Browsing by Author "Dube, Njabulo Happyboy."

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Exploration of Grade 11 learners’ mental constructions and difficulties in learning and solving trigonometric equations: a case of one school in Umlazi district.
(2023) Dube, Njabulo Happyboy.; Ngcobo, Zanele Annatoria.
Trigonometry is a particularly challenging area of mathematics for high school learners. This study investigated South African Grade 11 learners' mental constructions and difficulties when learning and solving trigonometric equations. Participants were selected from an after-school mathematics programme that they attended on a voluntary basis. Data was collected using an activity sheet and semi-structured interviews. Baseline data was collected using an activity sheet from 17 learners Grade 10 learners; data was collected from the same learners a year later using another activity sheet with a different set of problems. Semi-structured interviews were conducted with 7 learners to probe their responses on the activity sheet. Most of the learners were found to be unable to make the necessary mental constructions to solve trigonometric problems at the Grade 11 level. Dubinsky’s (1991) constructivist APOS theory, which describes how learners construct their knowledge of mathematics concepts in stages characterised by action, process, object and schema, was used to analyse the mental constructions of learners. During both phases of data collection, most learners were found to rely on explicit step-by-step calculations to solve problems, indicating that they were operating at the action stage; a smaller number were able to do some of the steps mentally without writing them out, indicating that they had advanced to the process stage. No evidence was found of learners having advanced to the object or schema stages. Moreover, the findings showed that, while the learners perform procedures correctly, they applied rules without giving reasons. Piaget and Garcia’s (1989) triad mechanism were used to analyse the difficulties that hindered learners’ mental construction of concepts. Learners’ difficulties included incorrect conceptions of the equal sign, overgeneralization of rules, and failure to integrate algebra concepts into their construction of trigonometric concepts. Based on the findings, the study recommends that teachers reinforce basic algebraic skills—such as collecting like and unlike terms, using brackets, and addition and subtraction of algebraic terms—before introducing trigonometric concepts. Teachers are urged to explore different methods for teaching trigonometric equations to enable learners to construct knowledge effectively, such as collaborative learning and differentiated classroom activities.
Exploring secondary (9, 10 & 11) Mathematics and Science teachers’ usage of the curriculum tracker in Pinetown and King Cetshwayo Districts.
(2019) Dube, Njabulo Happyboy.; Ndlovu, Annatoria Zanele.
In this study, the researcher explored secondary (9, 10 & 11) Mathematics and Science teachers’ usage of the curriculum tracker in Pinetown and King Cetshwayo districts. This study aimed at gaining a better understating of the usage of curriculum tracker in secondary schools. In 2015 curriculum tracker was introduced in two districts Pinetown and King Cetshwayo for the purpose of assisting teachers in curriculum coverage and for HODs to have a professional conversation with teachers. Therefore, the researcher decided to carry out this study to explore the usage of the curriculum tracker in secondary schools. Focus was on grades 9, 10 and 11. This study is qualitative and was carried out in six schools, three from Pinetown and three from King Cetshwayo district. Primary data was collected from mathematics and science teachers and from HODs through semi-structured interviews and secondary data was collected by PILO coaches in 2015 and 2016. The study is underpinned by the Whole Teacher Approach, which explores the teacher attitude, skills and practices of using the curriculum tracker. It was discovered in this study that the teachers were using the curriculum tracker but still lacked the knowledge and purpose of the curriculum tracker. During the interviews it was noted the teachers’ attitudes towards the curriculum tracker played a crucial role in either usage or non-usage. Most of the teachers that participated in this study felt that the curriculum tracker increased the paper work. However, the responses from teachers and HODs assisted the researcher in identifying the enabling factors and challenges associated with the curriculum tracker. The study concludes that HODs have knowledge of the curriculum tool and some are utilising the curriculum tool to track curriculum coverage in the success as compared to maths. Although the tools were used to track curriculum coverage there was lack of evidence showing of professional conversation taking place between teachers and HODs. The study also advances several recommendations for the teachers, HODs and as well as the department of education. The study recommends that the head of departments and teachers in the schools must be given enough support to implement Jiki imfundo successful in the schools.