Beyond Algorithms: A Portrait of Elementary Teachers’ Pedagogical Content Knowledge in Fractions

Abstract

This study explores elementary teachers’ Pedagogical Content Knowledge in the domain of fractions by analyzing their responses to fraction-based numeracy tasks and semi-structured interviews. Using a qualitative descriptive approach, five elementary teachers were asked to solve and explain fraction problems involving comparison, equivalence, addition, student misconceptions, and curriculum connections. The analysis focused on four dimensions of PCK: Content Knowledge, Knowledge of Students, Knowledge of Instructional Strategies, and Knowledge of Curriculum. The findings reveal that although all participants demonstrated procedural fluency in solving fraction tasks, their pedagogical orientations varied considerably. Two teachers exhibited a Procedural-Focused orientation, relying primarily on algorithmic procedures with limited conceptual explanation or use of representations. One teacher demonstrated an Algorithmic-Partial orientation, characterized by heavy dependence on rules and the presence of misconceptions. Two teachers showed more advanced orientations: one displayed Conceptual-Reflective PCK through the use of visual representations and anticipation of student misconceptions, while another demonstrated Integrated PCK by balancing procedural accuracy with conceptual understanding, effective representations, and explicit alignment with the national curriculum. These findings indicate that algorithmic competence alone is insufficient to support meaningful learning of fractions. Teachers who integrated conceptual explanations, representations, and curricular awareness were better positioned to address student thinking and misconceptions. This study contributes to the literature by illustrating a spectrum of teachers’ PCK profiles in the Indonesian context and highlights the need for professional development programs that support teachers in moving beyond algorithm-focused instruction toward more integrated and conceptually grounded approaches to teaching fractions.