Mathematizing verbal descriptions of situations: A language to support modeling

In this article, I concentrate on the linguistic aspects of modeling, primarily investigating the uses of notations over tasks that consist of multievent temporal phenomena. Specifically, I describe attempts by a group of 7th graders who were algebra beginners to reformulate narratives using two lexical sets: verbal and iconic. The 2 sets are parallel representations of the characteristics of any process that can be described by a function of a single variable. A software environment provides an opportunity to manipulate visual objects and to use a verbal set that is simpler and more abstract than natural language descriptions. The use of these lexical sets offers a path toward modeling that does not require the use of algebraic symbols, typically the only first route of employing mathematical notations. Over the course of the intervention, notations were introduced, and syntactic and semantic aspects of the language were developed. Along the course of the study, I observed how natural language text turns into a script of events and processes, how the qualitative graphic description of the script is sketched using iconic notations, and how the same graph turns into a subject for qualitative analysis of rate of change.