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School of Education

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    A new method with regularization for solving split variational inequality problem in real Hilbert spaces.
    (2022) Akutsah, Francis.; Narain, Ojen Kumar
    The concept of the optimization problem, fixed point theory and its application constitute the nucleus of nonlinear analysis, which is a major branch of mathematics. Optimization theory, fixed point theory and its applications have a wide range of application in practically every field of science, particularly mathematical sciences. The theory of optimization and fixed point have received great attention from authors around the world and these areas will continue to receive such great attention. The theory has been well developed by well-known researchers in these areas. However, there are still a lot of work to be done. The goal of this thesis is to advance the theory of optimization and fixed point in the framework of Hilbert and Banach spaces. The substance of this thesis is separated into two parts. The research efforts of the first part of this thesis (Chapter 3 to Chapter 6) has to do with introducing some new iterative methods for approximating the solution of a variational inequality problems, split variational inequality problems, equilibrium problems, split monotone variational inclusion problem, split generalized mixed equilibrium problem and fixed point problems in the framework of a Hilbert and Banach spaces. In addition, we introduce a new class of bilevel problem in the framework of real Hilbert spaces and a new regularization technique, and inertial terms for approximating solutions of split bilevel variational inequality problems. Furthermore, we establish that the proposed iterative methods converges strongly to the solution of the aforementioned problems as the case may be. Then, we present some numerical experiments to show the efficiency and applicability of our proposed methods in comparison with other state-of-the-art iterative methods in the literature. The second part (Chapter 7) of this thesis deals with developing iterative algorithms and introducing some nonlinear mappings in the framework of the Hilbert and Banach spaces. First, we present a modified (improved) generalized Miteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we present some fixed point results for a general class of nonexpansive mappings in the framework of the Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex Banach spaces. Finally, we apply our convergence results to certain optimization problems, integral equations, and we present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature.
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    School managers’ perceptions on the use of technological resources in curriculum supervision in the context of COVID-19.
    (2023) Biyela, Thokozani Andreas.; Mpungose, Cedric Bheki.
    This dissertation presents a qualitative case study of sixteen school managers specifically school principals. This study was conducted with the main purpose of exploring the school managers’ perceptions on the use of technological resources in curriculum supervision in the context of COVID-19 in the Zululand District. Furthermore, the study employed an interpretive paradigm. In addition, this paradigm has been utilised because the study aims at exploring the three missing levels of perception (knowledge, skill, and attitude) during curriculum supervision. The study sought to understand why school managers resist to use EdTech (educational technological) resources to supervise curriculum. In addition, an interpretive paradigm and case study were used on sixteen participants to gain the meaning in real situation. Subsequently, reflective activity, one-on-one semi-structured interviews, and focus groups were used to generate data. Moreover, the study used non-probability sampling methods, comprising purposive and convenient sampling. This study was framed by the by the curricular spider web (Van den Akker et al., 2010). Further to this, the theory that shapes this study is technological pedagogical content knowledge (TPACK). Data were analysed using guided analysis, which employed both deductive and inductive methods. Finally, ethical considerations related to qualitative research were explored such as trustworthiness, confirmability, dependability, transferability, and credibility. The findings of the study reveal that school managers were driven by knowledge perception to supervise curriculum when using EdTech supervision aids. The school managers could indicate the lack of technological resources and knowledge in schools. Even though there is a policy in place, some school managers are non-compliant with that policy. The study recommends the Department of Basic Education to install Wi-Fi in all schools to enforce the policy implementation. Moreover, the study further recommends that curriculum developers work alongside information and communication technologies (ICT) team specialists to advocate paperless curriculum supervision, train, and enhance school managers on software and ideological-ware EdTech supervision aids.