Interactions Between Natural Language and Mathematical Structures: The Case of "Wordwalking"

Abstract

In the course of solving relatively routine word problems, 7th-grade students sometimes made a substitution of a word or phrase in the original problem statement. The substitutions discussed here appeared insignificant because the natural language meaning overlapped with that of the replaced word or phrase, but they had major consequences mathematically because they affected the mathematical structure that modeled the resulting problem statement. The term wordwalking was coined to refer to such substitutions. Wordwalking was observed during qualitative data reduction required for the coding of a quantitative study. The relative ambiguity of natural language and the precision of mathematical expressions are invoked to explain the dynamics of wordwalking.