Positioning Mathematical Routine Enactments Along the Ritual–Explorative Continuum: The Case of Prospective Teachers’ Fraction Ordering

Abstract Learners may solve the same mathematical task correctly using the same solution strategy while engaging in qualitatively different mathematical participation. Such variation is difficult to identify through correctness-based assessments alone, limiting insights into students’ mathematical learning. Drawing on Sfard’s commognitive framework, this study investigates how three prospective teachers enacted the shared common denominator routine while solving the same fraction-ordering task. Using the ritual–explorative continuum as a cross-sectional analytic framework, we analyzed four discursive characteristics—bondedness, substantiation, objectification, and agency—and reconstructed each participant’s construed task from observable discourse. The findings indicate that differences in routine enactment were associated not with procedural performance but with how participants construed the task, connected and justified mathematical actions, and positioned mathematical authority in their discourse. These findings demonstrate the value of the ritual–explorative continuum for cross-sectional analyses of mathematical participation, identify three analytic prototypes of routine enactment, and suggest that routine enactment is multidimensional, with mathematically successful performances differing substantially in their learning potential despite producing the same correct solution.