Université Catholique de Louvain / Katholieke Universiteit Leuven
History and Epistemology in Mathematical Education. From play school to university. Proceedings of the 3rd European Summer University on History and Epistemology in Mathematical Education vol:1 pages:153-167
European Summer University on History and Epistemology in Mathematical Education edition:3 location:Louvain-la-neuve and Leuven date:15-18 July and 18-21 July 1999
Linear (proportional) functions are undoubtedly one of the most common models for representing and solving both pure and applied problems in 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. In this paper, we first present some historical examples of and comments on this "illusion of linearity". Second, we briefly discuss the results of five recent empirical studies about the occurrence of this phenomenon in 12-16-year old students working on problems about the relation between the linear measurements, the area and/or the volume of similar geometrical figures, as well as about the effect of several task variables on this improper use of linearity. Finally, we analyse the connection between this linear illusion and other intuitive rules and erroneous ways of thinking in mathematics education.