The fundamental goal of this study is to explore why so many students have difficulty learning mathematics. To achieve this goal, this study focuses on why so many students keep making the same errors over a long period of time. To explore such issues, three basic algebra concepts - variable, equation, and function – are used to analyze students’ errors, possible buggy algorithms, and the conceptual basis of these errors: misconceptions. Through the research on these three basic concepts, it is expected that a more general principle of understanding and the corresponding learning difficulties can be illustrated by the case studies. Although students’ errors varied to a great extent, certain types of errors related to students’ misconceptions occurred frequently and repeatedly after one year of additional instruction. Thus, it is possible to identify students’ misconceptions through working on students’ systematic errors. The causes of students’ robust misconceptions were explored by comparing high-achieving and low-achieving students’ understanding of these three concepts at the object (structural) or process (operational) levels. In addition, high achieving students were found to prefer using object (structural) thinking to solve problems even if the problems could be solved through both algebra and arithmetic approaches. It was also found that the relationship between students’ misconception and object-process thinking explained why some misconceptions were particularly difficult to change. Students’ understanding of concepts at either of two stages (process and object) interacted with either of two aspects (correct conception and misconception). When students had understood a concept as a process with misconception, such misconception was particularly hard to change. In addition, other concerns, such as rethinking the misconception of the “equal sign,” the influence of prior experience on students’ learning, misconceptions and recycling curriculum, and developing teachers’ initial subject knowledge were also discussed. The findings of this study demonstrated that the fundamental reason of misconception of “equal sign” was the misunderstanding of either side of equation as a process rather than as an object. Due to the existence of robust misconceptions as stated in this study, the use of recycling curriculum may have negative effect on students’ understanding of mathematics.

Often a manufacturing process may be a bottleneck or critical to a business. This thesis focuses on the analysis and modelling of such processest, to both better understand them, and to support the enhancement of quality or output capability of the process. The main thrusts of this thesis therefore are: To model inter-process physics, inter-relationships, and complex processes in a manner that enables re-exploitation, re-interpretation and reuse of this knowledge and generic elements e.g. using Object Oriented (00) & Qualitative Modelling (QM) techniques. This involves the development of superior process models to capture process complexity and reuse any generic elements; To demonstrate advanced modelling and simulation techniques (e.g. Artificial Neural Networks(ANN), Rule-Based-Systems (RBS), and statistical modelling) on a number of complex manufacturing case studies; To gain a better understanding of the physics and process inter-relationships exhibited in a number of complex manufacturing processes (e.g. pultrusion, bioprocess, and logistics) using analysis and modelling. To these ends, both a novel Object Oriented Qualitative (Problem) Analysis (OOQA) methodology, and a novel Artificial Neural Network Process Modelling (ANNPM) methodology were developed and applied to a number of complex manufacturing case studies- thermoset and thermoplastic pultrusion, bioprocess reactor, and a logistics supply chain. It has been shown that these methodologies and the models developed support capture of complex process inter-relationships, enable reuse of generic elements, support effective variable selection for ANN models, and perform well as a predictor of process properties. In particular the ANN pultrusion models, using laboratory data from IKV, Aachen and Pera, Melton Mowbray, predicted product properties very well.

Avec l’avènement des images satellitaires à très haute résolution, les approches pixelliques ne donnant plus entière satisfaction ont été remplacées par les approches objets. Cependant, ces approches restent tributaires de la première étape qui permet le passage du pixel vers l’objet, à savoir l’étape de construction. L’architecture séquentielle de ces approches fait que les erreurs de l’étape de construction se répercutent sur l’étape d’identification. Il devient donc primordial de passer de cette architecture séquentielle vers une architecture itérative permettant la collaboration entre les étapes de construction et d’identification. Dans le cadre de cette thèse, nous nous sommes concentrés sur l’étude de l’étape de construction(i.e., la segmentation) comme base de départ pour les approches proposées. Nous avons proposé deux approches objets basées sur les techniques de segmentation les plus propices à la collaboration, à savoir les techniques régions et les techniques collaboratives région/contour. La première approche proposée se base sur une croissance sémantique hiérarchique. Elle permet de combiner les algorithmes de croissance de régions et les approches d’analyse d’images orientées objets. La croissance étant spécifique à la classe du germe de départ, nous avons proposé deux adaptations de l’approche sur les objets les plus rencontrés dans le contexte urbain, à savoir, les routes et les bâtiments. La deuxième approche utilise un algorithme évolutionnaire local permettant un paramétrage local des différents agents régions et contours évoluant au sein d’un système multi-agents. / Object based image analysis is a rising research area in remote sensing. However, existing approaches heavily rely on the object construction process, mainly due to the lack of interaction between the two steps, i.e., Construction and identification.In this thesis, we focused on the study of the construction phase (i.e., segmentation) as a basis for the proposed approaches. The first proposed approach is based on a hierarchical semantic growth. This approach allows merging region-growing algorithms and Object Based Image Analysis approaches. Due to the dependency of the semantic growth on the seed class, we propose two adaptations of the approach on the most used class in the urban context, i.e., roadsand buildings. The second approach benefits of both multi-agent systems and genetic algorithms characteristics. It overcomes the threshold’s dependency of the proposed cooperative multi-agent system between an edge approach and a region approach. The genetic algorithm is used to automatically find building extraction parameters for each agent based on expert knowledge. The proposed approaches have been validated on a very high-resolution image of the urban area of Strasbourg.