Literature describes different stances with respect to conceptual and procedural mathematical knowledge. The concept-driven versus skills-orientated perspectives have led to “math wars” between researchers, while some mathematics education specialists advocate that the five strands of mathematical proficiency should be seen as interconnected. Conceptual knowledge is the knowledge of concepts or principles, and procedural knowledge the knowledge of procedures. Both types of knowledge are critical components of mathematical proficiency. This study used a mixed methods design to analyse the relationship between conceptual and procedural knowledge. The qualitative content analysis investigated relations between procedural and conceptual knowledge within the solutions of 33 calculus items. The analysis included the number of procedural and conceptual steps needed to answer the item, item label and item classification into one of four knowledge classes based on the type and quality of knowledge. The items were included in a data collection instrument used for quantitative analysis. Rasch analysis was performed to measure item difficulty and person proficiency, and describe the underlying cognitive construct between items. The Rasch person–item map confirmed that items were not clustered together per class and that item difficulty was not linked to the number of procedural and/or conceptual steps needed to do the mathematics. Confirmatory factor analysis showed over-correlation between classes and that defined classes cannot be separated, confirming integration of procedural and conceptual cognitive processes. The relationship between procedural and conceptual knowledge within and between items is complex. Findings indicated that item solutions drew on both procedural and conceptual components that cannot be separated. Solutions could follow more than one approach and analyses could differ, since what is conceptual for one student could be procedural for another. Therefore, teaching strategies should navigate between concepts and procedures, methods and representations. / Thesis (PhD)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / PhD / Unrestricted

Background. As computing power has increased over the years, larger parts of the digital graphics industries are moving towards using real-time rendering for their solutions. The fast iteration and visual response help make the creative processes and communication more accessible in both the desktop and smartphone markets. One noticeably growing area using real-time rendering is the communication between people and audiences using online chat applications with virtual avatars. As humans, social interaction is essential to every aspect of our health. The requirements of remote communications to satisfy the needs of social interaction are facial expressions. Facial expressions involve motion. Thus making real-time rendering mandatory for having facial expressions in computer-generated images. This thesis shows the performance result of having real-time procedural-generated eye features. Objectives. This thesis is based on an experiment by developing a data set of duration for computing different visual aspects of anime eyes, the aim is to help inform the creation of more complete and optimized shader solutions. The objectives of this thesis are to produce a profiling application, produce a collection of eye references, produce a collection of visual eye features, produce shaders based on the collections, and measure the time performance of the shaders. Method. Doing this experiment involves producing a profiling application in the C++ programming language using the OpenGL graphics API. The profiling application can render a set of shaders and measure time metrics. The experiment is executed on two different computers with different specifications. By gathering a collection of eye references from online resources, targeting popular media in the anime style, a collection of visual eye features can be established with common and unique attributes. The collections allow for the creation of a set of shaders that replicate the collected eye features. With the profiling application and shaders, a data collection of time metrics are composed. Results. The final results of the profiling experiment have a collection of 29 shaders representing different eye features. The profiling tests gave the results of how many milliseconds it took for a set number of frames to render each produced shader. This result is shown with the help of two different graphs for each computer that executed the experiment. Deconstructing the resulting data helps to analyze and distinguish interesting aspects. Conclusions. From the result of this thesis experiment, the conclusion can be made that an eye feature by itself is a fast process for the GPU to compute on its own. Aset of eye features combined to create a final eye shader including animation and eye tracking is a valid future work section regarding this thesis experiment.

Digitization and characterization of urban spaces are essential components as we move to an ever-growing ’always connected’ world. Accurate analysis of such digital urban spaces has become more important as we continue to get spatial and social context-aware feedback and recommendations in our daily activities. Modeling and reconstruction of urban environments have thus gained unprecedented importance in the last few years. Such analysis typically spans multiple disciplines, such as computer graphics, and computer vision as well as architecture, geoscience, and remote sensing. Reconstructing an urban environment usually requires an entire pipeline consisting of different tasks. In such a pipeline, data analysis plays a strong role in acquiring meaningful insights from the raw data. This dissertation primarily focuses on the analysis of various forms of urban data and proposes a set of techniques to extract useful information, which is then used for different applications. The first part of this dissertation presents a semi-automatic framework to analyze facade images to recover individual windows along with their functional configurations such as open or (partially) closed states. The main advantage of recovering both the repetition patterns of windows and their individual deformation parameters is to produce a factored facade representation. Such a factored representation enables a range of applications including interactive facade images, improved multi-view stereo reconstruction, facade-level change detection, and novel image editing possibilities. The second part of this dissertation demonstrates the importance of a layout configuration on its performance. As a specific application scenario, I investigate the interior layout of warehouses wherein the goal is to assign items to their storage locations while reducing flow congestion and enhancing the speed of order picking processes. The third part of the dissertation proposes a method to classify cities based on their functional behavior. Commonly used computational approaches concentrate on geometric descriptors, for both images and laser scans. Instead, I analyze street networks, both their topology (i.e., connectivity) and geometry (i.e., layout), in an attempt to understand the factors that play dominant roles in determining the characteristic of cities. A set of street network descriptors is proposed to capture the essence of city layouts and used, in a supervised setting, to classify and categorize various cities across the world. Each part of the dissertation shows the utility of the proposed methods through describing a variety of applications on different examples.

The diploma thesis presents current ideas and relevant psychological theories in the field of fairness and perceived justice, and in such context, it analyzes the mediation process, especially the process of court-initiated mediation in the Czech Republic as an alternative conflict resolution method. Moreover, the thesis aims to provide information on the attitudes of different public representatives to the court-initiated mediation, with special regard to the perception of fairness and justice of the mediation process and its outcome. The empirical part of the thesis introduces an attitudes research of various public representatives to the court-initiated mediation. The research proved a statistically significant difference in attitudes towards fairness and perceived justice of mediation among observed groups of attorneys, junior attorneys, mediators, judges, mediators with attorney license, and a group of other professions. Among the specific groups, there was a statistically significant difference between the groups of attorneys and mediators, attorneys and mediators with attorney license, and finally between the groups of attorneys and the group of other professions. The research data were collected through the newly developed attitude Questionnaire of Perceived Justice of Mediation (DVSM)....

Humans use creativity and manual dexterity to create things, usually in a labor-intensive process. Procedural content generation (PCG) is an approach where computers do most of the manual work of creating virtual objects, while a human leads the creative process. One problem with PCG is that created objects tend to look too perfect and artificial, leading to research into simulating the aging process of created virtual objects. Simulating the growth of living organisms such as lichens on existing virtual objects has been a focus of research. Most previous techniques lack a clear evaluation of the realism of the results. In this thesis, a lichen growth simulation is implemented and evaluated in terms of perceived realism. Specifically, the target of the simulation is lichen growth on horizontal stone surfaces represented using a set of textures. The lichen growth simulation is slow but robust and flexible, capable of generating a wide range of output textures. 75 participants were recruited among university students and video game industry professionals, asked to compare the realism of lichens generated with different parameter settings. The investigated parameters are the scale of the lichens, the compactness of the lichens, and the number of lichen clusters (density). Participants perceived surfaces with a dense or medium-dense cover of small scale, semi-compact lichen clusters as the most realistic, while surfaces with a sparse cover of large scale, very compact or very lacy lichen clusters were perceived as the least realistic. The lichens perceived as the most realistic are also among the most computationally expensive to produce. This outcome tells us that there is a trade-off between realism and simulation time in the lichen growth simulation. The simulation is able to generate a wide range of lichen appearances, though the speed of the simulation can be greatly improved in multiple ways. / Människor använder kreativitet och manuell färdighet för att skapa saker, vanligtvis i en arbetsintensiv process. Procedurell innehållsgenerering (eng. PCG) är ett tillvägagångssätt där datorer gör majoriteten av det manuella arbetet i skapandet av virtuella objekt, och en människa leder den kreativa processen. Ett problem med PCG är att de skapade objekten tenderar att ha ett för nytt och artificiellt utseende, vilket har lett till forskning kring att simulera åldrandeprocessen för virtuella objekt. Forskning har bland annat fokuserat på att simulera tillväxten av levande organismer såsom lavar på existerande virtuella objekt. Flera tidigare tekniker saknar en tydlig evaluering av resultatens realism. I denna studie implementeras en lavtillväxtsimulering som evalueras med avseende på upplevd realism. Simuleringens mål är specifikt att simulera lavar på horisontella stenytor representerade av en uppsättning texturer. Simuleringen är långsam men robust och flexibel, och kapabel till att generera ett brett omfång av resultat. 75 deltagare rekryterades bland universitetsstudenter och bland arbetare i datorspelsindustrin, och ombads jämföra realismen hos lavar genererade med olika parameterinställningar. De undersökta parametrarna är skalan på lavarna, kompaktheten på lavarna och antalet lavar (densitet). Deltagarna upplevde att ytor med hög och mellanhög densitet av småskaliga semikompakta lavar var mest realistiska, medan ytor med låg densitet av storskaliga kompakta eller mycket utspridda lavar upplevdes som minst realistiska. De lavar som upplevdes vara mest realistiska är också bland de beräkningsmässigt dyraste att generera. Detta resultat visar att det finns en avvägning mellan realism och simuleringstid i lavtillväxtsimuleringen. Simuleringen kan generera ett brett omfång av lavutseenden, men simuleringens snabbhet kan förbättras på flera sätt.

Background. Games are becoming increasingly large, and that includes space games. They require new features to be developed and planets to be generated. Heightmap- and marching cubes-algorithms, allow for the generation of spherical objects and planets when adapted. With the help of noise and these algorithms,spherical terrains are created in this project the performance of the individual solutions is measured. Objectives. It is the scope of this project to implement two planet generators, one based on heightmap technology and another based on the marching cube algorithm.These are then compared in terms of performance to see the differences in memory consumption and which one is faster.  Methods. The two techniques, planetary marching cubes, and a planetary heightmap-based solution are implemented in the Unity Engine. These generators then generate a set of different sized terrains multiple times and then average the results to gather performance data. This data is then used to compare the two solutions. This yields a comparable result between the two techniques which can then be analysed.  Results. The resulting measurements show the Marching cubes implementation uses a higher consumption of both VRAM and RAM than the heightmap solution, which is very memory efficient. Furthermore, the generation time of the heightmap solution is significantly faster than the marching cubes implementation. Conclusions. It is concluded that the planetary marching cubes algorithm utilizes more resources, consumes time to generate and is slower than the heightmap-based solution. The planetary marching cubes algorithm does however support additional features.

An addict to magic in an (alternate reality) magical world wakes up with the ability to talk to the dead and must navigate sobriety while reluctantly solving cold cases for the cops.

Together with the growth of procedural content generation in game development, there is a need for a viable generation method of procedural context to make sense of the content within game space. Previous research discusses how interactivity and narrative are almost opposite of each other and when combined needs to be generated in two steps, one for the game space and the other for context. We propose procedural narrative as context through objectives, as a useful means to structure content in games. In this paper we present and describe an artefact developed as a sub-system to the Evolutionary Dungeon Designer (EDD), that procedurally generates objectives for the dungeons created with the tool. The artefact is developed with macro patterns which can be defined as an extension of the existing meso patterns in EDD. The macro patterns are used to generate objectives in the rooms of the dungeons, and the system evaluates the priority of the room objectives based on the design of the dungeon and the quality of the objective to maximize the usage of game space and create a suitable narrative. The work for this thesis and its artefact resulted in a successful expansion on the knowledge of procedural narrative generation by presenting macro patterns as a viable solution for contextualization of procedural game content.

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