Investigating learners' misconceptions on division of whole numbers to identify a goal of research lesson-a case of lesson study

Abstract

Identifying and addressing learners’ misconceptions is critical for effective mathematical instruction, as unresolved conceptual gaps hinder long-term mathematical development. Diagnostic assessment provides a valuable means of uncovering these misconceptions and informing targeted teaching strategies. Despite this, classroom practices often prioritise procedural fluency over deep conceptual understanding, allowing learners to progress without fully addressing underlying difficulties. This study investigated Grade 6 learners’ misconceptions about the division of whole numbers using a two-tier multiple-choice diagnositc test and unstructured interviews. Guided by Revised Bloom’s Taxonomy and Newman’s Error Analysis Theory within an interpretivist qualitative case study design, the study employed thematic analysis to categorise learners’ errors. The findings revealed three dominant types of errors: transformation errors, comprehension errors, and processing skill errors. These results underscore the importance of strengthening learners’ grasp of foundational concepts such as place value and mathematical language. The study recommends that teachers explicitly integrate diagnostic assessments into classroom practice and design instructional interventions that directly target specific error types, thereby supporting both conceptual understanding and procedural fluency in division.