Exploring the discourses of preservice mathematics teachers when solving geometry problems.

Doctoral Degree. University of KwaZulu-Natal, Durban.Research on teaching and learning that aim to improve preservice mathematics teachers’ (PMTs) knowledge of geometry is increasing globally. The current study explored PMTs’ discourses when solving geometry problems. The amalgamation of the commognitive theory and the Van Hiele levels of geometrical thinking theory was used as the theoretical basis for this study. The study uses the difference between ritualistic and explorative discourse as explicated by Sfard (2008) in commognition together with the four Van Hiele levels of geometrical thinking to view and analyse the data. It goes deeper into the theory of commognition to use not only objectification of mathematical discourse but also the four elements of mathematical discourse to reach its conclusion. The current study aimed to answer the main question: How does preservice mathematics teachers’ thinking as evident in their mathematical discourse during Euclidean geometry problem solving relate to their teaching practices in Euclidean geometry? This will be done through answering four subsidiary questions. A qualitative research approach was used to generate rich and descriptive data to answer the posed research questions. Furthermore, the qualitative approach allowed for the collection of data representing participants’ geometry problem solving experiences which was the core of the current study. I purposively and conveniently sampled 6 participants in this study where they completed a task-based and face-to-face interviews. Consent was obtained from these participants prior their participation in the study. Data generated from the two instruments was thematically analysed. Findings from this study revealed that most PMTs use ritualistic discourse when communicating about their geometry problem solving actions. These findings are a consequence of them performing routines for social acceptance instead of generating endorsed narratives. Furthermore, it was observed that others used ritualistic discourse because they rely on scaffolding from others to perform their routines instead of developing their own routines. Despite the dominance of ritualistic discourse participation in the current study, there were instances where PMTs seemed to be using explorative discourse but get stuck somehow and return to ritualistic discourse. The Van Hiele theory revealed that most PMTs still operate within the lower levels of geometrical thinking. The main findings and contribution of this study is that for PMTs to advance their geometrical thinking from level 0 to level 3, they need to transform their discourse participation from ritualistic to explorative

A systematic review of the implications for teaching, learning and assessment at South African universities after the Covid-19 pandemic

This paper presents the results of a systematic review of literature, reported in research journals, on the experiences of higher educational institutions regarding teaching, learning, and assessment during the Covid-19 pandemic. Different studies related to the Covid-19 pandemic have been conducted within the South African context, but there has not been a systematic review of these studies highlighting the lessons learned, how these lessons have affected education in higher education institutions (HEIs), and how these lessons can inform future planning. This study aims to summarise literature on teaching, learning and assessment in higher education institutions and to conceptualise possible guidelines for future planning. An analysis of 52 research articles revealed 7 implications for the lessons learnt from the pandemic for future teaching, learning and assessment (TLA) in South African HEIs (realisation of the affordances of technology for TLA, institutional changes related to online TLA during the pandemic, students’ experiences related to TLA, lecturer’s experiences related to TLA, the need for care, assessment related matters, approaches to teaching, learning and assessment) and several recommendations for how these lessons can be leveraged to help HEIs to prepare effectively for future catastrophic disruptions to education in South African HEIs. The discussion shows the digital divide that exists within the South African population and other contextual challenges faced by higher education institutions during the pandemic, and the different sacrifices by both institutions and students to survive the pandemic. Overall, the findings of this review provide valuable guidance for HEIs and stakeholders involved in TLA, offering insights on how to integrate the lessons learned from the pandemic into their future planning and strategies

Blended learning environments to foster self-directed learning

This book on blended learning environments to foster self-directed learning highlights the focus on research conducted in several teaching and learning contexts where blended learning had been implemented and focused on the fostering of self-directed learning. Several authors have contributed to the book, and each chapter provides a unique perspective on blended learning and self-directed learning research. From each chapter, it becomes evident that coherence on the topics mentioned is established. One of the main aspects drawn in this book, and addressed by several authors in the book, is the use of the Community of Inquiry (CoI) framework when implementing teaching and learning strategies in blended learning environments to foster self-directed learning. This notion of focusing on the CoI framework is particularly evident in both theoretical and empirical dissemination presented in this book. What makes this book unique is the fact that researchers and peers in varied fields would benefit from the findings presented by each chapter, albeit theoretical, methodological or empirical in nature – this, in turn, provides opportunities for future research endeavours to further the narrative of how blended learning environments can be used to foster self-directed learning

Blended learning environments to foster self-directed learning

This book on blended learning environments to foster self-directed learning highlights the focus on research conducted in several teaching and learning contexts where blended learning had been implemented and focused on the fostering of self-directed learning. Several authors have contributed to the book, and each chapter provides a unique perspective on blended learning and self-directed learning research. From each chapter, it becomes evident that coherence on the topics mentioned is established. One of the main aspects drawn in this book, and addressed by several authors in the book, is the use of the Community of Inquiry (CoI) framework when implementing teaching and learning strategies in blended learning environments to foster self-directed learning. This notion of focusing on the CoI framework is particularly evident in both theoretical and empirical dissemination presented in this book. What makes this book unique is the fact that researchers and peers in varied fields would benefit from the findings presented by each chapter, albeit theoretical, methodological or empirical in nature – this, in turn, provides opportunities for future research endeavours to further the narrative of how blended learning environments can be used to foster self-directed learning