The paper presents a case study of the mathematics enculturation of a Grade 5 learner, (Sarah), at a school in Limpopo Province of South Africa. The case study sought to explore the attributes of mathematics enculturation in social interaction as a process of learning. A qualitative approach was adopted in collecting and analysing data. Data were constructed by capturing critical incidents and keeping a chronological account in a researcher journal of the discussion observed in Sarah's group during lessons. Qualitative data from Sarah's group, working together on activities, reveal the following constructs as key to understanding mathematics enculturation in the classroom: language, shaping of learners' ideas, and negotiation of meaning. The implication is that oral communication, which includes feedback, plays a major role in making social encounters into learning events that facilitate sense-making and understanding.
It is irrefutable that preparing successful mathematics teachers is a complex task, marked by a convergence of studies in content knowledge and instructional technologies. Considering the increasing number of students enrolling in South African teacher training institutions, it is essential to determine what mathematical knowledge gaps and understanding they bring from secondary school level for the purpose of configuring best strategies to prepare them to become effective teachers. This is the context for a study of first year undergraduate mathematics education students at the University of Limpopo. In this paper, we present our autoethnographical experiences of lecturing calculus courses for a teacher preparation programme. In this paper, we use autoethnography reflexivity to illustrate intersections between self and university society, the particular and the general, the personal and the politics of mathematical knowledge. The patterns that emerged from our interactions with students revealed that they experienced difficulties in understanding basic algebraic procedures and recognising structure to solve algebraic problems in the context of differentiation. This made us aware that we needed to configure effective strategies to make up for the identified elementary mathematics knowledge gaps, which we assumed students brought with from Grade 12. Our quest to make up for the algebraic knowledge gaps does not only serve the purpose of enabling our student teachers' mathematical knowledge, but to ensure that they develop good knowledge base needed to teach the subject during their training as well as once they qualify as teachers.
This article is vested on the need for higher education educators to be reflective on their practices in order to configure effective ways to interact with the students and knowledge for specific courses. It is uncontested that education systems globally are under constant pressure to respond to the changing needs of societies. The outbreak of COVID-19 has reminded us that the complexity of education needs responsive practices to facilitate effective teaching and learning across all levels of schooling globally. All over the world, the normative ways of teaching and learning evolved drastically in the first quarter of the 2020 academic year when teachers and students found online offerings to be the dominant option available as a sequel to the pandemic conditions. In South Africa specifically, students and teachers were thrust into virtual teaching and learning situations with the majority of them having no preparation for this shift. This article presents an auto-ethnographical account of the knowledge gaps in the teaching and learning of mathematics education in a first-year education course in an online space. We used auto-ethnography to discuss our experiences of teaching limits and continuity. We argue that teaching the topic on an online platform constrain student teachers’ procedural thinking, conceptual development, and demonstration of their thought processes during mathematics learning and assessment. We also discuss our experiences of developing assessment tasks for the topic and how students identified cheating mechanisms to answer questions in assessments.
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