Misconceptions on Interpreting and Modeling the Concept of Division Among Elementary School Teachers

This study investigates the nature and extent of conceptual misconceptions held by elementary school teachers in interpreting and modeling the mathematical concept of division. Motivated by the recognition that students’ misunderstandings often originate from teachers’ inadequate conceptual grasp, particularly regarding the use of partitive and quotative models, this research addresses a critical gap in the literature on teachers' mathematical representations. Although division is a foundational concept in mathematics instruction, limited empirical research has explored how teachers misconstrue its meanings in classroom contexts. Employing a descriptive qualitative design within a multiple-case study framework, the study involved 80 fifth-grade teachers from four major Indonesian cities: Jakarta, Bandung, Yogyakarta, and Surabaya. Participants were selected through purposive sampling. Data were collected through classroom observations, semi-structured interviews, and lesson plan analysis. Thematic analysis was used to identify recurring patterns of misconception across instructional practices. Findings in this study revealed misconceptions among many teachers in distinguishing between the partitive (repeated subtraction) and quotative (equal sharing) interpretations of division. This confusion results in the use of inappropriate, rigid, or overly simplified concrete models. The misconception distorts mathematical representations and contributes directly to the propagation of student misconceptions. The most prominent patterns occurred during story problem interpretation, where teachers struggled to match the semantic structure with the appropriate division model. These conceptual misconceptions not only distort instructional representations but also contribute to students' way of thinking. These findings highlight the urgent need for targeted professional development programs. Those would emphasize semantic analysis of word problems and the flexible use of multiple representations. Such interventions are essential to help teachers deliver instruction that fosters conceptual understanding beyond procedural fluency. Aligning teacher training with findings in this study may prevent the transfer of fundamental misconceptions to students and promote deeper mathematical thinking in early education contexts. Keywords: misconceptions, interpretations, division, elementary school, teacher.