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 narr atives using two lexical sets: verbal and iconic. The 2 sets are paral lel representations of the characteristics of any process that can be described by a function of a single variable. A software environment p rovides an opportunity to manipulate visual objects and to use a verba l set that is simpler and more abstract than natural language descript ions. The use of these lexical sets offers a path toward modeling that does not require the use of algebraic symbols, typically the only fir st route of employing mathematical notations. Over the course of the i ntervention, notations were introduced, and syntactic and semantic asp ects of the language were developed. Along the course of the study, I observed how natural language text turns into a script of events and p rocesses, how the qualitative graphic description of the script is ske tched using iconic notations, and how the same graph turns into a subj ect for qualitative analysis of rate of change.