The main focus of the research was to investigate the understanding of Euclidean
Geometry of a group of Grade 12 mathematics teachers, who have been teaching
Grade 12 mathematics for ten years or more. This study was guided by the
qualitative method within an interpretive paradigm. The theoretical framework of this
research is based on Bloom’s Taxonomy of learning domains and the Van Hiele
theory of understanding Euclidean Geometry.
In national matriculation examination, Euclidean Geometry was compulsory prior to
2006; but from 2006 it became optional. However, with the implementation of the
latest Curriculum and Assessment Policy Statement it will be compulsory again in
2012 from Grade 10 onwards.
The data was collected in September 2011 through both test and task-based
interview. Teachers completed a test followed by task-based interview especially
probing the origin of incorrect responses, and test questions where no responses
were provided. Task-based interviews of all participants were audio taped and
transcribed.
The data revealed that the majority of teachers did not posses SMK of Bloom’s
Taxonomy categories 3 through 5 and the Van Hiele levels 3 through 4 to
understand circle geometry, predominantly those that are not typical textbook
exercises yet still within the parameters of the school curriculum. Two teachers could
not even obtain the lowest Bloom or lowest Van Hiele, displaying some difficulty with
visualisation and with visual representation, despite having ten years or more
experience of teaching Grade 12. Only one teacher achieved Van Hiele level 4
understanding and he has been teaching the optional Mathematics Paper 3. Three
out of ten teachers demonstrated a misconception that two corresponding sides and
any (non-included) angle is a sufficient condition for congruency.
Six out of ten teachers demonstrated poor or non-existing understanding of the
meaning of perpendicular bisectors as paths of equidistance from the endpoints of
vertices. These teachers seemed to be unaware of the basic result that the
perpendicular bisectors of a polygon are concurrent (at the circumcentre of the
polygon), if and only if, the polygon is cyclic. Five out of ten teachers demonstrated
poor understanding of the meaning and classification of quadrilaterals that are
always cyclic or inscribed circle; this exposed a gap in their knowledge, which they
ought to know.
Only one teacher achieved conclusive responses for non-routine problems, while
seven teachers did not even attempt them. The poor response to these problems
raised questions about the ability and competency of this sample of teachers if
problems go little bit beyond the textbook and of their performance on non-routine
examination questions. Teachers of mathematics, as key elements in the assuring
of quality in mathematics education, should possess an adequate knowledge of
subject matter beyond the scope of the secondary school curriculum. It is therefore
recommended that mathematics teachers enhance their own professional
development through academic study and networking with other teachers, for
example enrolling for qualifications such as the ACE, Honours, etc. However, the
Department of Basic Education should find specialists to develop the training
materials in Euclidean Geometry for pre-service and in-service teachers. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2012.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/9486 |
| Date | January 2012 |
| Creators | Dhlamini, Sikhumbuzo Sithembiso. |
| Contributors | De Villiers, Michael. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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