Structures of constant rate word problems: A functional approach analysis

Many recent projects have lately explored function-based approaches to algebra. For the last five years we developed and tested such an approach to algebra, the 'Visual Mathematics'¹ curriculum, in grades seven to nine. While teaching this curriculum we learned from our students' work that while functions form an important basis for solving various sorts of algebra word problems, they introduce some tension in dealing with other sorts of word problems. The data accumulated during our experiments led us to conjecture that viewing algebra rate problems through a function lens offers new ways to look at similarities and differences among word problems. This article presents a theoretical framework for a systematic investigation of the structures of algebra word problems and their relationship to function-based solutions. We think that for those who take a function approach to algebra, this paper suggests new insights into the categorization of word problems.