Improper Applications of Proportional Reasoning
Abstract
One of the major goals of elementary and middle-grades mathematics education is for students to obtain a deep understanding of the proportional model in a variety of forms and applications. However, the reinforcement of proportionality at numerous occasions in school mathematics, along with the teaching of some standardized methods for solving proportionality problems, appear to lead to a resistant tendency in some students and adults to see and apply proportions everywhere. This same application occurs in situations where another method of solution is appropriate. Along with mastering the proportional scheme, its misuse seems to appear, as well. This overgeneralization of proportion has many faces: It has been found at different age levels and in a variety of mathematical domains, such as elementary arithmetic (Cramer, Post, and Currier 1993), algebra (Matz 1982), geometry (De Bock, Verschaffel, and Janssens 1998, 2002) and probability (Van Dooren et al. 2002).