries (Waltz et al. 1999), and stroke patients (Baldo et al. 2010). This diversity of samples can allow the field to make inferences on the development of this construct, as well as the ways that particular students may struggle with relational reasoning tasks based on their age and neurological condition. ...
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Relational reasoning, the ability to discern meaningful patterns within otherwise unconnected information, is regarded as central to human learning and cognition and as particularly critical for those functioning in today's information age. However, the literature on this foundational ability is currently housed within a range of domains of inquiry, where divergent terminology and methodologies are commonplace. This dispersion has made it difficult to harness the power of existing work to inform future research or guide educational practice. In order to address this lack of consolidation, a systematic review of relational reasoning was undertaken. Specifically, 109 empirical studies dealing with relational reasoning in general or one of four manifestations (i.e., analogy, anomaly, antinomy, and antithesis) were analyzed. Resulting data revealed trends across fields of inquiry, including a degree of conceptual ambiguity, conceptual and operational misalignment, and a lack of ecological validity in certain research paradigms. There were also particular forms and measures of relational reasoning that were more commonly investigated, as well as certain domains that were more often studied. Implications for how future research can examine relational reasoning as a multidimensional construct within educational contexts are also discussed.
... Similar advantages of perceptually simple objects have been found in studies examining the learning of relational categories (Amaya, Uttal, O'Doherty, Liu, & DeLoache, 2008;Kaminski & Sloutsky, 2010;Kaminski, Sloutsky, & Heckler, 2006, 2008Rattermann, Gentner, & DeLoache, 1990;Son, Smith, & Goldstone, 2011;Welling, 2011). First, Rattermann, Gentner, and DeLoache (1990) found that, in a relational mapping task where the relation match was pitted against the object match, young children made more relational choices when the objects were perceptually sparse than when they were perceptually rich. ...
... Despite findings pointing to the merits of simple objects in fostering generalization, there are studies that outline a more nuanced picture and suggest that simple objects may not always provide an advantage over complex objects (Paik & Mix, 2006;Petersen & McNeil, 2008;Son, Smith, & Goldstone, 2011;Welling, 2011). For instance, Petersen and McNeil (2008) reported that the beneficial effect of simplicity occurs only when the complex objects have established meanings as objects. ...
... The younger children failed to generalize in both conditions and interestingly learned the labels for dynamic relations slightly better when the relations were depicted with concrete, perceptually rich objects. Also, Son, Smith, and Goldstone (2011) found no difference between simple and complex objects in a relation-matching task when the relation exemplars varied from trial to trial. However, when a single exemplar of a relation was used across all trials, children still performed better with a simple shape as the exemplar. ...
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The present study investigated infants' ability to form a category of a support relation (i.e., "on") when the objects depicting the relation were perceptually simple versus more complex. Twenty Korean infants of 14 months were habituated to dynamic support events with objects that were either simple or more complex in appearance. They were then tested with events that differed from the habituation events in the specific objects, spatial relation, or both. Infants formed a support category whether familiarized to simple or complex objects, looking significantly longer at test events with a novel than familiar relation. The results indicate that at 14 months of age, object features do not impact infants' ability to form a categorical representation of support.
... Similarly, Andrews, Livingston, and Kurtz (2011) asked participants to categorize individual objects that were either presented alone on the screen or jointly with other objects; feedback was given after each trial. In a subsequent test phase, categorization accuracy was higher when the objects had been presented together with other objects rather than singly during training (for further examples, see Namy & Gentner, 2002;Son, Smith, & Goldstone, 2011). ...
... When objects are presented individually, comparing them requires retrieval from memory and comparison processes may therefore be less likely engaged than when objects are presented together. Facilitating cue comparison by presenting objects side by side could thus increase reliance on the abstracted regularities of the task environment (e.g., Andrews et al., 2011;Carvalho & Goldstone, 2015;Hammer, Bar-Hillel, hertz, Weinshall, & Hochstein, 2008;Son et al., 2011). ...
... Given that a substantial body of research has highlighted a role of the explicit opportunity for cue comparison in category learning and analogical reasoning (e.g., Markman & Gentner, 1993;Namy & Gentner, 2002;Son et al., 2011), it may seem surprising that cue comparison did not emerge as a driver of the differences between learning by comparison and direct criterion learning. What are the implications of our finding for the literature on the effects of cue comparison? ...
Article
In judgment and categorization, the task is to infer the criterion value of an object based on cues. The cognitive mechanisms underlying such inferences are often distinguished in terms of whether they rely on an abstracted cue-criterion rule or on retrieving exemplars. The use of cue-based and exemplar-based strategies (and the associated generalization ability) has been shown to be influenced by how people had previously learned about the structure of the environment: learning by comparing two objects on the criterion promotes the subsequent adoption of a cue-based strategy (and generalization ability); directly learning the continuous criterion for each individual object promotes the use of an exemplar-based strategy. It is currently unclear, however, how to explain these learning task effects theoretically. We disentangled the role of three theoretically relevant differences between the two types of learning task: (a) the opportunity to directly compare the cue profiles of the objects, (b) the provision of continuous criterion information, and (c) the relative (as opposed to absolute) nature of the feedback given. In three experiments, and consistently across a categorization task and a judgment task, we found that the learning task effects seem to be driven by the relative nature of the feedback in learning by comparison, and, to a lesser extent, by the provision of the object’s continuous criterion values in direct criterion learning. Cue comparison during training did not seem to contribute to the learning task effects. Our results extend existing theoretical frameworks for the use of cue-based and exemplar-based strategies.
... In comparison to abstract objects, realistic objects, such as trees and cars, may generate rich extraneous information, such as their usage or properties (e.g., it grows), and consequently may present a greater challenge relative to abstract objects in tasks of relational learning. In line with this possibility, children transfer relational structure more easily with abstract than realistic objects (Kaminski & Sloutsky, 2010;Kaminski, Sloutsky, & Heckler, 2008;Rattermann et al., 1990;Son, Smith, & Goldstone, 2011;Uttal et al., 2013). For example, in a match-to-sample task, young children were presented with a sample depicting an ABA or BAA relation and two response options depicting an ABA and a BAA. ...
... Multiple mechanisms have been proposed to explain the advantage of abstract over realistic objects in children's relational reasoning. One mechanism is that abstract objects shortcut the learner's abstraction of a relational structure by omitting distracting information that is irrelevant to the relation (Son et al., 2011). Another possible mechanism is that the symbolic simplicity of abstract objects underlies their advantage in tasks of relational transfer (Kaminski & Sloutsky, 2010;Kaminski et al., 2008;Uttal, Scudder, & DeLoache, 1997;Uttal et al., 2013). ...
... Lastly, we reduced the number of response options from four to three. Although the original task has been successfully used with 4-year-old children (Pruden et al., 2011), most previous studies examining preschool children's relational reasoning offered two (e.g., Christie & Gentner, 2014;Kotovsky & Gentner, 1996;Son et al., 2011) or three response options (Kaminski & Sloutsky, 2010;Rattermann et al., 1990). Moreover, we reasoned that keeping the choice number as four in the present study would significantly increase the amount of object information provided (ten diverse objects for each spatial analogy item and 120 diverse objects throughout the task), which we posited might overshadow relational information and hinder preschoolers' relational responses on the task. ...
Article
We tested young children’s spatial reasoning in a match-to-sample task, manipulating the objects in the task (abstract geometric shapes, line drawings of realistic objects, or both). Korean 4- and 5-year-old children (N = 161) generalized the target spatial configuration (i.e., on, in, above) more easily when the sample used geometric shapes and the choices used realistic objects than the reverse (i.e., realistic-object sample to geometric-shape choices). With within-type stimuli (i.e., sample and choices were both geometric shapes or both realistic objects), 5-year-old, but not 4-year-old, children generalized the spatial relations more easily with geometric shapes than realistic objects. In addition, children who knew more locative terms (e.g., “in”, “on”) performed better on the task, suggesting a link to children’s spatial vocabulary. The results demonstrate an advantage of geometric shapes over realistic objects in facilitating young children’s performance on a match-to-sample spatial reasoning task.
... Using perceptually rich materials alone is often not a very effective technique and can sometimes reduce learning and performance relative to less perceptually rich materials (e.g. Berends and van Lieshout 2009;Kaminski, Sloutsky, and Heckler 2013;Scheiter et al. 2009;Son, Smith, and Goldstone 2011). The potential drawback is related to the seductive details effect (e.g. ...
... For example, one common approach to connecting multiple representations is to engage in direct comparison or coordination, which involves the simultaneous presentation of examples and an explicit mapping process that highlights similarities and differences (e.g. Nathan et al. 2013;Rittle-Johnson and Star 2011;Son, Smith, and Goldstone 2011). Concreteness fading may support spontaneous comparison across representations, but the real goal is to think of the representations as one and the same, each an instantiation of a common invariant set of relations. ...
... Although this hypothesis contrasts with several pieces of evidence that suggest simultaneous viewing and comparison can promote learning more than sequential viewing of the same stimuli (e.g. Rittle- Johnson and Star 2011;Son, Smith, and Goldstone 2011), none of these studies have been conducted using a concreteness fading paradigm in which the representations vary systematically on the dimension of concreteness. Establishing this hypothesis within a concreteness fading progression would be a novel contribution to our understanding of cognitive development. ...
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To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. Concreteness fading is a theory of instruction that offers a solution for making these connections. As originally conceived, it is a three-step progression that begins with enacting a physical instantiation of a concept, moves to an iconic depiction and then fades to the more abstract representation of the same concept. The goals of this paper are: (1) to improve the theoretical framework of concreteness fading by defining and bringing greater clarity to the terms abstract, concrete and fading; and (2) to describe several testable hypotheses that stem from concreteness fading as a theory of instruction. Making this theory of instruction more “concrete” should lead to an optimised concreteness fading technique with greater promise for facilitating both learning and transfer.
... There is some evidence that comparing representations simultaneously is more effective for learning than viewing the same representations one at a time (e.g. Son et al., 2011). For example, preschoolers completed a category learning task, and performance was optimised when they compared two target pictures simultaneously than when they saw the same pictures sequentially (Christie & Gentner, 2010). ...
... Direct comparison has been shown to improve learning in a variety of domains for children and adults (e.g. Gentner et al., 2003;Rittle-Johnson et al., 2009;Son et al., 2011). The current findings do not contradict this work; rather, they suggest that comparing objects and symbols using the current implementation may be ineffective. ...
... They found that young children 105 made more relational choices (focusing on relative size) when the objects were perceptually simple 106 and identical to each other (three clay pots that differed from each other only in size) than when they 107 were perceptually rich and diverse from each other (a toy house, a toy car, and a decorative mug, each 108 also varying in size). Similarly, young children transferred an ABA or BAA relation better when it was 109 depicted with shapes such as three triangles than when it was depicted with perceptually rich objects 110 such as three dogs (Kaminski & Sloutsky, 2010;Son et al., 2011). In addition, the use of abstract geo-111 metric shapes was more effective than the use of perceptually rich and concrete objects in promoting 112 transfer of mathematical rules for both children and adults (Kaminski, Sloutsky, & Heckler, 2008; 113 Kaminski et al., 2006). ...
... Infants in the current study were habituated to four exem-528 plars of a relation prior to the test. In contrast, most of those studies documenting the benefit of sim-529 plicity in relational transfer presented their learners with a single set of objects (i.e., an instance of the 530 relation) as the basis of generalization (e.g.,Kaminski & Sloutsky, 2010; Kaminski et al., 2008; 531Rattermann et al., 1990;Son et al., 2008Son et al., , 2011. Possibly, the advantage of a simple instance as a 532 ready-made abstract representation is more pronounced when the learner must grasp the relational 533 structure from a single instance compared with when the learner is given multiple exemplars of534 the relation (and sufficient time to compare them). ...
... Kotovsky and Gentner (1996) found this to be an extremely difficult task for 4-year-olds, with most children not systematically selecting the relational match. In general, without perceptual training and/or other support from task structure, this is a very hard task for preschool children (Christie & Gentner, 2010Loewenstein & Gentner, 2005;Simms & Gentner, 2013;Son, Goldstone, & Smith, 2011) and is particularly so when the relational target choice has no object similarities with the standard, as in the example described above. However, a number of studies have shown that arbitrary, noniconic, and (at least initially) contentless novel labels often help preschool children perform better in this task, even if children are still not completely successfully (Kotovsky & Gentner, 1996;Loewenstein & Gentner, 2005;Namy & Gentner, 2002;Rattermann, Gentner, & DeLoache, 1990;Son, Goldstone, & Smith, 2011). ...
... In general, without perceptual training and/or other support from task structure, this is a very hard task for preschool children (Christie & Gentner, 2010Loewenstein & Gentner, 2005;Simms & Gentner, 2013;Son, Goldstone, & Smith, 2011) and is particularly so when the relational target choice has no object similarities with the standard, as in the example described above. However, a number of studies have shown that arbitrary, noniconic, and (at least initially) contentless novel labels often help preschool children perform better in this task, even if children are still not completely successfully (Kotovsky & Gentner, 1996;Loewenstein & Gentner, 2005;Namy & Gentner, 2002;Rattermann, Gentner, & DeLoache, 1990;Son, Goldstone, & Smith, 2011). These novel labels -in a sentence form indicating a name (e.g. ...
Article
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Known words can guide visual attention, affecting how information is sampled. How do novel words, those that do not provide any top-down information, affect preschoolers' visual sampling in a conceptual task? We proposed that novel names can also change visual sampling by influencing how long children look. We investigated this possibility by analyzing how children sample visual information when they hear a sentence with a novel name versus without a novel name. Children completed a match-to-sample task while their moment-to-moment eye movements were recorded using eye-tracking technology. Our analyses were designed to provide specific information on the properties of visual sampling that novel names may change. Overall, we found that novel words prolonged the duration of each sampling event but did not affect sampling allocation (which objects children looked at) or sampling organization (how children transitioned from one object to the next). These results demonstrate that novel words change one important dynamic property of gaze: Novel words can entrain the cognitive system toward longer periods of sustained attention early in development.
... For example, a child might be shown blue and red tiles with an ABAB relation (e.g., blue-red-blue-red) and be asked to create the same kind of pattern using green squares and circles (e.g., square-circle-square-circle). Although research suggests that most preschoolers can recognize an abstracted pattern in a relational match-tosample task (e.g., Kotovsky & Gentner, 1996;Son, Smith, & Goldstone, 2011), much less is known about preschoolers' ability to generate the abstracted pattern themselves. Some 4-year-olds are capable of pattern abstraction, but large individual differences exist (Rittle-Johnson, Fyfe, McLean, & McEldoon, 2013). ...
... First, abstract labels may draw children's attention to the structural aspects of the pattern materials as opposed to the surface features of the materials themselves. Abstract representations limit extraneous perceptual features and make the structure more apparent than concrete representations (e.g., Kaminski, Sloutsky, & Heckler, 2009;Son et al., 2011). For example, 4-year-olds are more successful at mapping objects based on the relations among those objects when the objects are generic (e.g., simple line drawing of a pot) as opposed to perceptually rich (e.g., detailed drawing of bouquet; Gentner & Rattermann, 1991). ...
Article
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The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (Mage = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g., blue-red-blue-red) and others were exposed to abstract labels (e.g., A-B-A-B). Children exposed to abstract labels solved more problems correctly than children exposed to concrete labels. Children's correct adoption of the abstract language into their own descriptions was particularly beneficial. Thus, using concrete learning materials in combination with abstract representations can enhance their utility for children's performance. Furthermore, abstract language may play a key role in the development of relational thinking.
... It is also important to identify the range of situations and contexts to which students' developing skills and understanding should be applicable. Continually varying contexts (which in statistics could be as simple as varying data sets) help hone students' perception and understanding of which features of a situation are critical, and which superficial, for the application of domain knowledge (Gentner 1983;Kellman et al. 2010;Son et al. 2011). When students learn about an abstract idea in one context, it is as if a rubber band is tightly bound around that first learning context. ...
... Research on learning from analogies (superficially dissimilar but structurally parallel instances) provides one example. When learners draw parallels between two cases and practice aligning similar elements across two systems (Gentner et al. 2003;Son et al. 2011), they are better able to transfer their knowledge to superficially dissimilar novel problems (Alfieri et al. 2013). Learning tasks that make relations explicit, while stripping away distracting details, results in more portable and generalizable knowledge (Gentner and Markman 1997;Kaminski et al. 2008;Son et al. 2008;Uttal et al. 2009). ...
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Research suggests that expert understanding is characterized by coherent mental representations featuring a high level of connectedness. This paper advances the idea that educators can facilitate this level of understanding in students through the practicing connections framework: a practical framework to guide instructional design for developing deep understanding and transferable knowledge in complex academic domains. We start by reviewing what we know from learning sciences about the nature and development of transferable knowledge, arguing that connectedness is key to the coherent mental schemas that underlie deep understanding and transferable skills. We then propose features of instruction that might uniquely facilitate deep understanding and suggest that the connections between a domain’s core concepts, key representations, and contexts and practices of the world must be made explicit and practiced, over time, in order for students to develop coherent understanding. We illustrate the practicing connections approach to instructional design in the context of a new online interactive introductory statistics textbook developed by the authors.
... Children become better able to interpret the relation between a symbol and its referent with age, but even older children need cumulative experience with a symbol to use it for sophisticated reasoning (Liben & Myers, 2007). Children are better able to identify the relation between two constructs (or in this case, a concept and a manipulative) when they have multiple opportunities to compare them (Gick & Holyoak, 1983;Son, Smith, & Goldstone, 2011). ...
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Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.
... Relational knowledge was assessed using a Match-To-Sample task used in previous research (Kotovsky & Gentner, 1996;Son, Smith, & Goldstone, 2011) that required children to match picture cards of objects sharing the same relational rule (i.e., A-B-A, A-A-B, or A-B-B). On each trial, children were shown a target card (e.g., big red circle, big white circle, big red circle) and two response cards, one of which shared the relational rule of the target card (e.g., big black square, little black square, big black square) and ...
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Children's knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers’ understanding of repeating patterns. 124 children between the ages of 4 and 5 years were administered a relational knowledge task, 3 EF tasks (working memory, inhibition, set shifting), and a repeating pattern assessment before and after a brief pattern intervention. Relational knowledge, working memory, and set shifting predicted preschoolers’ initial pattern knowledge. Working memory also predicted improvements in pattern knowledge after instruction. The findings indicated that greater EF ability was beneficial to preschoolers’ repeating pattern knowledge, and that working memory capacity played a particularly important role in learning about patterns. Implications are discussed in terms of the benefits of relational knowledge and EF for preschoolers’ development of patterning and mathematics skills.
... The research also has practical implications. To the extent that planning on tower tasks can be construed as relational processing, interventions designed to improve relational processing through for example, structural alignment training (Son et al., 2011;Hribar et al., 2012), use of relational language (Gentner et al., 2011), and techniques to improve access to relational components (e.g., might also have beneficial effects on planning. Thus the findings have the potential to inform cognitive rehabilitation of planning deficits following brain injury due to stroke and other factors. ...
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Planning on the 4-disk version of the Tower of London (TOL4) was examined in stroke patients and unimpaired controls. Overall TOL4 solution scores indicated impaired planning in the frontal stroke but not non-frontal stroke patients. Consistent with the claim that processing the relations between current states, intermediate states, and goal states is a key process in planning, the domain-general relational complexity metric was a good indicator of the experienced difficulty of TOL4 problems. The relational complexity metric shared variance with task-specific metrics of moves to solution and search depth. Frontal stroke patients showed impaired planning compared to controls on problems at all three complexity levels, but at only two of the three levels of moves to solution, search depth and goal ambiguity. Non-frontal stroke patients showed impaired planning only on the most difficult quaternary-relational and high search depth problems. An independent measure of relational processing (viz., Latin square task) predicted TOL4 solution scores after controlling for stroke status and location, and executive processing (Trail Making Test). The findings suggest that planning involves a domain-general capacity for relational processing that depends on the frontal brain regions.
... Recent research shows that simultaneous observation is particularly beneficial to relational learning of concepts. In a study on children, Son, Smith, and Goldstone (2011) find evidence that simultaneous viewing strengthens connections between multiple instances by giving children more time to link instances, whereas during sequential experience those connections are weaker or incomplete. They also argue that sequential viewing requires more working memory because children need to hold both instances in mind to compare them, whereas presenting instances all at once frees up working memory resources for attending to the relational structure. ...
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Recent theory suggests generalists are more likely than specialists to become self-employed. However, little research examines whether different career paths of generalists are equally effective. I argue those experiencing business-related functions in parallel rather than sequentially more likely become self-employed-as a career proceeds over years-because "connections" detected across domains during parallel work experience are particularly valuable in discovery of future opportunities. Yet, positive effects of experiencing domains sequentially are more strongly amplified when individuals are analytically disposed. Analyzing careers of scientists and engineers, SESTAT data broadly support the hypotheses but mostly for male, incorporated, and/or nonacademic entrepreneurial self-employment.
... Finally, we were concerned that a single training example would be ineffective at illustrating an abstract schema. Although a single example proved sufficient in Kelemen et al.'s (2014) (Catrambone & Holyoak, 1989;Christie & Gentner, 2010;Kurtz, Miao, & Gentner, 2001;Son, Smith, & Goldstone, 2011). By comparing examples, learners are able to ignore superficial differences in the examples' content and focus on the more substantive commonalities in their underlying structure. ...
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Research Findings: Evolution by natural selection is often relegated to the high school curriculum on the assumption that younger students cannot grasp its complexity. We sought to test that assumption by teaching children ages 4–12 (n = 96) a selection-based explanation for biological adaptation and comparing their success to that of adults (n = 30). Participants provided explanations before and after a 10-min, analogy-based tutorial illustrating the principles of variation, differential survival, differential reproduction, inheritance, and population change. Although younger children (ages 4–6) showed minimal evidence of learning these principles, older children (ages 7–12) showed robust evidence of doing so, learning them at rates equivalent to adults. Participants of all ages, however, provided nonevolutionary explanations for biological adaptations (i.e., explanations referencing need, growth, and creation) nearly as often at posttest as they did at pretest. Practice or Policy: These results suggest that older elementary school-age children can be taught evolutionary concepts but that learning such concepts does not lead to the automatic replacement of nonevolutionary views of biological adaptation, which must be addressed separately.
... Very little research has focused on the design and implementation of assessing students' ability to connect and translate across concrete and abstract MR. One study on pattern perception in preschool-aged children found that the direction of assessment, in this case an abstract cue with concrete answer choices versus a concrete and perceptually rich cue with abstract answer choices, can affect generalization (Son, Smith, & Goldstone, 2011). Research on the direction of assessment is critical because the way in which we query students defines the scope of understanding that students can demonstrate. ...
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Experts are more proficient in manipulating and translating between multiple representations (MRs) of a given concept than novices. Studies have shown that instruction using MR can increase student understanding of MR, and one model for MR instruction in chemistry is the chemistry triplet proposed by Johnstone. Concreteness fading theory suggests that presenting concrete representations before abstract representations can increase the effectiveness of MR instruction; however, little work has been conducted on varying the order of different representations during instruction and the role of concreteness in assessment. In this study, we investigated the application of concreteness fading to MR instruction and assessment in teaching chemistry. In two experiments, undergraduate students in either introductory psychology courses or general chemistry courses were given MR instruction on phase changes using different orders of presentation and MR assessment questions based on the representations in the chemistry triplet. Our findings indicate that the order of presentation based on levels of concreteness in MR chemistry instruction is less important than implementation of comprehensive MR assessments. Even after MR instruction, students display an asymmetric understanding of the chemical phenomenon on the MR assessments. Greater emphasis on MR assessments may be an important component in MR instruction that effectively moves novices toward more expert MR understanding.
... Some studies have shown improved mathematical performance for children taught using concrete models and manipulatives (see Carbonneau, Marley, & Selig, 2013, for a recent meta-analysis), including base-10 blocks (Fuson & Briars, 1990;Peterson, Mercer, & O'Shea, 1988). Yet, other researchers have reported either no effect of concrete models, effects that fail to transfer, or even performance decrements (Ball, 1992;Goldstone & Sakamoto, 2003;Kaminski & Sloutsky, 2009;McNeil, Uttal, Jarvin, & Sternberg, 2009;Mix et al., 2014;Son, Smith, & Goldstone, 2011;Uttal, Amaya, Maita, Hand, et al., 2013;Vance & Kieren, 1971). It has been argued that concrete models are detrimental because they themselves are symbolic; they introduce extraneous, distracting details; and they lead to entrenched, context-specific learning (Goldstone & Sakamoto, 2003;Kaminski, Sloutsky, & Heckler, 2008;McNeil et al., 2009;Uttal, Scudder, & DeLoache, 1997). ...
Article
Two experiments examined whether concrete models support place value learning. In Experiment 1 (N = 149), 7-year-olds were trained with either (a) symbols alone or (b) symbols and base-10 blocks. Children in both groups showed significant growth overall, but there were specific effects favoring one training type over another. Symbols Only training led to higher scores on a number line estimation task and was particularly effective among high ability students, whereas Blocks training led to better understanding of base-10 structure and was particularly effective among low ability learners. In Experiment 2 (N = 68), Montessori students, for whom concrete models play a major role in mathematics instruction, also demonstrated better understanding of base-10 structure than matched peers enrolled in mainstream elementary schools.
... If young children attend to and process information that is part of the to-be-learned concept and that is extraneous to it, the latter information may become a part of their representations following learning. Therefore, distributed attention may result in an exceedingly rich representation of a to-be-learned concept, thus impeding its generalization and transfer to novel situations (see Kaminski & Sloutsky, 2013;Son, Smith, & Goldstone, 2011, for examples pertaining to a mathematical concept and to properties of a set, respectively). ...
Article
How do people learn categories and what changes with development? The current study attempts to address these questions by focusing on the role of attention in the development of categorization. In Experiment 1, participants (adults, 7-year-olds, and 4-year-olds) were trained with novel categories consisting of deterministic and probabilistic features, and their categorization and memory for features were tested. In Experiment 2, participants’ attention was directed to the deterministic feature, and in Experiment 3 it was directed to the probabilistic features. Attentional cueing affected categorization and memory in adults and 7-year-olds: these participants relied on the cued features in their categorization and exhibited better memory of cued than of non-cued features. In contrast, in 4-year-olds attentional cueing affected only categorization, but not memory: these participants exhibited equally good memory for both cued and non-cued features. Furthermore, across the experiments, 4-year-olds remembered non-cued features better than adults. These results coupled with computational simulations provide novel evidence (1) pointing to differences in category representation and mechanisms of categorization across development, (2) elucidating the role of attention in the development of categorization, and (3) suggesting an important distinction between representation and decision factors in categorization early in development. These issues are discussed with respect to theories of categorization and its development.
... Comparison, the act of examining two like things in conjunction to assess commonalities and differences (Namy & Gentner, 2002), is thought to support transfer by helping learners abstract the key principles and features of the examples so that knowledge is not overly tied to narrow contexts (Goldstone, Day, & Son, 2010;Son, Smith, & Goldstone, 2011). Comparing two examples of a concept can highlight their shared relational structures so that learners can disregard superficial features and create generalized conceptual knowledge (Gentner & Markman, 1997). ...
Article
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Comparison and reminding have both been shown to support learning and transfer. Comparison is thought to support transfer because it allows learners to disregard non-matching features of superficially different episodes in order to abstract the essential structure of concepts. Remindings promote memory for the individual episodes and generalization because they prompt learners to retrieve earlier episodes during the encoding of later related episodes and to compare across episodes. Across three experiments, we compared the consequences of comparison and reminding on memory and transfer. Participants studied a sequence of related, but superficially different, proverb pairs. In the comparison condition, participants saw proverb pairs presented together and compared their meaning. In the reminding condition, participants viewed proverbs one at a time and retrieved any prior studied proverb that shared the same deep meaning as the current proverb. Experiment 1 revealed that participants in the reminding condition recalled more proverbs than those in the comparison condition. Experiment 2 showed that the mnemonic benefits of reminding persisted over a one-week retention interval. Finally, in Experiment 3, we examined the ability of participants to generalize their remembered information to new items in a task that required participants to identify unstudied proverbs that shared the same meaning as studied proverbs. Comparison led to worse discrimination between proverbs related to studied proverbs and proverbs unrelated to studied proverbs than reminding. Reminding supported better memory for individual instances and transfer to new situations than comparison. Electronic supplementary material The online version of this article (doi:10.1186/s41235-016-0028-1) contains supplementary material, which is available to authorized users.
... Young learners find object matches salient (e.g., Rattermann & Gentner, 1998;Richland et al., 2006;Son, Smith, & Goldstone, 2011). In analogy tasks where object and relational matches are pitted against each other, for example in the relational match to sample task (sample AA, choices BB, or AC), a strong preference for object matches (choosing AC) can impede perception of relational similarity (choosing BB) (Christie & Gentner, 2007). ...
Article
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Analogical reasoning is a foundational tool for human learning, allowing learners to recognize relational structures in new events and domains. Here I sketch some grounds for understanding and applying analogical reasoning in social learning. The social world is fundamentally characterized by relations between people, with common relational structures-such as kinships and social hierarchies-forming social units that dictate social behaviors. Just as young learners use analogical reasoning for learning relational structures in other domains-spatial relations, verbs, relational categories-analogical reasoning ought to be a useful cognitive tool for acquiring social relations and structures.
... Indeed, although concrete materials may facilitate initial understanding, learners often struggle to apply that understanding beyond the instructed context. For example, numerous studies have shown that concrete materials hinder transfer to new, dissimilar situations (e.g., Gentner, Ratterman, & Forbus, 1993;Goldstone & Sakamoto, 2003;Kaminski, Sloutsky, & Heckler, 2008;Son, Smith, & Goldstone, 2011). ...
Article
Children often struggle to gain understanding from instruction on a procedure, particularly when it is taught in the context of abstract mathematical symbols. We tested whether a “concreteness fading” technique, which begins with concrete materials and fades to abstract symbols, can help children extend their knowledge beyond a simple instructed procedure. In Experiment 1, children with low prior knowledge received instruction in one of four conditions: (a) concrete, (b) abstract, (c) concreteness fading, or (d) concreteness introduction. Experiment 2 was designed to rule out an alternative hypothesis that concreteness fading works merely by “warming up” children for abstract instruction. Experiment 3 tested whether the benefits of concreteness fading extend to children with high prior knowledge. In all three experiments, children in the concreteness fading condition exhibited better transfer than children in the other conditions. Children's understanding benefits when problems are presented with concrete materials that are faded into abstract representations.
... The relationship between multiple domains (i.e., events, locations, objects, movement, time, sound, color) is iteratively assessed working toward a predicted goal . Where a factor is not productive, it is set aside leaving the remaining "domains" that increasingly acquire meaning in relation to each other and together contribute to the explanation, description or affirmation of a particular truth (Landy and Goldstone 1991, Goel and Dolan 2001, Hummel and Holyoak 2005, Crone, Wendelken et al. 2009, Son, Smith et al. 2010. ...
Chapter
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Fourth World Theory (FWT) emerged in the experience of political leaders and scholars seeking to explain the position of non-state nations and peoples in their political and sometimes violent interactions with other non-state nations and with states' governments that pursue dominance and control over territories and peoples inside claimed boundaries. The conceptual framework of FWT is rooted in the dynamic and evolving relationships between people, the land and the cosmos. Authors explain the globally shared Four Directions metaphor as symbolic of the relational connection of human experience with the land and the cosmos; and how this emblematic instrument blends qualitative, quantitative and relational reasoning to apply knowledge systems that have local, regional and global applications. The authors seek to present a tested conceptual framework that permits one to explain social, economic, political, environmental, strategic and cultural phenomena blending indigenous scientific knowledge with conventional sciences.
... Comparison involves the simultaneous presentation of two examples and the mapping of elements across examples to highlight similarities or differences. For example, in one study, preschoolers were tested on their ability to detect patterns (i.e., ABA) by asking them to match one pattern (e.g., small square, large square, small square) with one of two other patterns (e.g., diamond, circle, diamond versus circle, diamond, diamond; Son et al. 2011). Children who were trained to align and compare the elements in each set were better able to detect and generalize the pattern than children who did not make this direct comparison. ...
Article
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A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and combines their advantages. Specifically, we recommend beginning with concrete materials and then explicitly and gradually fading to the more abstract. Theoretical benefits of this “concreteness fading” technique for mathematics and science instruction include (1) helping learners interpret ambiguous or opaque abstract symbols in terms of well-understood concrete objects, (2) providing embodied perceptual and physical experiences that can ground abstract thinking, (3) enabling learners to build up a store of memorable images that can be used when abstract symbols lose meaning, and (4) guiding learners to strip away extraneous concrete properties and distill the generic, generalizable properties. In these ways, concreteness fading provides advantages that go beyond the sum of the benefits of concrete and abstract materials.
... Relational reasoning, the ability to discern meaningful patterns within any informational stream (Alexander & the Disciplined Reading and Learning Research Laboratory, 2012), has been cited as a critical capacity for learning in both formal and informal settings (Chuang & She, 2013;Gentner, 1989;Son, Smith, & Goldstone, 2011). Indeed, this construct has enjoyed a rich history within the educational psychology canon. ...
Article
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Relational reasoning, the ability to discern meaningful patterns within a stream of information, is considered a critical capacity for students. However, little is known about how this ability is demonstrated by children of different ages in the context of discourse with a more knowledgeable other. Thus, this study sought to investigate the ways in which 4 forms of relational reasoning (i.e., analogy, anomaly, antinomy, and antitheses) manifested in semistructured conversations between a researcher and child about the form and function of more or less familiar objects. Participants were a nationally representative cross-sectional sample of 61 New Zealand primary and secondary students, divided into 3 grade groups: early (Kindergarten through second), middle (fourth through eighth), and late (tenth through eleventh). Results indicated that children as young as 5 years old were capable of using all 4 forms of relational reasoning in discourse. Furthermore, analysis revealed a curvilinear trajectory in the observed versus expected frequencies of relational reasoning among the groups. Finally, in terms of the individual forms of relational reasoning, analogies and anomalies occupied a smaller proportion of relational talk when children were older, whereas antinomies and antitheses occupied a greater proportion. Implications for research and practice are forwarded. (PsycINFO Database Record
... The plausibility of the complex dynamic systems approach for the study of cognitive problem-solving in an activity context has been shown for a variety of problem contexts (examples are Fischer & Bidell, 2006;Mercer, 2011;Schöner & Thelen, 2006;Smith, 2005;Smith & Thelen, 1993;Son, Smith, & Goldstone, 2011;Steenbeek, Jansen, & van Geert, 2012;Street, James, Jones, & Smith, 2011). In the present study, we sought to investigate whether inquiry processes have a number of properties that are characteristic of complex dynamic systems. ...
Article
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From the literature, we know that young children engage in inquiry as an organized activity aimed either at confirming or refuting the relevance of certain ideas. The current study provides a characterization of changes in inquiry using a multiple case study of four 5-year old children. Three computer-based tasks were presented to the children as multivariable problem solving situations concerning moving objects. A description of the temporal unfolding of real-time action on a short-term time scale and long-term time scale of learning and development is provided. The results indicated that the development of inquiry did not follow linear growth but included advances and relapses, exploratory states and transitions. The data were compatible with the view that the child's thinking and acting form a complex dynamic system.
... Afin d'assurer une concordance entre ce que les enseignantes déclarent et ce qu'elles font, plusieurs chercheurs utilisent les observations en classe (Varghese, 2017). Au cours des dernières années, des recherches ont utilisé l'observation directe afin d'évaluer le niveau de la qualité des interactions enseignante-enfants au regard de l'enseignement des mathématiques (Hill et al., 2005;Son et al., 2011;Sullivan et al., 2015;Weiland et Yoshikawa, 2013). À cet effet, les observateurs de l'étude de Weiss et ses collaborateurs (2003) Ces trois sous-tests du WPPSI-III permettent également de mesurer les deux habiletés du raisonnement spatial, soit l'orientation spatiale, et la visualisation et l'imagerie. ...
Thesis
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The purpose of this research is to investigate the relationship between the quality of teacher-child interactions and the development of spatial reasoning among four year old children in full time kindergarten in a disadvantaged environment. The sample is made up on one hand of 415 children data (215 girls, 200 boys) aged 58.29 months (SD=4.93), and on the other hand, it consists of five female teachers holding bachelor’s degree, with an average of 19.6 years of teaching experience (SD=4.3). The study took place over a period of four years, with two measurement times each year (fall and spring). In order to evaluate the quality of teacher-child interactions, the Classroom Assesment Scoring System Kindergarten (CLASS Pre-k) was used (Pianta et al., 2011) and the development of children’s spatial reasoning was evaluated from the Wechsler Preschool and Primary Scale of Intelligence-Third Edition (WPPSI-III) subtests blocks, matrices, and concept images (Gerber, 2015). The results reveal, in particular, that in general the quality of teacher-child interactions is at a medium-high level for the areas of emotional support and classroom organization. With regard to support for learning, it is at a medium-low level. The results also reveal that the level of development of children’s spatial reasoning is at an average score of 98.27 which is comparable to the average of the general population (M=100). In addition, multiple-effect-mixed regression analyzes significantly predicted each of the spatial reasoning variables (WPPSI-III) according to the domains of quality of teacher-child interactions (emotional support, classroom organization, and support learning). These results confirm the conclusions of previous studies on the subject and demonstrate that the quality of teacher-child interactions is very important for the development of spatial reasoning in all children, and particularly in children from disadvantaged backgrounds. Thus, the quality of teacher-child interactions stimulates intellectual curiosity, encourages questioning, exploration and discussion with peers (Wood and Frid, 2005), which favor the development of spatial reasoning. La présente recherche a pour but d’étudier la relation entre la qualité des interactions enseignante-enfants et le développement du raisonnement spatial chez des enfants de la maternelle quatre ans temps plein en milieu défavorisé (TPMD). L’échantillon apparié est composé, d’une part, de 415 données enfants (215 filles, 200 garçons) âgés de 58.29 mois (ÉT=4.93), et d’autre part, de cinq enseignantes titulaires d’un baccalauréat, ayant en moyenne 19.6 ans d’expérience en enseignement (ÉT=4.3). L’étude s’est échelonnée sur une période de quatre ans, avec deux temps de mesure à chaque année (automne et printemps). Afin d’évaluer le niveau de la qualité des interactions enseignante-enfants, l’outil de mesure Classroom Assesment Scoring System Kindergarten (CLASS Pre-k) a été utilisé (Pianta et al., 2011), alors que le développement du raisonnement spatial des enfants a été mesuré à partir des sous-tests blocs, matrices et concepts en images du Wechsler Preschool and Primary Scale of Intelligence-Third Edition (WPPSI-III) (Gerber, 2015). Les résultats révèlent notamment que de façon générale, la qualité des interactions enseignante-enfants se situe à un niveau moyen-élevé pour les domaines du soutien émotionnel et de l’organisation de la classe. En ce qui concerne le soutien à l’apprentissage, il se situe à un niveau moyen-faible. Les résultats révèlent également que le niveau de développement du raisonnement spatial des enfants se situe à un score moyen de 98.27, ce qui est comparable à la moyenne de la population générale (M=100). De plus, des analyses de régressions multiples à effet mixte ont prédit de manière significative chacune des variables du raisonnement spatial (WPPSI-III) en fonction des domaines de la qualité des interactions enseignante-enfants (soutien émotionnel, organisation de la classe et soutien aux apprentissages). Ces résultats vont dans le même sens que les conclusions des précédentes études sur la question et démontrent que la qualité des interactions enseignante-enfants parait déterminante pour le développement du raisonnement spatial chez tous les enfants, et particulièrement chez les enfants issus de milieux qui sont dits défavorisés. Ainsi, la qualité des interactions enseignante-enfants stimule la curiosité intellectuelle, encourage le questionnement, l’exploration et la discussion avec les pairs (Wood et Frid, 2005), ce qui favorise le développement du raisonnement spatial.
... , 3 , (Park, 2015). ABA, BAA (Son et al., 2011) . , Kim (2006) : :: : ? ...
... The present findings demonstrate the importance of considering how the environment shapes hypothesis generation in self-directed conditions. Materials may differ in how they prompt the retrieval of existing concepts from memory (Dougherty, Thomas, & Lange, 2010), encourage consideration of alternative explanations (Van Joolingen & De Jong, 1991), and set the stage for the perception of relevant features or relationships (Christie & Gentner, 2010;Goldstone & Son, 2005;Goldstone, Landy, & Son, 2010;Son, Smith, & Goldstone, 2011). For instance, Christie and Gentner (2010) examined the likelihood of 3-to 4-year-old children discovering a relational feature shared by two stimuli based on whether the stimuli were presented in sequence or simultaneously. ...
Article
Psychologists and educators have long pointed to myriad benefits of self-directed learning. Yet evidence of its efficacy in real-world domains is mixed and it remains unclear how it is constrained by basic perceptual and cognitive processes. Previous work suggests that, in particular, self-directed learning is affected by the way that people generate hypotheses as they learn. This study examines how biased hypothesis generation affects the learning of categorical rules, a basic building block of concept learning, through self-directed selection of training data. In both perceptual and abstract category learning tasks, participants’ hypotheses regarding an unknown classification boundary were influenced by how features were represented. This bias had persistent effects on their ability to learn the underlying categorical relationship despite their opportunity to control the selection of training items. The results demonstrate that self-directed control can be beneficial for both perceptual and abstract category learning, but that the ability to discover rules of a particular form depends on how the learning environment guides the generation of new hypotheses.
... Throughout the lesson, and particularly during the discussion and summarise phase, students will then be given opportunities to make connections between these various representations, and to the underlying mathematical ideas. This is likely to generate an environment conducive to rich mathematical learning, given the abundant opportunities for comparing different approaches and relational reasoning (Rittle-Johnson & Star, 2011;Son et al., 2011). ...
Article
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How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school’s experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically pursuing structured inquiry in a multi-age setting.
... In easy situations, the salient properties are central to defining concepts (Murphy, 2002). However, in many cases, irrelevant superficial and salient similarities or differences can be more cognitively prominent than variations along more relevant dimensions, which has been shown to be challenging in learning conditions with one training stimulus or in situations in which several stimuli are introduced sequentially (Augier & Thibaut, 2013;Lawson, 2017;Son, Goldstone et Smith, 2011). Recent studies have suggested that the opportunity to compare two or more learning exemplars of a target category that are introduced simultaneously lead to better generalization performance than single presentations. ...
Conference Paper
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In this study, 4-year-old children were tested in an object name generalization task with a stimulus comparison design. Performance in the generalization task was correlated with performance in a vocabulary test and three executive function tasks assessing inhibition, flexibility, and working memory. Correlational analyses revealed a significant association with flexibility but not with inhibition, working memory or vocabulary test. We interpret the results in terms of a capacity to flexibly generate novel dimensions rather than inhibiting irrelevant dimensions. Individual differences in working memory and inhibition did not significantly influence performance in the word extension task. Moreover, the absence of correlation with the vocabulary performance supports the idea that children did not rely on existing knowledge to find out the relevant dimension.
... Relational reasoning, the ability to discern meaningful patterns within any informational stream (Alexander & the Disciplined Reading and Learning Research Laboratory, 2012), has been cited as a critical capacity for learning in both formal and informal settings (Chuang & She, 2013;Gentner, 1989;Son, Smith, & Goldstone, 2011). Indeed, this construct has enjoyed a rich history within the educational psychology canon. ...
Article
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For several decades, there has been a push to advance students’ knowledge and abilities in science, technology, engineering, and mathematics (STEM). One capacity that has been linked positively to STEM achievement is relational reasoning, which involves identifying associations between objects, ideas, and situations. Yet, few studies have examined relational reasoning and its component forms (i.e., analogy, anomaly, antinomy, antithesis) within the domain of technology or how these abilities might change over time. The present study explored the development of primary and secondary school students’ relational reasoning over a period of 2 years as they interacted with technological objects. Participants (n = 59) were a subset of a nationally representative random sample between 5 and 18 years old. Students met with a researcher to discuss the form and function of a familiar and unfamiliar technological object at two time points. Results demonstrated that students of all ages used relational reasoning to identify associations between objects’ functionality and form, but that the types and amounts of relational reasoning varied by grade group, time, and object familiarity. This study has implications for researchers and practitioners interested in the development of relational reasoning and technological literacy, and suggests possible ways of enhancing both.
... Finally, we were concerned that a single training example would be ineffective at illustrating an abstract schema. Although a single example proved sufficient in Kelemen et al.'s (2014) (Catrambone & Holyoak, 1989;Christie & Gentner, 2010;Kurtz, Miao, & Gentner, 2001;Son, Smith, & Goldstone, 2011). By comparing examples, learners are able to ignore superficial differences in the examples' content and focus on the more substantive commonalities in their underlying structure. ...
... This work suggests that the general relational shift seen across development may be a consequence of the accumulation of many local shifts that occur within particular content and contexts. For example, comparing multiple examples highlights relational commonalities and supports insights about those relations (e.g., Begolli & Richland, 2016;Christie & Gentner, 2010;Son, Smith, & Goldstone, 2011). Likewise, providing relational labels can help children attend to and represent relational information (e.g., Fyfe, McNeil, & Rittle-Johnson, 2015;Loewenstein & Gentner, 2005). ...
Article
Relational reasoning is a hallmark of human higher cognition and creativity, yet it is notoriously difficult to encourage in abstract tasks, even in adults. Generally, young children initially focus more on objects, but with age become more focused on relations. While prerequisite knowledge and cognitive resource maturation partially explains this pattern, here we propose a new facet important for children's relational reasoning development: a general orientation to relational information, or a relational mindset. We demonstrate that a relational mindset can be elicited, even in 4‐year‐old children, yielding greater than expected spontaneous attention to relations. Children either generated or listened to an experimenter state the relationships between objects in a set of formal analogy problems, and then in a second task, selected object or relational matches according to their preference. Children tended to make object mappings, but those who generated relations on the first task selected relational matches more often on the second task, signaling that relational attention is malleable even in young children.
... We use a variety of representations in our curriculum, but we focus throughout on three that specifically support the connections that create coherent knowledge of statistics. Research on comparison (Namy & Gentner, 2002), symbolic reasoning (Son, Smith, & Goldstone, 2011), and math manipulatives (Uttal, Scudder, & DeLoache, 1997) shows that tying disparate instances to one stable, repeating, relatively abstract instance leads to flexible generalization. ...
Article
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Students learn many concepts in the introductory statistics course, but even our most successful students end up with rigid, ritualized knowledge that does not transfer easily to new situations. In this article we describe our attempt to apply theories and findings from learning science to the design of a statistics course that aims to help students build a coherent and interconnected representation of the domain. The resulting practicing connections approach provides students with repeated opportunities to practice connections between core concepts (especially the concepts of statistical model, distribution, and randomness), key representations (R programming language and computational techniques such as simulation and bootstrapping), and real-world situations statisticians face as they explore variation, model variation, and evaluate and compare statistical models. We provide a guided tour through our curriculum implemented in an interactive online textbook (CourseKata.org) and then provide some evidence that students who complete the course are able to transfer what they have learned to the learning of new statistical techniques.
... This superficial information may capture the learner's attention, diverting it from the less salient relational information that defines the mathematics. Instantiating simple mathematical concepts with perceptually rich, real objects has been shown to hinder very young children's detection of relations (Mix, 1999;Son, Smith, & Goldstone, 2011). For example, 3-and 4year-old children more accurately recognized numerical equivalence between two sets of simple, generic objects than between a set of perceptually rich objects and a set of generic objects (Mix, 1999). ...
Article
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Background There is anecdotal evidence that many elementary teachers integrate mathematics lessons and art activities by having students first make colorful, rich material that is subsequently used in an instructional activity. However, it is unclear whether such activities effectively promote learning and transfer of mathematical concepts. The goal of the present research was to examine the use and effectiveness of such “math-and-art” activities on children’s ability to acquire basic fraction knowledge. We report the results of a survey of practicing elementary school teachers in the United States, their use of activities involving physical material, and the resources they use for ideas to supplement the standard curriculum. Two experiments examined first-grade students’ learning, transfer, and recognition of fraction knowledge from rich, contextualized material versus simple, generic material. Results The survey results confirm that many U.S. teachers use math-and-art activities and are often inspired by informal sources, such as Pinterest and YouTube. Experiment 1 examined the effectiveness of colorful, contextualized student-constructed material (paper pizzas) versus simple, pre-made material (monochromatic paper circles) in an instructional activity on fractions. Students who used the pre-made circles scored higher than those who used the student-made pizzas on pre-instruction tests of basic fraction knowledge, immediate tests of learning, and delayed tests of transfer. Experiment 2 tested students’ ability to spontaneously write fractions to describe proportions of pizzas and circles. Students who answered generic circle questions first were markedly more accurate than those who answered pizza questions first. Conclusions These findings suggest that rich, contextualized representations, including those made by the student, can hinder students’ learning and transfer of mathematical concepts. We are not suggesting that teachers never integrate mathematics and colorful, contextualized material, and activities. We do suggest that elementary students’ mathematics learning can benefit when initial instruction involves simple, generic, pre-made material and opportunities for students to make and use colorful, contextualized representations come later.
... Rapid and far generalization has also been characterized as a form of "generative learning" because the learner seems not to just learn about specifically experienced instances but rather to learn principles through which new instances may be generated (Lake, Linzen, & Baroni, 2019;Son, Smith, & Goldstone, 2012). For example, typically-developing preschool children learning English can generate the regular plural form for a seemingly unlimited number of nouns, needing only one exposure to the singular form of the noun to do so (Berko, 1958;Brown, 1973;Mervis & Johnson, 1991;Treiman, 1993). ...
... Relational reasoning, or the ability to reason about the relationship between objects entities in the environment, is considered a fundamental aspect of intelligence (Krawczyk et al., 2011;Halford et al., 2010). Relational reasoning is known to play a critical role in cognitive growth of children (Son et al., 2011;Farrington-Flint et al., 2007;Richland et al., 2010). This ability to infer relations between Figure 1. ...
Preprint
Recent research has highlighted the role of relational inductive biases in building learning agents that can generalize and reason in a compositional manner. However, while relational learning algorithms such as graph neural networks (GNNs) show promise, we do not understand how effectively these approaches can adapt to new tasks. In this work, we study the task of logical generalization using GNNs by designing a benchmark suite grounded in first-order logic. Our benchmark suite, GraphLog, requires that learning algorithms perform rule induction in different synthetic logics, represented as knowledge graphs. GraphLog consists of relation prediction tasks on 57 distinct logical domains. We use GraphLog to evaluate GNNs in three different setups: single-task supervised learning, multi-task pretraining, and continual learning. Unlike previous benchmarks, our approach allows us to precisely control the logical relationship between the different tasks. We find that the ability for models to generalize and adapt is strongly determined by the diversity of the logical rules they encounter during training, and our results highlight new challenges for the design of GNN models. We publicly release the dataset and code used to generate and interact with the dataset at https://www.cs.mcgill.ca/~ksinha4/graphlog.
... Both research groups found that children demonstrated fewer learning gains under such 'perceptually rich' conditions. Thus, children demonstrate persistent difficulties in overcoming distractions, and this difficulty may impede their learning (see also Kaminski & Sloutsky, 2013b;Son, Smith, & Goldstone, 2011). ...
Article
Selective attention is fundamental for learning across many situations, yet it exhibits protracted development, with young children often failing to filter out distractors. In this research, we examine links between selective attention and working memory (WM) capacity across development. One possibility is that WM is resource‐limited, with development resulting in an increase in the amount of resources available for processing information. However, it is also possible that development results in greater efficiency of using available resources. In the current research, we explore the latter possibility by examining the developmental trajectory of selectivity and filtering in relation to WM capacity. We report that filtering efficiency of adults (N = 30), 7‐year‐olds (N = 29), and 4‐year‐olds (N = 28) was uniquely predictive of WM capacity. We also report that filtering efficiency continues to develop after 7 years of age, whereas WM capacity may reach an asymptote around 7 years of age. The latter finding suggests that selective attention plays a critical role in developmental and individual differences in visual working memory capacity. We examined links between selective attention and working memory (WM) capacity across development. We report that filtering efficiency of adults (N = 30), 7‐year‐olds (N=29), and 4‐year‐olds (N=28) was uniquely predictive of WM capacity. We also report that filtering efficiency continues to develop after 7‐years of age, whereas WM capacity may reach an asymptote around 7‐years of age. The latter finding suggests that selective attention plays a critical role in developmental and individual differences in visual working memory capacity.
... However, literature makes it clear that if the mapping is not supported, it does more harm than it helps [2,21]. Fyfe [29] suggests that this sequential presentation approach is what differentiates concreteness fading from other approaches-that present multiple representations simultaneously and highlight the similarities and differences for mapping [62,73]and that it plays an important role in the fading progression by reinforcing the notion that the representations at each stage are mutual referents possessing the same set of invariant relations. ...
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The role of relational similarity in 3-year-old children’s understanding of the relation between a scale model and the space it represents was investigated in two studies. Relational similarity was manipulated by arranging the objects within the two spaces in either the same or different configurations; thus, the internal relations among the objects were either identical or very different. The pattern of results across studies revealed that multiple factors interacted to determine the children’s appreciation of the higher-level model–room relation. When other information about the model–room relation was provided via explicit instructions (Experiment 1), relational similarity did not affect performance. However, relational similarity did have a significant effect on performance when only minimal information regarding the model–room relation was given (Experiment 2). These results established that the children were sensitive to the relations among the objects within each space, as well as to whether those relations were similar across spaces. Furthermore, the results indicated that successful performance was supported by appreciation of the higher-level model–room relation, not merely the detection of individual object correspondences.
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4 experiments investigated the development of children's ability to recognize perceptual relational commonalities such as symmetry or monotonicity. In Experiment 1, 6- and 8-year-olds were able to recognize higher-order relational similarity across different dimensions (e.g., size/saturation) and across different polarities (e.g., increase/decrease), whereas 4-year-olds could recognize higher-order relational matches only when they were supported by lower-order commonalities (e.g., size/size but not size/saturation matches). Further experiments tested how the processes of comparison and categorization affected 4-year-olds' ability to recognize relational similarity. The results of the experiments supported the hypothesis that comparison and categorization processes lead to changes in children's representations of relational structure, enabling them to recognize more abstract commonalities. A computational model lent further support to the claims.
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Intelligent tutoring systems are highly interactive learning environments that have been shown to improve upon typical classroom instruction. Cognitive Tutors are a type of intelligent tutor based on cognitive psychology theory of problem solving and learning. Cognitive Tutors provide a rich problem-solving environment with tutorial guidance in the form of step-by-step feedback, specific messages in response to common errors, and on-demand instructional hints. They also select problems based on individual student performance. The learning benefits of these forms of interactivity are supported, to varying extents, by a growing number of results from experimental studies. As Cognitive Tutors have matured and are being applied in new subject-matter areas, they have been used as a research platform and, particularly, to explore interactive methods to support metacognition. We review experiments with Cognitive Tutors that have compared different forms of interactivity and we reinterpret their results as partial answers to the general question: How should learning environments balance information or assistance giving and withholding to achieve optimal student learning? How best to achieve this balance remains a fundamental open problem in instructional science. We call this problem the “assistance dilemma” and emphasize the need for further science to yield specific conditions and parameters that indicate when and to what extent to use information giving versus information withholding forms of interaction.
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Despite a large literature on infants' memory for visually presented stimuli, the processes underlying visual memory are not well understood. Two studies with 4-month-olds (N†=†60) examined the effects of providing opportunities for comparison of items on infants' memory for those items. Experiment 1 revealed that 4-month-olds failed to show evidence of memory for an item presented during familiarization in a standard task (i.e., when only one item was presented during familiarization). In Experiment 2, infants showed robust memory for one of two different items presented during familiarization. Thus, infants' memory for the distinctive features of individual items was enhanced when they could compare items.
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This paper is concerned with some of the factors that determine the difficulty of material that needs to be learned. It is suggested that when considering intellectual activities, schema acquisition and automation are the primary mechanisms of learning. The consequences of cognitive load theory for the structuring of information in order to reduce difficulty by focusing cognitive activity on schema acquisition is briefly summarized. It is pointed out that cognitive load theory deals with learning and problem solving difficulty that is artificial in that it can be manipulated by instructional design. Intrinsic cognitive load in contrast, is constant for a given area because it is a basic component of the material. Intrinsic cognitive load is characterized in terms of element interactivity. The elements of most schemas must be learned simultaneously because they interact and it is the interaction that is critical. If, as in some areas, interactions between many elements must be learned, then intrinsic cognitive load will be high. In contrast, in different areas, if elements can be learned successively rather than simultaneously because they do not interact, intrinsic cognitive load will be low. It is suggested that extraneous cognitive load that interferes with learning only is a problem under conditions of high cognitive load caused by high element interactivity. Under conditions of low element interactivity, re-designing instruction to reduce extraneous cognitive load may have no appreciable consequences. In addition, the concept of element interactivity can be used to explain not only why some material is difficult to learn but also, why it can be difficult to understand. Understanding becomes relevant when high element interactivity material with a naturally high cognitive load must be learned.
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Around the age of 18 months, children begin to classify objects spatially by kind, placing objects of the same kind close together in space and placing unlike objects apart. This behavior may be symbolic in the sense that children use spatial proximity to represent similarity. We examined the possibility that spatial classification is discovered during play—that the external products of play lead children to use space to represent similarity. Experiment 1 was a longitudinal study of four children's classification behaviors, observed from the age of 16 to 21 months. Results suggest that play with one kind of object to the exclusion of another kind leads to the discovery of spatial classification. Experiment 2 examined how children's tendencies to interact with one category might promote spatial classification of multiple categories. Twenty-four 18-month-old children who did not yet spatially classify objects by kind participated. Children who were given the experience of playing with two kinds of objects in a context that promoted interaction with only one kind were more likely to demonstrate spontaneous spatial classification of multiple kinds in a subsequent test period. Children who played equally with both kinds did not show heightened spontaneous classification. The results further suggest that comparison of different kinds during play is critical to the spontaneous occurrence of spatial classification.
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This paper describes the development of number concepts from infancy to early childhood. The results of a diary study on a child’s one-to-one correspondence activities from 12 to 38 months of age are presented. The diary study suggested that social activities, such as distributing objects to people, play a greater role in early numerical development than conservation-like activities, such as matching object sets. There also was evidence that early number concepts are highly context-dependent. Specifically, although this child represented and matched equivalent sets in a few highly constrained contexts, he could not do so in others. An alternative to the competence–performance distinction is developed for explaining such cross-task variability.
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This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distinction between concrete and abstract forms of mathematical expression may not be justified. We believe instead that manipulatives are also symbols; teachers intend for them to stand for or represent a concept or written symbol. Consequently, research on how young children comprehend symbolic relations is relevant to studying their comprehension of manipulatives. We review evidence that many of the problems that children encounter when using manipulatives are very similar to problems that they have using other symbol systems such as scale models. Successful use of manipulatives depends on treating them as symbols rather than as substitutes for symbols.
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A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.
Article
Recent research on children's word learning has led to a paradox. Although word learning appears to be a deep source of insight into conceptual knowledge for children, preschoolers often categorize objects on the basis of shallow perceptual features such as shape. The current studies seek to resolve this discrepancy. We suggest that comparing multiple instances of a category enables children to extract deeper relational commonalities among category members. We examine 4-year-olds' categorization behaviors when asked to select a match for a target object (e.g., an apple) between a perceptually similar, out-of-kind object (e.g., a balloon) and a perceptually different category match (e.g., a banana). Children who learn a novel word as a label for multiple instances of the category are more likely to select the category match over the perceptual match. Children who learn a label for only one instance are equally likely to select either alternative. This effect is present even when individual target instances are more perceptually similar to the perceptual choice than to the category choice. We conclude that structural alignment processes may be important in the development of category understanding.
Article
This research investigates the development of analogy: In particular, we wish to study the development of systematicity in analogy. Systematicity refers to the mapping of systems of mutually constraining relations, such as causal chains or chains of implication. A preference for systematic mappings is a central aspect of analogical processing in adults ( [20] and [21]). This research asks two questions: Does systematicity make analogical mapping easier? And, if so, when, developmentally, do children become able to utilize systematicity? Children aged 5–7 and 8–10 acted out stories with toy characters. Then they were asked to act out the same stories with new characters. Two variables were manipulated: systematicity, or the degree of explicit causal structure in the original stories, and the transparency of the object-mappings. Transparency was manipulated by varying the similarity between the original characters and the corresponding new characters: it was included in order to vary the difficulty of the transfer task. If children can utilize systematicity, then their transfer accuracy should be greater for systematic stories. The results show: (1) As expected, transparency strongly influenced transfer accuracy (for both age groups, transfer accuracy dropped sharply as the object correspondences became less transparent); and (2) for the older group, there was also a strong effect of systematicity and an interaction between the two variables. Given a systematic story, 9-year-olds could transfer it accurately regardless of the transparency of the object correspondence.
Article
Four experiments examined the hypothesis that simple attributional features and relational features operate differently in the determination of similarity judgments. Forced choice similarity judgments (“Is X or Y more similar to Z?”) and similarity rating tasks demonstrate that making the same featural change in two geometric stimuli unequally affects their judged similarity to a third stimulus (the comparison stimulus). More specifically, a featural change that causes stimuli to be more superficially similar and less relationally similar increases judged similarity if it occurs in stimuli that already share many superficial attributes, and decreases similarity if it occurs in stimuli that do not share as many superficial attributes. These results argue against an assumption of feature independence which asserts that the degree to which a feature shared by two objects affects similarity is independent of the other features shared by the objects. The MAX hypothesis is introduced, in which attributional and relational similarities are separately pooled, and shared features affect similarity more if the pool they are in is already relatively large. The results support claims that relations and attributes are psychologically distinct and that formal measures of similarity should not treat all types of matching features equally.
Article
A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure-mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons. Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher-order relations.