Basic mathematical competency seems to be lacking for engineering students starting their studies in this field. Students generally find the cognitive transition from secondary to tertiary mathematics challenging which in turn negatively influences their academic achievement in mathematics. The cognitive challenge is the transition from the application of mathematics to familiar questions to applying mathematical principles to varying practical application and problem solving. Mathematics provides the foundation for the cognitive toolset required for the development of skills required for analysing engineering systems and processes. It is therefore important to assess mathematical and cognitive competency and ability at the time of admission to a tertiary institution in order to identify and address gaps. This research demonstrates that first-year engineering students need to have a specific level of mathematical competency and cognitive ability to use mathematics within the context of engineering studies. This research attempts to connect the mathematic competency of first year engineering students to their academic results for subjects in the first year curriculum that rely heavily on mathematical competency. To satisfy the research question, the study firstly looks at relevant literature to identify the mathematical competency levels as well as the operational specification. Secondly, development theories and taxonomies were analysed to gain insight into the development processes associated with learning, cognitive development and the gap between cognitive competencies in transition from secondary to tertiary education. Further, cognitive competencies were identified that are essential for successful completion of first year engineering modules. Through synthesis of the different theories and taxonomies a framework was identified. This framework was used to analyse secondary data in order to measure mathematical and cognitive levels. Thirdly, the theoretical investigation was followed by a three-phase empirical study. A mixed quantative-qualitative (QUAN-qual) approached was followed. Phase 1 uses the assessment framework to measure first year students‟ mathematical competency at the inception of their studies as well as at the completion of their first semester. The mathematical competency at inception was measured with their Grade 12 mathematics marks and with relevant analysis of their initial bridging assessments, on a question by question basis. In addition, their first semester exams questions were analysed using the same approach as above. Phase 2 comprises the measurement of the relationship between the mathematical competency of first year enigineering students at admission and their achievement levels in selected first year subjects that required mathematical competency. Phase 3 includes the guidelines derived from the gaps and shortcomings identified. These gaps were identified in order to inform appropriate study support to first year students and to assists academic personnel with setting appropriate and dependable admission standards. The analysis of mathematical competency creates quality data that gives a clearer picture than a simple comparison of admission scores and first semester marks. The empirical study contributes to a better understanding of the problems associated with the transition from secondary to tertiary learning environments. From the study it was derived that study inception information of the students correlated only with their academic results on questions that tested mathematical and programming application. The inception information was not a predictor of mathematical achievement and results for both the lowest and highest mathematical competency levels. Futher study in this field is required to create frameworks for the measurements of both low and high levels of mathematical competency. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

<p>Professional engineers think and act in distinctive ways when addressing engineering problems. Students need to develop this reasoning or engineering thinking during their education. Unfolding the undergraduate students’ thinking is a necessary step in designing experiences and teaching materials that foster not only their understanding of engineering concepts but also their learning to think as professional engineers. While there are previous studies about the students' thinking in other disciplines, more research is needed in engineering. This three-study dissertation aims to further our comprehension of undergraduate students’ engineering thinking using an adapted version of the Engineering Habits of Mind (EHoM) model. Specifically, the dissertation’s studies work together to continue the research that addresses the question:<em> What are the characteristics of undergraduate students</em>’ <em>engineering thinking?</em></p> <p><br></p> <p>The first study used naturalistic inquiry to holistically explore the cognition associated with the EHoM of senior chemical engineering students when improving a chemical plant. The analysis of students’ interactions showed that their redesign process followed an iterative co-evolution of the problem and solution spaces. Furthermore, they treated the task as a socio-technical problem considering engineering and non-engineering factors. In addition, while exploring problem and solution entities, they used multiple representations to communicate ideas but had difficulties translating symbolic representations into more physical, concrete representations. Regardless the technical issues and time constraints, the students completed the conceptual redesign and communicated their proposal to the client.</p> <p><br></p> <p>The second study used qualitative content analysis to examine first-year engineering students’ ideation as a cognitive skill associated with the EHoM of problem finding and creative problem solving. Particularly, it focused on students’ ideation of questions and recommendations when doing data analytics to help improve a client’s enterprise. The analysis of students’ reports showed that they expanded the problem space of the task by bringing additional information that was not provided. They asked questions focused on performing statistical analysis of the dataset and requesting information about the company’s business model. At the end of their data analytics, students made high- and low-quality recommendations considering their alignment with a specific problem, robust evidence, and the client’s needs. </p> <p><br></p> <p>The third study used qualitative descriptive research to investigate undergraduate participants' cognitive competencies within engineering systems thinking at the International Genetically Engineered Machine (iGEM) competition. These competencies are associated with the EHoM of problem finding, creative problem solving, systems thinking, and visualization. Mainly, the study focused on analyzing the evidence of cognitive competencies documented in the publicly available participants’ wikis where they registered their design process. Results showed that iGEM teams developed solutions with biological systems interacting with other systems and used concepts and tools from multiple disciplines. They also cooperated with stakeholders, which helped them analyze their system from multiple lenses. Moreover, depending on their upfront task, they fluidly represented their systems from structural, behavioral, and functional perspectives. </p> <p><br></p> <p>The final chapter of this dissertation presents an overarching discussion across the studies. The findings and implications will support curriculum designers, instructors, and other interested readers to prepare learning environments that promote undergraduate students’ engineering thinking. Furthermore, they may guide future efforts to continue exploring the students' thinking process when addressing engineering problems. </p>