The Predominance of the Linear Model in Secondary School Students' Solutions of Word Problems Involving Length and Area of Similar Plane Figures

Linear (proportional) functions are undoubtedly one of the most common models for representing and solving both pure and applied problems in elementary mathematics education. But according to several authors, different aspects of the current culture and practice of school mathematics develop in students a tendency to use these linear models also in situations in which they are not applicable. This article reports two closely related studies about this phenomenon in 12–13- and 15–16-year old students working on word problems involving lengths and areas of similar plane figures of different kinds of shapes, as well as about the influence of drawings in breaking this improper use of linearity. Generally speaking, the results provide a convincing demonstration of the predominance of the linear model in secondary students' solutions of this kind of mensurational problem.