An Apos theory analysis of the understanding of vectors involving plane concepts by advanced level mathematics learners: a case study of high schools in Shamva district
- Author
- Sitima, Raymond
- Title
- An Apos theory analysis of the understanding of vectors involving plane concepts by advanced level mathematics learners: a case study of high schools in Shamva district
- Abstract
- This study investigated the understanding of vectors involving plane concepts among Advanced Level Mathematics learners in Shamva District using the APOS (Action, Process, Object, Schema) theoretical framework. The study aims to analyse students' cognitive development in interpreting planes in three-dimensional space, focusing on normal vectors, vector and Cartesian equations of planes, and their interconnections. This study followed a mixed methods approach with a descriptive design., Questionnaires and interviews were used to gather data from Advanced Level Mathematics teachers and36 pupils who were selected using stratified random sampling from 3 High Schools in Shamva District. Data was collected through diagnostic assessments, structured interviews, and classroom observations to determine students’ APOS levels and pre-tests and post-tests. Preliminary findings indicate that most learners operate at the Action and Process levels, demonstrating procedural fluency but struggling with conceptual transitions to Object and Schema thinking. The study further explored how interactive and visual-based learning approaches enhance comprehension and facilitate cognitive progression. Based on the findings, pedagogical recommendations were proposed so as to strengthen conceptual understanding and problem-solving skills in vector geometry. The study findings contribute to Mathematics Education domain by providing insights into effective instructional strategies for teaching 3D vector geometry concepts within the Zimbabwean Advanced Level curriculum. Factors such as lack of knowledge by teachers, lack of adequate lesson time to effectively carry out an APOS analysis in teaching vectors of planes, lack of relevant knowledge and skills to effectively teach the concept, poor self-efficacy among learners. Need for capacitation of schools the provision of workshops and APOS analysis training initiatives were some of the recommendations made to improve the degree of minimizing challenges when dealing with vectors of planes.
- Date
- February 2025
- Publisher
- BUSE
- Keywords
- Apos theory
- Action, Process, Object, Schema
- Advanced Level Mathematics
- Supervisor
- Dr. L. Mukavhi
- Media
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Sitima - MSc Maths.pdf