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The COVID-19 pandemic has had a significant impact on high-stakes testing, including the national benchmark tests in South Africa. Current linear testing formats have been criticized for their limitations, leading to a shift towards Computerized Adaptive Testing [CAT]. Assessments with CAT are more precise and take less time. Evaluation of CAT programs requires simulation studies. To assess the feasibility of implementing CAT in NBTs, SimulCAT, a simulation tool, was utilized. The SimulCAT simulation involved creating 10,000 examinees with a normal distribution characterized by a mean of 0 and a standard deviation of 1. A pool of 500 test items was employed, and specific parameters were established for the item selection algorithm, CAT administration rules, item exposure control, and termination criteria. The termination criteria required a standard error of less than 0.35 to ensure accurate abilities estimation. The findings from the simulation study demonstrated that fixed-length tests provided higher testing precision without any systematic error, as indicated by measurement statistics like CBIAS, CMAE, and CRMSE. However, fixed-length tests exhibited a higher item exposure rate, which could be mitigated by selecting items with fewer dependencies on specific item parameters (a-parameters). On the other hand, variable-length tests demonstrated increased redundancy. Based on these results, CAT is recommended as an alternative approach for conducting NBTs due to its capability to accurately measure individual abilities and reduce the testing duration. For high-stakes assessments like the NBTs, fixed-length tests are preferred as they offer superior testing precision while minimizing item exposure rates.

This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students' initially developed conceptual and procedural knowledge gains. The rectangular and polar forms of the complex number were connected and merged using GeoGebra's computer algebra systems and dynamic geometric systems platforms. Despite the centrality of complex numbers to the undergraduate mathematics curriculum, students tend to experience conceptual and procedural obstacles in mathematics-dependent physics engineering topics such as mechanical vector analysis and electric-circuit theory. The study adopted an exploratory sequential mixed methods design and involved purposively selected first-year engineering mathematics students at a South African university. The constructivist approach and Realistic Mathematical Education underpinned the empirical investigation. Data were collected from students' scripts. Implementing GeoGebra-enriched activities and providing carefully designed representational support sought to enhance students' conceptual and procedural knowledge of complex numbers and problem representational competence. The intervention additionally helped students to conceptualise and visualise a complex rectangular number. Implications for technology-enhanced pedagogy are discussed. Contribution: The article provides exploratory insights into the development of undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers using GeoGebra as a dynamic digital tool. Key findings from the study demonstrated that GeoGebra appears to be an effective modelling tool that can be harnessed to demystify the complexity of mathematics students' conceptual and procedural knowledge of complex numbers.