The Notion of Compartmentalization: The Case of Richard

One of the important phenomena observed in the learning of mathematics is compartmentalization. This phenomenon occurs when a learner has two different, potentially contradictory schemes in his or her cognitive structure; in a typical case, a student deals with the same mathematical concept in an inconsistent or incoherent way, or activates a less relevant scheme to the situation in his or her mind. This research reports a case of compartmentalization phenomenon in which Richard, a tenth-grade algebra honours student, was interviewed on quadratic tasks. Results show evidence for the existence of compartmentalization related to the vertex of a parabola. The article concludes with some suggested educational implications. (Contains 4 figures.)