Bridging Misconceptions and Representations in Teaching Division: Insights from Bruner’s Theory in Indonesian Classrooms

Abstract

This qualitative study investigates elementary school teachers’ conceptual understanding and instructional strategies for teaching division, with a focus on Bruner’s stages of representation—enactive, iconic, and symbolic. Data were collected from 32 Indonesian teachers through open-ended prompts exploring their interpretations of division and classroom practices. Findings reveal a predominant reliance on procedural models, particularly repeated subtraction, with limited use of conceptual models like equal grouping or inverse multiplication. While many teachers employ concrete strategies, few demonstrate coherent transitions to visual and symbolic representations, resulting in fragmented instruction. The analysis also highlights inconsistencies between teachers' conceptual models and instructional methods, underscoring gaps in pedagogical content knowledge. By integrating frequency tables and case comparisons, the study identifies the need for professional development that supports representational fluency and conceptual alignment. Bruner’s framework is proposed as a guide to scaffold instruction that supports diverse learners and fosters deeper mathematical understanding. Implications for teacher education and curriculum design are discussed.