Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

Structure learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One of them is to generate multiple approximate structures and then to reduce the ensemble to a representative structure. It is possible to use the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this doctoral research, it was made an analogy with an adapted one-dimensional random-walk for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across benchmark datasets applying the Matthews Correlation Coefficient as the performance metric. In the experiments using a recent medical dataset, the BN resulting from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed. In literature, the feature accounted along of the perturbed structures has been the edges and not the directed edges (arcs) as in this thesis. That modified strategy still was applied to an elderly dataset to identify potential relationships between variables of medical interest but using an increased threshold instead of the predict by the proposed formula - such prudence is due to the possible social implications of the finding. The motivation behind such an application is that in spite of the proportion of elderly individuals in the population has increased substantially in the last few decades, the risk factors that should be managed in advance to ensure a natural process of mental decline due to ageing remain unknown. In the learned structural model, it was graphically investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome and the indicator of mental decline referred to as Cognitive Impairment. In this investigation, the concept known in the context of BNs as D-separation has been employed. Results of the carried out study revealed that the dependence between Metabolic Syndrome and Cognitive Variables indeed exists and depends on both Body Mass Index and age. / O aprendizado da estrutura de uma Rede Bayesiana (BN) é um problema NP-difícil, e o uso de estratégias sub-ótimas é essencial em domínios que envolvem muitas variáveis. Uma delas consiste em gerar várias estruturas aproximadas e depois reduzir o conjunto a uma estrutura representativa. É possível usar a frequência de ocorrência (no conjunto de estruturas) como critério para aceitar um arco dominante entre dois nós e assim obter essa estrutura única. Nesta pesquisa de doutorado, foi feita uma analogia com um passeio aleatório unidimensional adaptado para deduzir analiticamente um limiar de decisão apropriado para essa frequência de ocorrência. A expressão de forma fechada obtida foi validada usando bases de dados de referência e aplicando o Coeficiente de Correlação de Matthews como métrica de desempenho. Nos experimentos utilizando dados médicos recentes, a BN resultante da frequência de corte analítica capturou as associações esperadas entre os nós e também obteve melhor desempenho de predição do que as BNs aprendidas com limiares vizinhos ao calculado. Na literatura, a característica contabilizada ao longo das estruturas perturbadas tem sido as arestas e não as arestas direcionadas (arcos) como nesta tese. Essa estratégia modificada ainda foi aplicada a um conjunto de dados de idosos para identificar potenciais relações entre variáveis de interesse médico, mas usando um limiar aumentado em vez do previsto pela fórmula proposta - essa cautela deve-se às possíveis implicações sociais do achado. A motivação por trás dessa aplicação é que, apesar da proporção de idosos na população ter aumentado substancialmente nas últimas décadas, os fatores de risco que devem ser controlados com antecedência para garantir um processo natural de declínio mental devido ao envelhecimento permanecem desconhecidos. No modelo estrutural aprendido, investigou-se graficamente o mecanismo de dependência probabilística entre duas variáveis de interesse médico: o fator de risco suspeito conhecido como Síndrome Metabólica e o indicador de declínio mental denominado Comprometimento Cognitivo. Nessa investigação, empregou-se o conceito conhecido no contexto de BNs como D-separação. Esse estudo revelou que a dependência entre Síndrome Metabólica e Variáveis Cognitivas de fato existe e depende tanto do Índice de Massa Corporal quanto da idade.

Structure learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One of them is to generate multiple approximate structures and then to reduce the ensemble to a representative structure. It is possible to use the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this doctoral research, it was made an analogy with an adapted one-dimensional random-walk for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across benchmark datasets applying the Matthews Correlation Coefficient as the performance metric. In the experiments using a recent medical dataset, the BN resulting from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed. In literature, the feature accounted along of the perturbed structures has been the edges and not the directed edges (arcs) as in this thesis. That modified strategy still was applied to an elderly dataset to identify potential relationships between variables of medical interest but using an increased threshold instead of the predict by the proposed formula - such prudence is due to the possible social implications of the finding. The motivation behind such an application is that in spite of the proportion of elderly individuals in the population has increased substantially in the last few decades, the risk factors that should be managed in advance to ensure a natural process of mental decline due to ageing remain unknown. In the learned structural model, it was graphically investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome and the indicator of mental decline referred to as Cognitive Impairment. In this investigation, the concept known in the context of BNs as D-separation has been employed. Results of the carried out study revealed that the dependence between Metabolic Syndrome and Cognitive Variables indeed exists and depends on both Body Mass Index and age. / O aprendizado da estrutura de uma Rede Bayesiana (BN) é um problema NP-difícil, e o uso de estratégias sub-ótimas é essencial em domínios que envolvem muitas variáveis. Uma delas consiste em gerar várias estruturas aproximadas e depois reduzir o conjunto a uma estrutura representativa. É possível usar a frequência de ocorrência (no conjunto de estruturas) como critério para aceitar um arco dominante entre dois nós e assim obter essa estrutura única. Nesta pesquisa de doutorado, foi feita uma analogia com um passeio aleatório unidimensional adaptado para deduzir analiticamente um limiar de decisão apropriado para essa frequência de ocorrência. A expressão de forma fechada obtida foi validada usando bases de dados de referência e aplicando o Coeficiente de Correlação de Matthews como métrica de desempenho. Nos experimentos utilizando dados médicos recentes, a BN resultante da frequência de corte analítica capturou as associações esperadas entre os nós e também obteve melhor desempenho de predição do que as BNs aprendidas com limiares vizinhos ao calculado. Na literatura, a característica contabilizada ao longo das estruturas perturbadas tem sido as arestas e não as arestas direcionadas (arcos) como nesta tese. Essa estratégia modificada ainda foi aplicada a um conjunto de dados de idosos para identificar potenciais relações entre variáveis de interesse médico, mas usando um limiar aumentado em vez do previsto pela fórmula proposta - essa cautela deve-se às possíveis implicações sociais do achado. A motivação por trás dessa aplicação é que, apesar da proporção de idosos na população ter aumentado substancialmente nas últimas décadas, os fatores de risco que devem ser controlados com antecedência para garantir um processo natural de declínio mental devido ao envelhecimento permanecem desconhecidos. No modelo estrutural aprendido, investigou-se graficamente o mecanismo de dependência probabilística entre duas variáveis de interesse médico: o fator de risco suspeito conhecido como Síndrome Metabólica e o indicador de declínio mental denominado Comprometimento Cognitivo. Nessa investigação, empregou-se o conceito conhecido no contexto de BNs como D-separação. Esse estudo revelou que a dependência entre Síndrome Metabólica e Variáveis Cognitivas de fato existe e depende tanto do Índice de Massa Corporal quanto da idade.