An exploratory study of direct proportional covariation

This book discusses the importance of the development of proportional reasoning in elementary education, based on the idea that this should not be restricted in the teaching process to the exclusive use of the rule of three, since this way concepts and significant processes that involve the development of variational thinking are ignored. The alternative proposed is to explore proportionality through the formulation of problems in which the covariation relationship is promoted, with the purpose that students identify the two quantities that vary and how each of them changes with respect to the other. This relation of covariation is presented not only in the solution of problems, but also in the use and translation into different representation registers such as the pictorial, the tabular and the Cartesian. Different theoretical positions are presented that argue how the relation of covariation, the solution of problems and the use of representations contribute significantly to the understanding of proportionality. Finally, some reflections and suggestions are made.