Problem-solving in geometry: A multilingual perspective through commognitive and Polya’s steps of problem-solving

Abstract

Based on the first author’s doctoral research, this article explores the connection between Sfard’s commognition theory and Polya’s four steps of problem-solving. The article highlights how commognition, through its focus on language and discourse, helps explain learners’ problem-solving approaches as either ritualistic or explorative. The study emphasises that for multilingual learners, understanding mathematical problems, especially in geometry, depends on grasping terminology and visual elements. By combining commognition with Polya’s framework, the analysis suggests that learners’ problem-solving and visualisation skills can be improved, though language remains a key challenge.
Contribution: This article establishes a theoretical connection between Sfard’s commognition and Polya’s problem-solving steps, highlighting their complementary roles in mathematics education. The article validates how commognitive elements, particularly word use and visual mediators, support multilingual learners in understanding and solving geometry problems. The study offers insights into how discourse influences learners’ problem-solving routines, with implications for teaching in linguistically diverse classrooms.