Use of signifiers in discourse on the derivative in Korean and English speaking mathematics classroom

Based on the observation that there is a common signifier “derivative” in English used for both the derivative at a point and the derivative function and that there are two phonetically and semantically different signifiers for those objects in Korean, we explored potential differences in classroom teaching discourses aimed to teach canonic mathematical discourses about the mathematical objects that those terms signify and their relations in Korean and English. Our analysis of one Korean teacher’s and one American teacher’s classroom discourse about the derivative using the commognitive approach uncovered differences in their teaching discourse in terms of addressing metarules about the terms and connections to colloquial discourse that exist in English, but not in Korean. We also found differences in how the American teacher made connections between the derivative at a point and the derivative function and how the Korean teacher connected the two signifiers in Korean - the American teacher extended a realization of the first defined object to define the second object, and after that, made shifts in a way that precludes simultaneous use of the common signifier for both objects whereas, in Korean teacher’s discourse, no extensions were observed and the first defined object gained additional realizations.