NCPDJE Articles

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Browsing NCPDJE Articles by Subject "Geometry"

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    Effective teaching practices from the perspective of Kilpatrick, Swafford and Findell’s (2001) model: A video-based case study analysis of the teaching of Geometry in Namibia
    (University of Namibia, 2014) Stephanus, Garvasius H.
    This paper presents findings from a broader PhD study that was undertaken at Rhodes University. The purpose of this qualitative case study was to explore and analyse the Geometry teaching practices of five purposefully selected secondary school teachers in Namibia who are regarded as effective mathematics teachers by the broader professional community including teachers, education ministry officials and University of Namibia lecturers. It also aimed to understand teachers’ perceptions of factors that contributed towards their effective teaching of geometry. The selected case study schools where the teachers taught were representative of high performing Namibian schools in terms of learners’ mathematics performance in the annual national examinations. This investigation was done through a process of classroom observations where the teachers’ instructional practices were observed and analysed using an adapted model of teaching for mathematical proficiency as developed by Kilpatrick, Swafford and Findell (2001) and an enactivist theoretical perspective. The study also used open-ended and semi-structured interviews with the five participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions with the participating teachers. In this paper, we only focus on the qualitative analysis of videotaped geometry lessons taught by three teachers. We analyse vignettes of selected lessons for effective teaching using the five strands of the Kilpatrick’s model for proficient teaching. The analysis indicated that conceptual understanding (CU), procedural fluency (PF) and productive disposition (PD) were reflected regularly by all three teachers. However, the development of strategic competence (SC) or adaptive reasoning (AR) appeared relatively rarely. We observed many occasions where Namibian students were engaged in conceptually rich mathematical activities or invited to solve authentic problems. The tentative conclusion of the study is that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick’s model.
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    Using the van Hiele phases of instruction to design and implement a circle Geometry teaching programme in a secondary school in Oshikoto region: A Namibian case study
    (University of Namibia, 2014) Dongwi, Beata Lididimikeni
    Despite my positive views of geometry as one of the most interesting topics in the mathematics curriculum, others find it rather complicated and sometimes unbearable to successfully complete a geometry course. It is a common phenomenon that secondary school students globally struggle with simple geometric problems and their thinking and reasoning are generally below average. Although difficulties in geometric thinking and reasoning are prevalent in global educational research, problems in geometric conceptualisation still prevail. It is therefore the aim of this paper to report on the case study research that was conducted to examine, analyse and report on the findings of the experiences of selected mathematics teachers when they used the Van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected Grade 11 mathematics teachers from the school where the researcher taught. The findings of this research revealed that teachers used and implemented all the five Van Hiele phases of instruction in their lessons whilst navigating quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Teachers also saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. The majority of the learners followed the instructions and seemed to obtain the answers faster than expected.