Intuitions on functions

A theoretical model is presented for commencing a systematic assessment of students’ intuitions on the mathematical notion of functions. This model considers functions in terms of a three-dimensional block, with specific function settings running along its x-axis, function topics running along its y-axis, and levels of abstraction running along its z-axis. Questionnaire booklets assessing specific notions of a function were written and administered to 127 junior high school students. It was found that high ability students tended toward a graphical approach to the notions, while low ability students were attracted to pictorial and tabular presentations of the notions. The model and its implications are discussed.