On differentiation: A case study of the development of the concepts of size, weight, and density

This paper presents a case study of 3- to 9-year-old children\u27s concepts of size, weight, density, matter, and material kind. Our goal was to examine two claims: (1) that individual concepts undergo differentiation during development; and (2) that young children\u27s concepts are embedded in theory-like structures. To make progress on the first issue, we needed to specify in representational terms what an undifferentiated concept is like and in what sense this undifferentiated concept is a parent of the more differentiated concepts. Our strategy was to use a model of conceptual differentiation suggested by the history of science to guide our search for evidence. In this model, undifferentiated concepts, like differentiated concepts, can be analyzed in terms of their component properties, features, or dimensions. The key difference is that an undifferentiated concept unites certain components which will subsequently be analyzed as components of distinct concepts, and that the undifferentiated concept is embedded in a different theoretical structure from the differentiated concepts. In our study, the same group of 78 children (18 3-year-olds, 18 4-year-olds, 18 5-year-olds, 12 6-7-year-olds, and 12 8-9-year-olds) were given a range of tasks probing their understanding of size, weight, and density; a subgroup of these children were given additional tasks probing their concepts of matter and material kind. We found that young children had a theoretical system which included distinct concepts of size, weight, and material kind and were beginning to form generalizations relating these concepts (e.g., size is crudely correlated with weight, steel objects are typically heavy). The core of their weight concept was felt weight, with density absent from their conceptual system; material kinds were defined in terms of properties which characterize large scale chunks of stuff. Slightly older children (5-7-year-olds) had made modifications to their concepts of weight and material kind. At these ages, their concept of weight now contained both the properties heavy and heavy for size (which we take as evidence of their having an undifferentiated weight/density concept) and they were coming to see weight differences as important in distinguishing whether large-scale objects were made of the same kind of stuff. However, the core of their weight concept was still felt weight and material kinds were still defined in terms of properties of large scale objects. Finally, still older children (8-9-year-olds) had a theoretical system in which weight and density were articulated as distinct concepts, material kinds were reconceptualized as the fundamental constituents of objects, and weight was seen as a fundamental property of matter. We conclude that children\u27s concepts of weight and density do differentiate in development and that it does make sense to view children\u27s concepts in the context of theory-like structures. © 1985