Abstract

Modeling Learning via Progressive Alignment using Interim Generalizations Subu Kandaswamy ([email protected]) Kenneth D. Forbus (forbus@ northwestern.edu) Qualitative Reasoning Group, Northwestern University, 2133 Sheridan Road Evanston, IL 60208 USA Dedre Gentner (gentner@ northwestern.edu) Department of Psychology, Northwestern University, 2029 Sheridan Road Evanston, IL 60208 USA Abstract There is ample empirical evidence that children can sometimes learn during the course of even a few experimental trials. We propose that one mechanism for this is the use of analogical generalizations constructed in working memory, producing what we call interim generalizations. Prior research suggests that such generalizations can be constructed when there is high similarity between closely spaced items. This paper describes how structure-mapping simulations can be adapted to capture this phenomenon, using automatically encoded stimuli. It is an advance over prior models in that it automatically detects when rerepresentation should be tried and carries it out to improve its performance. Keywords: Analogy; Computational modeling; Symbolic Modeling; Cognitive Development. Introduction People have relational comparison capacities that seem to outstrip any other primate (Gentner, 2003; Penn, Holyoak & Povinelli, 2008). Yet young children are prone to focus on object matches rather than relational matches. The Relational Shift hypothesis (Gentner & Rattermann, 1991) suggests that this difference is due to a lack of knowledge about relational structures in younger children, and that as they learn more, they gain the ability to make more relational matches. Indeed, there is evidence that, under the right conditions, preschool children can learn to carry out relational matches. In one such study, modeled here, Kotovsky & Gentner (1996) explored children’s performance on comparison tasks involving simple higher-order patterns, such as symmetry and monotonic increase (Figure 1). In each triad, the top figure is the standard, and the bottom two figures are the choices from which a participant must pick. One choice always has the same higher-order relationship between its entities as does the standard, while the other has the same entities as the relational choice, but permuted so that the relationship does not apply. The triads in Figure 1 illustrate the 2x2 manipulation, namely the polarity (same or opposite) of the higher-order relation and the dimension (size or brightness) over which the relationship holds. Children were asked to choose which one of bottom choices was most like the top one. No feedback was given at any time. However, some easy high-similar triads were provided as check trials. The Relational Shift hypothesis predicts that older children will do better than younger children, and that all children will do better when there are lower-order commonalities supporting the higher-order commonalities. The results were consistent with these predictions: 4 year olds performed below chance on all but the same dimension/same polarity stimuli, where they were above chance. By contrast, 6 year old and 8 year old children were able to see the relational pattern to some degree without the support of first-order relational overlap, but better with it. The cross dimension/opposite polarity case was the hardest condition, even for eight year olds. Yet some children discovered this match over the course of the study. As Kotovsky & Gentner (1996) remark: “The emerging appreciation of relational commonality can be seen in this comment by an eight year old, who after struggling with her first several cross-dimension matches, then excitedly articulated a startlingly apt description of relational similarity: “It’s exactly the same, but different!” She proceeded to choose relationally for all the remaining triads” Figure1: An example of four types of triads for a size symmetry standard How can we explain such learning within less than 20 trials, without feedback? It requires that a child be able to detect that they do not know a good answer. There is informal evidence for this in that children in the study often puzzled over the cross-dimensional triads, saying things like “A dark one and a big one make daddies. The other one has two twins and a daddy on the side.” Children further need to figure out ways to rerepresent the stimuli so that the choice