The Linear Imperative: An Inventory and Conceptual Analysis of Students' Overuse of Linearity

Abstract

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it in a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use linear methods beyond their applicability range. We start from an analysis of the linearity concept and its properties and representations. The main part consists of a summary and discussion of unwarranted applications of each of these properties and representations in various mathematical content domains in order to unravel similarities and differences. After that, we speculate on the factors that seem to be at the roots of the occurrence and persistence of the overreliance on linearity. Finally, we discuss educational implications and suggest perspectives for further research.