Proportional reasoning in the learning of chemistry: levels of complexity

This interdisciplinary study sketches the ways in which proportional reasoning is involved in the solution of chemistry problems, more specifically, problems involving quantities in chemical reactions (commonly referred to as stoichiometry problems). By building on the expertise of both mathematics and chemistry education research, the present paper shows how the theoretical constructs in proportional reasoning in mathematics education offer rich explanatory accounts of the complexities involved in solving stoichiometry problems. Using Vergnaud's concept of measure spaces, the theoretical analysis shows that proportionality situations are relatively more intricate, involving various layers of complexity in chemistry as compared to those in the mathematics curriculum. Knowledge of proportionality and chemistry are simultaneously required to provide solutions to chemical reactions. Our analysis of a range of stoichiometry situations led us to propose a problem analysis framework involving five levels of difficulty. Further, the specificity of proportionality in stoichiometry is that it can only be established when quantities are interpreted in the unit “mole,” a unit which does not have any physical embodiment in terms of a measure of quantity unlike mass and volume. Our analysis of student-teachers' solution to the stoichiometry problems, shows that they tend to incorrectly (probably intuitively) set proportional relationships when two quantities in a reaction are expressed in non-molar quantities such as mass. The data also bring to the fore the primarily formulaic approach that student-teachers use in setting inherent proportionality relationships. An important finding is the interpretation of a chemical equation as a mathematical equation, rather than a statement of proportionality.