Comparison and Categorization in the Development of Relational Similarity

Abstract

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 higherorder 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 I 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.1 The relational shift is not a shift away from object similarity; even adults find it easier to process overall similarity (that includes object matches as well as relational matches) than to process pure analogy, and there is evidence that object matches are processed before relational matches (Goldstone & Medin, 1994; Markman & Gentner, 1996).2 These levels of similarity are more precisely defined using a propositional representation. Attributes are defined as predicates taking one argument (e.g., BIG [a]), and relations as predicates taking two or more arguments (e.g., BIGGER [a,b];Gentner, 1983Gentner, , 1989Palmer, 1975). The difference between first-order and higher-order relations is that first-order relations take objects or functions as arguments, and higher-order relations take propositions as arguments. That is, a higher-order relation is a relation between relations. Using this representation, object similarity involves a match at the level of attributes, lower-order relational similarity involves a match at the level of first-order relations, and higher-order relational smilarity involves a match at the level of higher-order relations.

Detecting anomalous features in complex stimuli: The role of structured comparison.

“…processing (e.g., Gentner et al, 2011;Kotovsky & Gentner, 1996;Markman & Gentner, 1993a), we would expect that the kinds of skeletal configurations that are highlighted as in previous comparisons would be more likely to be picked out in new cases. Such effects may be similar to chess experts' use of their knowledge of allowable spatial configurations in chess to quickly and accurately identify violations (Chase & Simon, 1973).…”

“…Going further, structure-mapping theory could be used to develop design principles for using comparison to accelerate learning in complex pattern-detection tasks. Borrowing techniques from developmental studies, training sequences could be designed to use progressive alignment, beginning with highly alignable pairs and progressing through less alignable pairs (Gentner et al, 2007(Gentner et al, , 2011Haryu et al, 2011;Kotovsky & Gentner, 1996;Thompson & Opfer, 2010). Other possibilities could also be investigated, such as permitting learners to store items (such as ideal exemplars or borderline cases) that they wish to use in future comparisons.…”

Developmental Continuity in the Link Between Sensitivity to Numerosity and Physical Size

“…In particular, the process of comparison may promote the recognition of the structural similarities between prothetic magnitude dimensions (Gentner & Medina, 1998). Older children, for example, readily match relational similarity (e.g., increasing monotonic order) both within and across perceptual dimensions, whereas younger children succeed only at same-dimension matches (Kotovsky & Gentner, 1996). However, when younger children are given practice with same-dimension matches before being asked to perform cross-dimension matches, they then succeed at making cross-dimension matches, suggesting that experience with same-dimension matches facilitates children's recognition of abstract relational rules that can be applied across perceptual dimensions.…”

Exploring the conceptual universe.

“…Feature alignment may also be possible in domains that do not rely on additive features. For example, learners may find it natural to align a size feature (big/small) with a volume feature (loud/soft) because the values of both features indicate quantities of some kind (L. Kotovsky & Gentner, 1996). Characterizing the full set of cases where features can be aligned is a challenge for future work, and addressing this challenge will help to explain how people think about the full set of domains in the conceptual universe (see Table 2).…”