|dc.description.abstract||The research conducted in this study is inextricably linked to a larger study of teacher
quality and student performance in KwaZulu-Natal. The aim of the larger study was to
explore and establish the relationship between teachers’ mathematical content
knowledge, teachers’ practice and learner outcomes in grade 6 mathematics classrooms.
This meant ascertaining teachers’ mathematical content knowledge, teachers’
pedagogical content knowledge and teachers’ practice in mathematics classrooms. Videos
of lessons were analysed for the following aspects: content coverage, mathematical
proficiencies facilitated by the teacher, cognitive demand on learners and teachers’
content knowledge. The analyses of all aspects were initiated at the same time, with
different researchers/post-graduate students coding for separate aspects.
In this study, the notion of mathematical proficiency as originally developed by Kilpatrick
and colleagues (Kilpatrick, Swafford, & Findell, 2001) was used to ascertain the promotion
of the strands in the district of Umgungundlovu of KwaZulu-Natal. Essentially the larger
study hoped to establish the prevalence and quality of these strands by viewing video
recordings of lessons obtained from schools. This in turn would present a view on
mathematics learning in the district. The larger study used random stratified sampling to
identify schools after which the necessary ethical approval and clearance was obtained.
Mathematics lessons of the identified schools were then video-taped and questionnaires
and both teacher and learner tests were conducted. I have not included examples of test
questions due to agreements about not reproducing these.
However, analysis of the recordings, in my view required the formulation of a construct
that would interrogate the extent to which the strands of mathematical proficiency are
promoted. This was necessary since the five strands in the original formulation represent
‘goals of mathematical understanding. ’In order to achieve these goals, tangible evidence
of teacher classroom practice must be observable. Using opportunities as a vehicle of
identification of such practice, the notion was formulated. The analytical framework
entrenches the notion of ‘opportunity to develop mathematical proficiency’ as a construct
with its corresponding descriptor table and is the main feature of this study. This in turn
informed the design of the instrument which reflected the notion introduced and allowed
ease of use. The research was not simply finding instances of what the instrument
describes, but also trailing the applicability and strength of the instrument and the
underlying notion of ‘opportunities to develop mathematical proficiency’.
The findings reflect the current state of the promotion of mathematical proficiency. Not
only is the quality of the promotion weak it is also irregular. An important off spin of the
results is the alignment of these results to many studies including the recent ‘Report on
the Annual National Assessments 2011’ issued by the Department of Basic Education.
The notion introduced in this study with its corresponding analytic scoring method indeed
proved to be a useful key to unravelling the answers to the questions posed. The results
and findings give a detailed description to the aspect of mathematical proficiencies
facilitated by the teacher, one of the aspects the larger study aimed to explore and
establish. In this respect, it also shows the applicability and relevance of the developed
theoretical notion and the related instrument.||en