Cross-Proportions: A Conceptual Method for Developing Quantitative Problem-Solving Skills

Abstract

This paper focuses attention on the cross-proportion (C-P) method of mathematical problem solving, which was once widely used in chemical calculations. We propose that this method regain currency as an alternative to the dimensional analysis (DA) method, particularly in lower-level chemistry courses. In recent years, the DA method has emerged as the only problem solving mechanism offered to high-school and general chemistry students in contemporary textbooks, replacing more conceptual methods, C-P included. The C-P method emphasizes basic scientific principles through application during the process of solving numerical problems, which in turn promotes student understanding of these principles by constantly reinforcing basic concepts. We believe that appropriate teaching of chemistry needs to model its conceptual character as well as address students' different learning styles. Examples of C-P applications to molar mass and stoichiometry are given.