Intuitive Functional Concepts: A Baseline Study on Intuitions

The intuitions that junior high school students have on selected functional concepts were investigated. The concepts were presented on an abstract and a concrete level, in arrow diagrams, graphical, and tabular settings. The investigation was carried out with reference to a theoretical framework for the study of intuitions and transfer of functional concepts. In this framework, the concept of function was analyzed as corresponding to a 3-dimensional block structure as follows: The function settings correspond to the x-axis of the block, the function concepts to the y-axis, and the levels of abstraction of the concepts to the z-axis. The subjects were 443 students in Grades 6-9 chosen from differing social and ability levels. Different populations were found to possess different intuitions on the concepts, but these intuitions were independent both of the settings in which they were presented and of the levels of abstraction.