This study uses a discourse analysis from the perspectives of James Paul Gee (2005; 1999) in order to establish a socio-situated view of why grade 10 students often experience difficulties in representing mathematical word problems into appropriate equations and expressions that enable a solution to the problems. A discursive methodology was used to throw light on the difficulties that students experience that was different from the perspectives adopted previously, viz. from a view of the structure of the problems, from a pedagogic point of view and a cognitive understanding. An initial case study in one school in which four students were selected revealed that a master model existed that students were enacting when doing and talking about their experiences with word problems, viz. that word problems are obfuscatory. This master model rendered the students relatively mathematically helpless within a Discourse of school mathematics word problems. In order to more fully understand these findings an extended study was set up in which the methodology and analytic framework were refined. This extended study saw four students at each of three different sites selected to participate. The findings of this extended study were that the students enacting a situated Discourse model were more enabled within the Discourse of school mathematics word problems, whilst those enacting a deficit Discourse model were either peripheral or outside of that Discourse. This study contributes in that the constructs for the phenomena and the analytic tools within the context of school mathematics needed to be pioneered, adapted and refined over a period of time to address aspects particular to school mathematics. This resulted in a view from a socio-situated perspective which saw a shift in seeing what students do with the problem to what students do in the social setting associated with the problem. From this shift in focus came a new understanding of student difficulties with word problems that gave rise to a sub-Discourse within the Discourse surrounding school mathematics word problems, and students finding themselves in this sub-Discourse becoming marginalised through enacting a deficit Discourse model because they are unable to ascribe to the success model, or situated Discourse model.

A sumarização automática multidocumento visa à produção de um sumário a partir de um conjunto de textos relacionados, para ser utilizado por um usuário particular e/ou para determinada tarefa. Com o crescimento exponencial das informações disponíveis e a necessidade das pessoas obterem a informação em um curto espaço de tempo, a tarefa de sumarização automática tem recebido muita atenção nos últimos tempos. Sabe-se que em um conjunto de textos relacionados existem informações redundantes, contraditórias e complementares, que representam os fenômenos multidocumento. Em cada texto-fonte, o assunto principal é descrito em uma sequência de subtópicos. Além disso, as sentenças de um texto-fonte possuem graus de relevância diferentes. Nesse contexto, espera-se que um sumário multidocumento consista das informações relevantes que representem o total de textos do conjunto. No entanto, as estratégias de sumarização automática multidocumento adotadas até o presente utilizam somente os relacionamentos entre textos e descartam a análise da estrutura textual de cada texto-fonte, resultando em sumários que são pouco representativos dos subtópicos textuais e menos informativos do que poderiam ser. A fim de tratar adequadamente a relevância das informações, os fenômenos multidocumento e a distribuição de subtópicos, neste trabalho de doutorado, investigou-se como modelar o processo de sumarização automática usando o conhecimento semântico-discursivo em métodos de seleção de conteúdo e o impacto disso para a produção de sumários mais informativos e representativos dos textos-fonte. Na formalização do conhecimento semântico-discursivo, foram utilizadas as teorias semântico-discursivas RST (Rhetorical Structure Theory) e CST (Cross-document Structure Theory). Para apoiar o trabalho, um córpus multidocumento foi anotado com RST e subtópicos, consistindo em um recurso disponível para outras pesquisas. A partir da análise de córpus, foram propostos 10 métodos de segmentação em subtópicos e 13 métodos inovadores de sumarização automática. A avaliação dos métodos de segmentação em subtópicos mostrou que existe uma forte relação entre a estrutura de subtópicos e a análise retórica de um texto. Quanto à avaliação dos métodos de sumarização automática, os resultados indicam que o uso do conhecimento semântico-discursivo em boas estratégias de seleção de conteúdo afeta positivamente a produção de sumários informativos. / The multi-document summarization aims at producing a summary from a set of related texts to be used for an individual or/and a particular task. Nowadays, with the exponential growth of available information and the peoples need to obtain information in a short time, the task of automatic summarization has received wide attention. It is known that in a set of related texts there are pieces of redundant, contradictory and complementary information that represent the multi-document phenomenon. In each source text, the main subject is described in a sequence of subtopics. Furthermore, some sentences in the same text are more relevant than others. Considering this context, it is expected that a multi-document summary consists of relevant information that represents a set of texts. However, strategies for automatic multi-document summarization adopted until now have used only the relationships between texts and dismissed the analysis of textual structure of each source text, resulting in summaries that are less representative of subtopics and less informative than they could be. In order to properly treat the relevance of information, multi-document phenomena and distribution of subtopics, in this thesis, we investigated how to model the summarization process using the semantic-discursive knowledge and its impact for producing more informative and representative summaries from source texts. In order to formalize the semantic-discursive knowledge, we adopted RST (Rhetorical Structure Theory) and CST (Cross-document Structure Theory) theories. To support the work, a multi-document corpus was annotated with RST and subtopics, consisting of a new resource available for other researchers. From the corpus analysis, 10 methods for subtopic segmentation and 13 orignal methods for automatic summarization were proposed. The assessment of methods for subtopic segmentation showed that there is a strong relationship between the subtopics structure and the rhetorical analysis of a text. In regards to the assessment of the methods for automatic summarization, the results indicate that the use of semantic-discursive knowledge in good strategies for content selection affects positively the production of informative summaries.

A sumarização automática multidocumento visa à produção de um sumário a partir de um conjunto de textos relacionados, para ser utilizado por um usuário particular e/ou para determinada tarefa. Com o crescimento exponencial das informações disponíveis e a necessidade das pessoas obterem a informação em um curto espaço de tempo, a tarefa de sumarização automática tem recebido muita atenção nos últimos tempos. Sabe-se que em um conjunto de textos relacionados existem informações redundantes, contraditórias e complementares, que representam os fenômenos multidocumento. Em cada texto-fonte, o assunto principal é descrito em uma sequência de subtópicos. Além disso, as sentenças de um texto-fonte possuem graus de relevância diferentes. Nesse contexto, espera-se que um sumário multidocumento consista das informações relevantes que representem o total de textos do conjunto. No entanto, as estratégias de sumarização automática multidocumento adotadas até o presente utilizam somente os relacionamentos entre textos e descartam a análise da estrutura textual de cada texto-fonte, resultando em sumários que são pouco representativos dos subtópicos textuais e menos informativos do que poderiam ser. A fim de tratar adequadamente a relevância das informações, os fenômenos multidocumento e a distribuição de subtópicos, neste trabalho de doutorado, investigou-se como modelar o processo de sumarização automática usando o conhecimento semântico-discursivo em métodos de seleção de conteúdo e o impacto disso para a produção de sumários mais informativos e representativos dos textos-fonte. Na formalização do conhecimento semântico-discursivo, foram utilizadas as teorias semântico-discursivas RST (Rhetorical Structure Theory) e CST (Cross-document Structure Theory). Para apoiar o trabalho, um córpus multidocumento foi anotado com RST e subtópicos, consistindo em um recurso disponível para outras pesquisas. A partir da análise de córpus, foram propostos 10 métodos de segmentação em subtópicos e 13 métodos inovadores de sumarização automática. A avaliação dos métodos de segmentação em subtópicos mostrou que existe uma forte relação entre a estrutura de subtópicos e a análise retórica de um texto. Quanto à avaliação dos métodos de sumarização automática, os resultados indicam que o uso do conhecimento semântico-discursivo em boas estratégias de seleção de conteúdo afeta positivamente a produção de sumários informativos. / The multi-document summarization aims at producing a summary from a set of related texts to be used for an individual or/and a particular task. Nowadays, with the exponential growth of available information and the peoples need to obtain information in a short time, the task of automatic summarization has received wide attention. It is known that in a set of related texts there are pieces of redundant, contradictory and complementary information that represent the multi-document phenomenon. In each source text, the main subject is described in a sequence of subtopics. Furthermore, some sentences in the same text are more relevant than others. Considering this context, it is expected that a multi-document summary consists of relevant information that represents a set of texts. However, strategies for automatic multi-document summarization adopted until now have used only the relationships between texts and dismissed the analysis of textual structure of each source text, resulting in summaries that are less representative of subtopics and less informative than they could be. In order to properly treat the relevance of information, multi-document phenomena and distribution of subtopics, in this thesis, we investigated how to model the summarization process using the semantic-discursive knowledge and its impact for producing more informative and representative summaries from source texts. In order to formalize the semantic-discursive knowledge, we adopted RST (Rhetorical Structure Theory) and CST (Cross-document Structure Theory) theories. To support the work, a multi-document corpus was annotated with RST and subtopics, consisting of a new resource available for other researchers. From the corpus analysis, 10 methods for subtopic segmentation and 13 orignal methods for automatic summarization were proposed. The assessment of methods for subtopic segmentation showed that there is a strong relationship between the subtopics structure and the rhetorical analysis of a text. In regards to the assessment of the methods for automatic summarization, the results indicate that the use of semantic-discursive knowledge in good strategies for content selection affects positively the production of informative summaries.

This study used discourse analysis (Gee, 2011; 2005; 1999) in order to explore a socio-situated view of how teachers created learning opportunities for the participation of immigrant learners when learning linear programming in a Grade 11 mathematics classroom in South Africa. The aim was to explore that which mathematics teachers do in classrooms with immigrant learners that they will not do if there were no immigrants. A discourse analysis approach was used in order to view the opportunities created through language use not as a tool for communication only but also as a tool for building reality. The study reported in this thesis was conducted in three different settings which are in; urban, township and rural environments. The urban environment focuses on immigrant learners who were born in the Democratic Republic of Congo (DRC), and started schooling there, in the township and rural environment it focuses on immigrant learners born in South Africa with parents born in the Republic of Mozambique or Angola. Three different mathematics classrooms were observed in their natural environment during lessons focusing on linear programming. Data was collected through a learner questionnaire issued before lesson observations. The aim of the learner questionnaire was to understand the language background of the learners in the mathematics classrooms selected for the study. The second method included lesson observation for at most five consecutive days at each setting. It involved observing teachers and immigrant learners during teaching sessions of linear programming activities. The activities included reading, writing, speaking and participating in mathematical activities. These activities were then analysed to understand how teachers created learning opportunities for the immigrant learners. The study contextualised the results from lesson observations by conducting clinical interviews with three immigrant learners, one from each site, to provide insights into the explanations on immigrant learners approaches when solving a linear programming task. The main conclusion in this study is that immigrant learners were successful in linear programming when teachers’ created learning opportunities by using code switching to support them. The main contribution of this study is that it focuses on multilingual mathematics classrooms of immigrant learners in South Africa – a context that has not yet been researched in South African vi mathematics education. Exploring language practices in multilingual mathematics classrooms of immigrant learners provides a different gaze into teaching and learning mathematics in multilingual classrooms in South Africa. Equally important is the extent to which immigrant learners are distinct to multilingual learners in the teaching and learning of linear programming. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)

This study used discourse analysis (Gee, 2011; 2005; 1999) in order to explore a socio-situated view of how teachers created learning opportunities for the participation of immigrant learners when learning linear programming in a Grade 11 mathematics classroom in South Africa. The aim was to explore that which mathematics teachers do in classrooms with immigrant learners that they will not do if there were no immigrants. A discourse analysis approach was used in order to view the opportunities created through language use not as a tool for communication only but also as a tool for building reality. The study reported in this thesis was conducted in three different settings which are in; urban, township and rural environments. The urban environment focuses on immigrant learners who were born in the Democratic Republic of Congo (DRC), and started schooling there, in the township and rural environment it focuses on immigrant learners born in South Africa with parents born in the Republic of Mozambique or Angola. Three different mathematics classrooms were observed in their natural environment during lessons focusing on linear programming. Data was collected through a learner questionnaire issued before lesson observations. The aim of the learner questionnaire was to understand the language background of the learners in the mathematics classrooms selected for the study. The second method included lesson observation for at most five consecutive days at each setting. It involved observing teachers and immigrant learners during teaching sessions of linear programming activities. The activities included reading, writing, speaking and participating in mathematical activities. These activities were then analysed to understand how teachers created learning opportunities for the immigrant learners. The study contextualised the results from lesson observations by conducting clinical interviews with three immigrant learners, one from each site, to provide insights into the explanations on immigrant learners approaches when solving a linear programming task. The main conclusion in this study is that immigrant learners were successful in linear programming when teachers’ created learning opportunities by using code switching to support them. The main contribution of this study is that it focuses on multilingual mathematics classrooms of immigrant learners in South Africa – a context that has not yet been researched in South African vi mathematics education. Exploring language practices in multilingual mathematics classrooms of immigrant learners provides a different gaze into teaching and learning mathematics in multilingual classrooms in South Africa. Equally important is the extent to which immigrant learners are distinct to multilingual learners in the teaching and learning of linear programming. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)