Collaboration toward teaching proficiency of mathematical concepts in secondary schools

Abstract

In South Africa learner performance in mathematics is alarmingly low in comparison with other countries. Literature reveals that mathematics teachers play a prominent role toward helping learners perform well and learn mathematics in a meaningful way. As such it is important for teachers to possess adequate mathematical knowledge for teaching. Mathematics teachers are advised to take into account learning theories advocated by mathematics education research, for instance constructivist and sociocultural learning theories. Such theories place focus on the learner as well as the context in which the teaching and learning take place, describing both as significant toward facilitating meaningful learning of mathematics. This implies that mathematics teachers need to know and understand that learners learn in different ways, bring different backgrounds, ideas, and views into the mathematics classroom, and, most importantly, the mathematics teacher needs to know that mathematical tasks that learners will solve should be contextualized, e.g. posed in real-world problems related to learners’ prior knowledge. Henceforth, I carried out this study to investigate the notion of collaboration toward teaching proficiency of mathematical concepts, specifically the function concept and Euclidean geometry. In particular, this study intended to investigate the influence of a Collaborative Learning Programme (CLP) on teachers’ conceptual understanding of mathematical concepts. This study was centred on the three C’s: Content, Collaboration and Context. The rationale for placing this study around the three C’s will be evident in the following paragraphs. This study was entrenched in an interpretive paradigm and the research design was qualitative in nature and rooted in a multisite case study. Consequently data were collected by means of task sheets, semi-structured interviews, field notes, Self-Directed Learning Instrument as well as open-ended surveys. The population informing the central phenomenon in the study consisted of secondary school mathematics teachers as well as final-year mathematics education students. The population included both males and females. Since the study was qualitative in nature it is important to note that the findings cannot be generalised. Crystallisation of the data emanating from numerous data gathering techniques led to the findings that the participants reacted in different ways, and positively, to the CLP. In Case 1, the findings revealed that the CLP did not have any impact on one of the participants’ views and beliefs about the teaching and learning of mathematics, as well as the conceptual understanding of the function concept. Contrary to this, the participant maintained that she gained a lot from the CLP and she was interested to participate in the future CLP. In Case 2 the findings indicated that the CLP did have an influence on students’ conceptual understanding Euclidean geometry, but not for all students. Findings also indicated that the CLP did not have viii any influence on students’ self-directed learning abilities concerning mathematics. These findings were then used to make recommendations in order to address the impact of a Collaborative Learning Programme on participants’ proficiency in the teaching of mathematical concepts.