The Manipulation of Algebraic Expressions: Deepening of a Widespread Difficulties and New Characterizations

The learning of algebra represents a difficulty within the mathematics learning process. Precisely because of their epistemological and ontological nature, semiotics provides a good key to understanding the main difficulties that hinder the learning of algebraic objects. The answers to a large scale assessments task that requires a treatment in the sense of Duval of sizeable sample of upper secondary school student is analysed. Statistical analysis allows the nationwide data to be considered according to students’ ability levels. The study confirms and quantifies the distance between personal meaning and the cultural meaning attributed to algebraic objects. The difficulties of the manipulation of algebraic expressions is deepened and characterized.