Abstract
This study investigated the misconceptions and errors exhibited by Grade 4 learners when dividing multiple‑digit whole numbers. Division is widely regarded as one of the most conceptually and procedurally demanding mathematical operations, and learners’ persistent difficulties in this area continue to present challenges in primary mathematics classrooms. The study, therefore, sought to explore the nature of these difficulties, with particular attention to how learners’ conceptual understanding and procedural knowledge influence their performance in division tasks. The study was framed within Vygotsky’s sociocultural theory of learning, specifically the concept of the Zone of Proximal Development, to understand how instructional support may mediate learners’ mathematical learning.
A qualitative research design was adopted to gain in‑depth insight into learners’ mathematical thinking. Data were collected through classroom observations, semi‑structured interviews, and document analysis in a primary school in the Mopani West District. The findings were analysed thematically, revealing distinct themes that clearly distinguished learners’ conceptual misconceptions from procedural errors. Identified misconceptions included limited understanding of place value, misunderstandings about the inverse relationship between multiplication and division, and incorrect interpretations of remainders. In contrast, procedural errors were evident in learners’ application of division algorithms, estimation practices, and sequencing of division steps, reflecting weaknesses in procedural fluency and number sense.
The findings highlighted the importance of instructional practices that explicitly address both conceptual understanding and procedural competence. The study highlighted the value of scaffolding, systematic error analysis, and concrete teaching and learning resources to support learners’ development of meaningful and accurate division strategies. The study concludes with recommendations aimed at strengthening learners’ conceptual understanding of division and improving classroom practices in the teaching of multiple‑digit division.