A Proposed Constructive Itinerary from Iterating Composite Units to Ratio and Proportion Concepts

In this article, the meanings students construct and the conceptual advances they make as they deal with ratio and proportion problems are described. The study cites episodes with a second grader, two fifth graders, and three seventh graders. A critical factor in students' comprehension of and solution to ratio and proportion problems is their explicit recognition of the action that links composite units. Critical transitions in students' constructive itineraries are highlighted, showing that an essential component of these transitions is students' development of related concepts and their integration of that conceptual knowledge with ratio and proportion reasoning. (Author/MKR)