How does language impact the learning of mathematics? Comparison of English and Korean speaking university students’ discourses on infinity

Commognitive analyses of the learning and teaching of mathematics at university level: the case of discursive shifts in the study of Calculus

“…For example, in Korean and in Japanese it is not, as there are two distinct words for "the derivative function" and "the derivative at a point". Kim, Ferrini-Mundy, and Sfard (2012) explore a similar point in the case of discourses on infinity (in the case of learning about infinity in Korean and in English) and use these analyses to interpret the different discourses on infinity of the Korean (apparently more structural and formal) and the English (apparently more procedural and informal) students. Ioannou (2012), in the as yet minimally charted territory of commognitive analyses at university level outside Calculus, focuses on students' first encounters with Group Theory to observe: the intertwined nature of object-level and meta-level learning in Group Theory (for example, when the students learn about equivalence relations and normality); the commognitive conflicts that students experience both within Group Theory and in relation to other mathematical topics that they are engaging with at the same time (for example, in relation to the perceived relevance and usefulness of visual mediation in different mathematical domains); and the adjustments in the approaches to study (such as ways to prepare coursework and revise for examinations) and communicative practice that above discursive shifts imply for students.…”

Teaching and Learning of Calculus

“…This study shows that students have difficulties in linking the operational perspective of completeness and the supremum of subsets to the structural concept of real numbers. Based on COF constructs, Kim et al (2012) point out that in the case of the notion of infinity, student understandings are highly correlated to their use of words and visual mediators. According to these researchers, the analysis of the discourses on infinity of Korean and English students can lead to their categorisation in terms of process and object point of views.…”

Conceptualizing Mathematics as Discourse in Different Educational Settings

“…The second study (Kim et al, 2012) investigated and compared how native-English and native-Korean speaking university students, who received their education in the U.S. and in Korea respectively, thought about the concept of infinity. The primary motivation for this study was the lexical discontinuity of the Korean infinity discourse and the lexical continuity of the English infinity discourse between everyday and mathematical discourses.…”

“…The framework provides insights regarding the importance of culture and language in making sense of particular mathematical concepts and teachers' awareness of the influences of culture and students' uses of everyday language on mathematical learning (Kim et al, 2012). The framework also underlines the importance of teachers' awareness about the development of their students' discourses in terms of the discursive variations across students as well as within an individual student (Wang, 2011).…”