High School Students’ Discursive Routines in the Context of Linear Equations

Purpose: This case study explores the discursive routines of three 11th-grade students from a public high school as they engaged with single-variable linear equations. Specifically, it aims to reveal the nature and structure of their participation in mathematical discourse and to examine how their algebraic understanding of linear equations is constructed from a commognitive perspective. Method: A qualitative case study design was employed. Data were collected via semi-structured individual interviews, lasting between 40 and 60 minutes, and recorded using two cameras to capture the students’ mathematical communication in detail. The analysis focused on how students participated in mathematical discourse, particularly using ritual and exploration routines. Findings: The findings reveal that students mainly relied on ritual routines, concentrating on performing rigid procedures rather than producing mathematical narratives. Their discourse centered on calculations, treating equations as sequences of symbols to manipulate rather than as mathematical objects. Exploration routines—which involve making sense of mathematical discourses—were infrequent but emerged primarily during discussions about the solution set and its elements. Conclusion: The findings emphasize the significance of the variable, equal sign, and task situation in constructing algebraic understanding. Therefore, in the context of linear equations, these findings suggest that students’ developing understanding of how concepts such as variables, equality, equations, and solution sets function as mathematical objects may encourage them to engage in exploration routines.