Struggling with variables, parameters, and indeterminate objects or how to go insane in mathematics

Pursuing our investigation on students’ use and understanding of algebraic notations, this paper examines students’ cognitive difficulties related to the designation of an indeterminate but fixed object in the context of the generalization of patterns. Stressing the semiotic affinities and differences between unknowns, variables and parameters, we examine a Grade 11 mathematical activity in which the core of the students’ relationship to algebraic formula comes to light. We show how the semiotic problem of indeterminacy reveals the frailty of students’ understanding of algebraic formulas and how it puts into evidence the limited scope of the use of formulas as schemas, strongly rooted in student’s relationship to algebra.