https://ir.unisa.ac.za/handle/10500/2736 2026-06-22T23:49:22Z 2026-06-22T23:49:22Z Dlamini, Reuben https://ir.unisa.ac.za/handle/10500/32652 2026-06-22T11:46:52Z 2026-01-01T00:00:00Z

Investigating grade eleven learners’ mathematical modelling competencies in algebraic problem solving Dlamini, Reuben The National Curriculum Statement (NCS), implemented in 2003, marked the formal introduction of mathematical modelling into the South African curriculum. This represented a significant shift, as mathematical modelling had previously been largely absent from the curriculum. This study investigated the mathematical modelling proficiency of Grade 11 learners from three high schools in the Pongola Circuit, KwaZulu-Natal Province, with a specific focus on determining their competency in solving non-routine problems. The study was motivated by the observation that many teachers did not receive adequate training in mathematical modelling during their pre-service education. Existing research indicates that inadequately trained teachers can negatively affect learners’ academic performance. Furthermore, the teacher is widely regarded as the most critical agent in the successful implementation of instructional reforms at the classroom level (Shepherd, 2019; Theophile et al., 2020). It was therefore necessary to examine learners’ competencies in mathematical modelling. Learners’ competencies were assessed using the five-step modelling process proposed by Kaiser and Stender (2013), which includes: (1) understanding the problem, (2) formulating a mathematical model, (3) solving the model, (4) interpreting the results, and (5) validating the results. For a learner to be considered competent in mathematical modelling, all five stages of the process had to be correctly executed. A total of 75 Grade 11 learners from three purposively selected schools participated in the study. Qualitative data were collected through document analysis. The data analysis process involved familiarisation with learners’ written responses, followed by thematic analysis to interpret meaning, identify patterns, and generate insights related to the research questions. The findings revealed that all learners demonstrated incomplete competency in mathematical modelling. Specifically: • None of the learners successfully completed all five stages of the modelling process in any of the four test questions. • Learners did not make or attempt to make assumptions, which are essential in solving real-life problems. - 6 - • Variables were used without clear definitions, and final solutions were often expressed in terms of unidentified variables. This indicated a lack of interpretation of results within the context of the real-world problems. Interpretation involves translating mathematical outcomes back into meaningful real-life conclusions. • Learners did not verify or validate their solutions. Validation is critical for assessing the accuracy and appropriateness of both the mathematical model and its results in relation to the real-world context. The findings suggest that Mathematics teachers should be encouraged to adopt a mathematical modelling approach in teaching and learning. It can be inferred that learners had limited or no exposure to mathematical modelling, as key processes—such as defining variables, making assumptions, interpreting results, and validating solutions—were consistently omitted. According to the Curriculum and Assessment Policy Statement (CAPS), mathematical modelling should serve as a central focus of the Mathematics curriculum (Department of Basic Education [DBE], 2011). Therefore, the Department of Education has a responsibility to ensure the effective implementation of mathematical modelling, emphasising the integration of real-life contexts across all aspects of the curriculum.

2026-01-01T00:00:00Z Olivier, Christiaan https://ir.unisa.ac.za/handle/10500/32632 2026-06-17T08:04:56Z 2026-02-01T00:00:00Z

A study of synchronisation in the classical phase-oscillator model of an electrical power grid Olivier, Christiaan In this work, we study synchronisation in power grids using a classical phase oscillator model that can be thought of as a variant of the famous Kuramoto model for coupled phase oscillators. In the recent literature, the connection between a Kuramoto-like model and power grids has been made by Filatrella, Nielsen and Pedersen. Here, we will show that this connection goes much further back, to the so-called Classical Model of power grids that was introduced in 1951 by the work of Boast and Rector. We also observe that in 2018, Arinushkin and Anishchenko developed a Kuramotolike model for power grids in which, for the first time, there appear non-negligible phase-lag parameters as a result of the Kron reduced approximation. Although a single phase-lag (or frustration) parameter had been introduced much earlier in the so-called Kuramoto-Sakaguchi model (from 1986), Arinushkin and Anishchenko were the first to introduce multiple phase-lag parameters into a Kuromoto-like model for power grids. Unfortunately, our attempts to replicate their results soon revealed that they used a too-large, fixed time step for the numerical time integration of their equations, and that this led them to make several erroneous conclusions about the grid which they modelled. Therefore, in Chapter 3, we give a detailed critique of the 2018 paper by Arinushkin and Anishchenko. Then, in a follow-up work by Arinushkin and Vadivasova, from 2021, we observe that use was made of nonlinear damping to control the synchronicity of the Kron reduced grid. In this case, we were able to reproduce all the results of Arinushkin and Vadivasova. We were able to develop a more efficient proportional control scheme, based on the global order parameter. Our proposed control scheme and its results were presented at the 2023 International Conference on Electrical, Computer, and Energy Technologies (ICECET). The resulting conference proceeding is included here, in slightly revised form, as Chapter 4. Finally, in Chapter 5, we provide a brief summary of our main findings and some suggestions for future work.

2026-02-01T00:00:00Z Kgwadibane, Tshupo https://ir.unisa.ac.za/handle/10500/32566 2026-06-07T13:17:25Z 2025-12-05T00:00:00Z

Nickel-manganese phosphate/electrochemical exfoliated graphene nanocomposites for hybrid supercapacitors Kgwadibane, Tshupo The global shift toward sustainable energy technologies has increased the demand for advanced energy storage systems that deliver both high energy and power densities. Conventional supercapacitors provide excellent power output, rapid charge-discharge capability, and superior cycling stability; however, their low energy density restricts practical applications. In contrast, rechargeable batteries offer higher energy densities but are limited by slower charge rates and reduced cycling stability. Hybrid configurations that integrate the complementary advantages of both systems have therefore emerged as a promising approach to achieving balanced performance. Nickel-manganese phosphate/electrochemically exfoliated graphene NiMn(PO4)2/EEG) nanocomposite was synthesized via a hydrothermal method. Structural and morphological analyses, including X-ray diffraction (XRD), scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS), high-resolution scanning electron microscopy (HRSEM), Fourier-transform infrared spectroscopy (FTIR), and Raman spectroscopy, confirmed the formation of well well-crystallised composite with homogeneous morphology. The NiMn(PO4)2/EEG composite leverages the multiple redox-active sites and structural robustness of bimetallic phosphate combined with the high conductivity of electrochemically exfoliated graphene, resulting in enhanced charge transport efficiency and electrochemical performance. Additionally, this work presents an investigation of heteroatom-doped EEG thin film synthesised via a two-step process involving graphite intercalation and electrochemically exfoliation in sulphuric-phosphoric acid medium, enabling in-situ doping with nitrogen (N), phosphorus (P), and sulphur (S). The exfoliation products were vacuum filtered to form porous films. Raman spectroscopy revealed Fermi-level shifts of approximately 0.5 eV and heterogeneous defect distributions. The doped EEG films exhibited enhanced electrical conductivity (~10,000 S·m-1) and improved interfacial properties, as evidenced by reduced adhesion forces in force-distance measurements. Electrochemical analyses demonstrated that Fermi-level modulation facilitated rapid interfacial charge transfer by lowering the electrode-electrolyte potential barrier. The doped EEG films achieved a specific capacitance of 150.5 F·g-1 at 1.0 A·g-1, confirming their potential as highly conductive supports for hybrid electrode configurations. Furthermore, a NiMn(PO4)2/EEG composite was integrated with activated carbon (AC) derived from wastewater sludge to fabricate energy storage devices. The NiMn(PO4)2/EEG composite was synthesised hydrothermally, while AC was produced via phosphoric acid activation. Characterisation verified the formation of a mixed-metal phosphate phase anchored on few-layer graphene. The optimised NiMn(PO4)2/50 mg EEG electrode achieved a high specific capacity of 822.1 C·g-1 at 1 A·g-1, significantly outperforming pristine NiMn(PO4)2. In an asymmetric configuration (NiMn(PO4)2/EEG//AC), the device delivered an energy density of 40.0 Wh·kg-1, a peak power density of 6538 W·kg-1, and retained 87% of its capacitance after 5000 cycles at 5 A·g-1. These results underscore the synergistic contribution of EEG towards improved electrical conductivity and redox kinetics, while demonstrating the potential of wastewater sludge-derived AC for sustainable electrode development. Overall, this research integrates synthesis, characterisation, and electrochemical evaluation to elucidate the role of heteroatom-doped EEG in enhancing the electrochemical behaviour of NiMn(PO4)2-based electrodes. By uniquely combining NiMn(PO4)2, heteroatom-doped graphene, and waste-derived activated carbon, this study presents an innovative, sustainability-oriented approach to device design. These findings contribute to the advancement of scalable, sustainable energy storage technologies.

2025-12-05T00:00:00Z Nompetsheni, Indiphile https://ir.unisa.ac.za/handle/10500/32534 2026-06-04T10:00:57Z 2025-10-22T00:00:00Z

Nano-engineered electrochemical aptasensors for label-free detection of cryptosporidium, cadmium and arsenic in water Nompetsheni, Indiphile Water is an essential resource for human survival, agriculture, and livestock. However, over the past thirty years, the World Health Organization has reported growing concerns about the impact of environmental pollution on water quality. Water quality is deteriorating due to contamination from microbes and heavy metals. Among the major microbial and potential heavy metals in water are Cryptosporidium (Crypto), cadmium (Cd2+) and arsenic. Crypto is an intestinal protozoan parasite that has become a significant cause of cryptosporidiosis, a gastrointestinal disease that can affect healthy adults and may be fatal for children and individuals with weakened immune systems. In contrast, Cd2+ and arsenic are amongst the most toxic and harmful metal ions found in the environment. These metals are highly mobile and can accumulate and spread throughout ecosystems. When ingested, they cause various health issues, including cardiovascular diseases, acute poisoning and cancer. These contaminants pose serious risks to aquatic species and the ecosystem at large. Early diagnostic methods for detecting Crypto, Cd2+, and arsenic were developed using microscopy, molecular, and spectroscopic techniques. However, these methods often yield false-negative results, are time-consuming, lack sensitivity and specificity, and have low detection limits. Crypto, arsenic, and Cd2+ pose a challenge to delivering safe drinking water due to their low concentrations in large volumes. Consequently, there is a need to develop portable, sensitive, and selective methods for detecting Crypto, arsenic, and Cd2+ at trace levels. This work develops a novel carbon quantum dot viii titanium dioxide (CQD-TiO2), Mil101(Fe)-CQD-TiO2 based-aptasensor platform capable of label-free simultaneous detection of Crypto and heavy metals at trace levels in phosphate buffer solutions and real water samples. The electrocatalysts used in this work were synthesized using precipitation and hydrothermal methods. Various characterization techniques, such as High-resolution transmission electron microscopy (HR-TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS), were employed to confirm the structural and morphological properties of the synthesized materials. The electrochemical properties of the modified electrodes were studied using cyclic voltammetry (CV), Electrochemical impedance spectroscopy (EIS), square-wave voltammetry (SWV), and Chronopotentiometry (CP), revealing enhanced reaction kinetics and improved stability. The use of various electrocatalysts as aptamer vehicles on the electrode surface has significantly improved the performance of aptasensors, resulting in greater selectivity, higher accuracy, and lower detection limits. As a result, a CQD-TiO2-based aptasensor platform was developed for detecting Crypto, achieving a detection limit of 0.0024 ng L-1, and a sensitivity of 0.27 mA μM-1. In another study, an electrochemical aptasensor platform based on Mil101(Fe)-CQD-TiO2 ternary composite achieved a detection limit of 0.001 ng L-1 for Crypto with a sensitivity of 0.529 mA μM-1. The aptasensor demonstrated excellent performance in detecting Cd2+ and arsenic, achieving low detection limits of 0.073 ng L-1 for Cd2+ and 0.092 ng L-1 for arsenic, with sensitivities of 0.127 mA μM-1 and 0.0065 mA μM-1. All developed aptasensor platforms demonstrated limits of detection within the limits reported in the literature. Thus, GCE-Mil101(Fe)-CQD-TiO2-Apt-BSA platform showed a low limit of detection, demonstrating high sensitivities and selectivity compared to conventional techniques. The aptasensor platforms showed acceptable recovery rates when tested with real water samples and demonstrated ix good stability, reproducibility, and selectivity. These aptasensors have significant potential for integration with microfluidic and on-chip technology, enabling the early detection of pathogens and trace metals.

2025-10-22T00:00:00Z