Development of intuitive and numerical proportional reasoning

Abstract

The relationship between intuitive and numerical proportional reasoning was examined using a temperature-mixing task with fifth graders, eighth graders, and college students. In the intuitive task the temperatures and quantities were described verbally, whereas in the numerical task, numbers were used and subjects were instructed to try to use math. Half the subjects were given the intuitive version first, and half were given the numerical version first. To the extent that subjects are capable of using their intuitive knowledge to direct their numerical performance, performing the intuitive version first should make intuitive knowledge more salient and improve performance on the numerical task. Performance in the numerical condition depended on the task-order manipulation, but performance in the intuitive condition was almost the same in the two task orders. Five components were used to generate a profile representing each person's performance on each task version. Subjects were grouped according to the degree of similarity of their component profiles to several hypothesized, qualitatively different prototype patterns. This “fuzzy set” analysis showed that the frequencies of subjects showing different patterns varied across versions of the task and were age related. Performing the intuitive version first decreased the likelihood that numerical temperature would be treated as an extensive rather than an intensive quantity. A theoretical framework is outlined for the relationship between intuitive and numerical task performance.