Abstract
The purpose of this study was to explore the misconceptions and the errors displayed by Grade 3 to 6 learners in the learning of place value at Maraba Circuit, Capricorn District, Limpopo Province. The study followed a qualitative research approach where a multiple case study research design was adopted. A total of 601 (Grade 3, 133; Grade 4, 179; Grade 5, 146; Grade 6,143) learners were sampled from Grades 3 to 6 in six primary schools through a convenience sampling strategy. Phase 1 data were collected through tests on the place value concept appropriate to each grade. Data were analysed through a thematic approach. The study came up with three findings about errors that are displayed by learners in learning place value. First, the learners in the sample made factual errors in carrying out place values when handling the four mathematical operations. Second, the learners displayed procedural errors in operationalising the concept of place values of the four mathematical operations (addition, subtraction, division, and multiplication). Third, the learners displayed conceptual errors in carrying out place values on the four mathematical operations. Data from teachers showed that teachers also experienced challenges in teaching place value. The findings therefore resolved that the concept of place value which is fundamental to the four mathematics operations is not well conceptualised by the learners from grade 3 to 6. One of the main reasons was that the concept is not well taught at these grades and as a result learners display misconcepts that result in conceptual and procedural errors. These findings have at least three implications for teachers, teacher education institutions, and policymakers. First, the findings have implications for primary school teachers who are daily confronted with learners that struggle with learning place value. They may use these identified errors provide remedial teaching. Second, policymakers, in their search for answers to why learners performance in mathematics is weak at these grades especially in South African schools to consider revisiting documents such as CAPS on the learning of place value to include error analysis and paying more attention to causes of errors, effective instruction and constance reflections on remedial and inrichment activities. Third, more studies are required to fully understand how place value can be taught, especially in poorly resourced schools such as the ones in the case studies. In an effort to contribute to the solution, an intervention manual has been developed centering on how to address learners conceptual and procedural errors that permeate from their learning of the four mathematics operation at primary school.
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Keywords: misconceptions, conceptual errors, procedural errors, place value