Analytical rubrics for mathematical representation behaviour assessment: Development, validation, and cross-cultural application

Abstrak

Mathematical representation plays a pivotal role in students’ understanding, reasoning, and problem-solving processes. Despite its centrality in mathematics education, systematic approaches to assessing representational behavior remain limited, particularly within diverse cultural and curricular contexts. Existing assessment practices often emphasize cognitive outcomes, overlooking affective, psychomotor, and meta-representational dimensions that shape students’ mathematical understanding. Addressing this gap, the present study developed and validated an analytical rubric designed to assess mathematical representation behavior comprehensively across these four domains. Grounded in the Educational Design Research (EDR) framework, the rubric was constructed through four iterative stages, namely reflection, recording, grouping and naming, and application. Six mathematics education experts from Indonesia and Malaysia participated in the validation process, while empirical data were collected from 42 undergraduate students who had completed a geometry course. The analysis revealed strong content validity, with Aiken’s V coefficients ranging from 0.78 to 0.93 and full expert agreement, confirming the rubric’s clarity and relevance in evaluating representational behaviors. The rubric categorized student performance into three levels, namely Eikasia, Dianoia, and Intellectus, providing a nuanced diagnostic framework for assessing students’ mathematical representation. This study contributes to the field by introducing a cross-culturally grounded assessment tool that integrates cognitive, affective, psychomotor, and meta-representational perspectives. The findings highlight the rubric’s potential as both a formative and diagnostic instrument, enhancing the precision of assessment and offering insights for improving mathematics instruction and future digital-based evaluation practices.