The Relative Interdependency of Colloquial and Mathematical Discourses Regarding the Notion and Calculations of Limit: an Evidence-Based Cross-Cultural Study

This study compares English- and Korean-speaking university students’ colloquial and mathematical discourses on the notion and practice of limit. There exists a lexical discontinuity in Korean with the word limit, since the mathematical word for limit is not commonly used as a colloquial word in Korean, unlike its use in English. This study discusses similarities and differences with regard to ways students in each country use the word limit in colloquial contexts and in mathematical tasks. Data include surveys and interviews, and participants’ discourses, which were analyzed using Sfard’s (2008) discursive framework. Findings indicate that the mathematical discourse of the Korean speakers was structural (i.e. formal or mathematical) and the one for the English speakers was processual. Further, the differences between the US and Korean participants’ use of limit in everyday and mathematical discourses informed the language-dependent properties of school mathematics discourses in terms of word use, routines, endorsed narratives, and visual mediators. This study discusses different discursive needs—linguistically and culturally—to support meaningful mathematical discourses.