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

Abstract

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.