ABSTRACT
This chapter deals with the learning of higher-order algebraic concepts, namely, equations in two variables, their graphs, and the notion of function. New cognitive structures must be constructed, and the process of accommodation may necessarily confront the student with major cognitive obstacles. The notion of cognitive obstacle is a promising one, with many pedagogical implications. From the Piagetian perspective, the acquisition of knowledge is a process involving a constant interaction between the learning subject and his or her environment. The impact of a formal approach to the teaching of functions was investigated in the late sixties at the height of the "new math" movement. In the most general sense, cognitive obstacles can be identified with learning difficulties that are not of an idiosyncratic nature, but whose occurrence is widespread. Three distinct sources have been described in this survey: obstacles induced by instruction, obstacles of an epistemological nature, and obstacles associated with the learner's process of accommodation.
