Year: 2012
Type: dissertation
Abstract: The main focus of the research was to investigate the understanding of Euclidean \nGeometry of a group of Grade 12 mathematics teachers, who have been teaching \nGrade 12 mathematics for ten years or more. This study was guided by the \nqualitative method within an interpretive paradigm. The theoretical framework of this \nresearch is based on Bloom’s Taxonomy of learning domains and the Van Hiele \ntheory of understanding Euclidean Geometry. \nIn national matriculation examination, Euclidean Geometry was compulsory prior to \n2006; but from 2006 it became optional. However, with the implementation of the \nlatest Curriculum and Assessment Policy Statement it will be compulsory again in \n2012 from Grade 10 onwards. \nThe data was collected in September 2011 through both test and task-based \ninterview. Teachers completed a test followed by task-based interview especially \nprobing the origin of incorrect responses, and test questions where no responses \nwere provided. Task-based interviews of all participants were audio taped and \ntranscribed. \nThe data revealed that the majority of teachers did not posses SMK of Bloom’s \nTaxonomy categories 3 through 5 and the Van Hiele levels 3 through 4 to \nunderstand circle geometry, predominantly those that are not typical textbook \nexercises yet still within the parameters of the school curriculum. Two teachers could \nnot even obtain the lowest Bloom or lowest Van Hiele, displaying some difficulty with \nvisualisation and with visual representation, despite having ten years or more \nexperience of teaching Grade 12. Only one teacher achieved Van Hiele level 4 \nunderstanding and he has been teaching the optional Mathematics Paper 3. Three \nout of ten teachers demonstrated a misconception that two corresponding sides and \nany (non-included) angle is a sufficient condition for congruency. \nSix out of ten teachers demonstrated poor or non-existing understanding of the \nmeaning of perpendicular bisectors as paths of equidistance from the endpoints of \nvertices. These teachers seemed to be unaware of the basic result that the \nperpendicular bisectors of a polygon are concurrent (at the circumcentre of the \npolygon), if and only if, the polygon is cyclic. Five out of ten teachers demonstrated \npoor understanding of the meaning and classification of quadrilaterals that are \nalways cyclic or inscribed circle; this exposed a gap in their knowledge, which they \nought to know. \nOnly one teacher achieved conclusive responses for non-routine problems, while \nseven teachers did not even attempt them. The poor response to these problems \nraised questions about the ability and competency of this sample of teachers if \nproblems go little bit beyond the textbook and of their performance on non-routine \nexamination questions. Teachers of mathematics, as key elements in the assuring \nof quality in mathematics education, should possess an adequate knowledge of \nsubject matter beyond the scope of the secondary school curriculum. It is therefore \nrecommended that mathematics teachers enhance their own professional \ndevelopment through academic study and networking with other teachers, for \nexample enrolling for qualifications such as the ACE, Honours, etc. However, the \nDepartment of Basic Education should find specialists to develop the training \nmaterials in Euclidean Geometry for pre-service and in-service teachers.
Author: Sikhumbuzo Sithembiso. Dhlamini
Language: English
Subfield: Education
Field: Social Sciences
Domain: Social Sciences
SDG: Quality education
Open Access status: green
OpenAlex ID: W2125419582