| Abstract: | The development of proportional reasoning was examined using a temperature mixture task. Each individual's task understanding was assessed by components measuring understanding of various principles of the task. Age differences were found in the mean component scores. More important, different patterns of components were found depending on whether the task was presented numerically or nonumerically. Component patterns also depended on whether the task was presented such that subjects predicted the outcome of combining 2 containers of water at different temperatures (prediction task) or such that subjects inferred 1 of the 2 initial temperatures given the final temperature (reverse task). The results show the importance of distinguishing between intuitive knowledge and formal computational knowledge of proportional concepts and provide a new perspective on how intuitive and computational knowledge are related during development. Finally, the results also led to a new conceptualization of developmental levels as categories with fuzzy boundaries. Under this conceptualization, individuals can have different degrees of membership in "fuzzy developmental levels." This new concept preserves individual differences but also describes the sequence of development. |
