Abstract

Young children‟s performance on certain mapping tasks can be improved by introducing relational language (Gentner, 1998). We show that children‟s performance on a spatial mapping task can be modeled using the Structure-Mapping Engine (SME) to simulate the comparisons involved. To model the effects of relational language in our simulations, we vary the quantity and nature of the spatial relations and object descriptions represented. The results reproduce the trends observed in the developmental studies of Loewenstein & Gentner (1998; in preparation). The results of these simulations are consistent with the claim that gains in relational representation are a major contributor to the development of spatial mapping ability. We further suggest that relational language can promote relational representation. 1 Computer Science Department 2 Psychology Department Introduction Spatial reasoning is one of the core abilities in human cognition. An important test of spatial reasoning is the mapping task (DeLoache, 1987, 1995; Huttenlocher, Newcombe, & Sandberg, 1994; Uttal, Schreiber, & DeLoache, 1995; Uttal, Gregg, Tan, Chamberlin, & Sines, submitted). In a mapping task, the goal is to find a correspondence between two different spatial situations. In DeLoache‟s classic task, a child is shown two rooms, similar in layout and furniture (though not necessarily in size). A toy is hidden in one room and the child must look for another toy in the corresponding place in the other room (e.g., DeLoache, 1995). It has been proposed (Gentner & Rattermann, 1991) that the same process of structural alignment that is used in analogy and similarity may play a role in spatial mapping tasks. That is, spatial mapping tasks can be viewed as a kind of analogy in which the spatial relationships of the situations involved provide the base and target descriptions for the structural alignment, and the correspondences computed in structural alignment provide the basis for inferring the correct answer. This paper provides evidence for the role of structural alignment in spatial mapping tasks. We show how the pattern of developmental results found by Loewenstein and Gentner (1998, in preparation) can be modeled using SME (the Structure-Mapping Engine (Falkenhainer, Forbus, & Gentner, 1989; Forbus, Ferguson, & Gentner 1994)) a simulation of Gentner‟s (1983) structure-mapping theory. We start by describing Loewenstein and Gentner‟s spatial mapping task. Next we describe how we used SME to model the results. Spatial Mapping Tasks Mapping and symbolic reference is ubiquitous in adult daily life, but it develops only gradually in children. Studies by Blades and Cooke (1994), DeLoache (1995), Uttal (Uttal, Schreiber, & DeLoache, 1995), and others have shown that preschool children have great difficulty with the seemingly simple task of finding an object in the „same place‟ as an object in an almost identical model, even though they can easily retrieve the original hidden object. Gentner and her colleagues have suggested that one contribution to the great gains children make in their performance on spatial mapping tasks is relational knowledge, and further, that acquiring relational language promotes this relational knowledge (Gentner & Loewenstein, in preparation; Gentner & Rattermann, 1991; Gentner, Rattermann, Kotovsky, & Markman, 1995; Kotovsky & Gentner, 1996; Loewenstein & Gentner, 1998). Experiment 1. The first study (Loewenstein & Gentner, 1998) used the setup in the left of Figure 1, with neutral appearances for the cards. Three cards are placed on, in, and under the Hiding box. The instructions given in the baseline condition avoided language that used spatial relationships. During the orientation trial, the experimenter said “I‟m putting the winner right here” while placing the card in its location at the Hiding box. The instructions in the language condition used spatial relationships during the orientation task to describe where the cards were being placed: The experimenter said, “I‟m putting the winner [in/on/under] the box.” For both conditions, no language was used in the finding task: The Experimenter gestured generally towards the Finding box, saying “Can you find the winner here, in the very same place?” In the baseline condition, 44-month-olds found the sticker only 42% of the time, not significantly above chance performance of 33%. However, in the language condition, they performed far better, finding the winner 70% of the time (see Figure 2, left). The 49-month-olds performed fairly well in both the baseline (63%) and language (73%) conditions. It appears that hearing spatial relational terms led the younger children to form stronger representations of the spatial relational structure. Experiment 2. Gentner and Loewenstein (in preparation) use a similar task as in Experiment 1, but the three cards associated with a box were all distinctive and unique, as shown in Figure 1. While there is an exact object match for each card, the cards that match in appearance have different spatial relationships with the box. For example, the card that is ON the Hiding box matches the card that is IN the Finding box. This is an example of a cross-mapping task (Gentner & Toupin, 1986; Gentner & Rattermann, 1991), in which object similarity is pitted against relational similarity. Such tasks are useful in testing for the availability and salience of the child‟s relational knowledge. The results bore out previous findings that cross-mapping tasks are difficult: 49-month-olds were at chance at finding the winner in both conditions. Even 62-month-olds were correct only 53% of the time in the baseline condition. However, in the language condition, when given the spatial relation during the hiding task, their performance improves to 73% correct (see Figure 2, right). These results suggest the following conjectures: Age-related improvements are largely due to improved understanding of spatial relationships. Relational language highlights spatial relationships, supporting children‟s relational mapping abilities. This pattern of results is consistent with other findings on the role of relational language in domain learning (e.g., Gentner & Rattermann, 1991; Gentner, Rattermann, Markman & Kotovsky, 1995; Kotovsky & Gentner, 1996), and lends evidence to the position that relational language fosters the development of relational thought (Gentner, 1998). Modeling Spatial Mapping as Visual Comparisons The spatial mapping task above involves encoding descriptions of the hiding box and the finding box and comparing these descriptions to predict, based on the location of the winner in the hiding box, where the winner will be in the finding box. Since we are modeling the comparison process via structure-mapping, we first briefly review structure-mapping theory and SME. Review of Structure-Mapping According to structure-mapping theory, the process of structural alignment takes as input two structured representations (base and target) and produces as output a set of Language