Made available in DSpace on 2014-12-17T15:04:54Z (GMT). No. of bitstreams: 1 EnneKVS_DISSERT.pdf: 2363484 bytes, checksum: 6f0cc9586e37c59c35e9c468df85b7d1 (MD5) Previous issue date: 2010-10-25 / Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject / As demonstra??es s?o ferramentas fundamentais para a Matem?tica e, como tal, s?o frequentemente usados por matem?ticos, professores de matem?tica e estudantes. De fato, as demonstra??es fazem parte de todo o contexto de ensino de Matem?tica, porque na Matem?tica consideramos algo como verdadeiro quando isso pode ser demonstrado. Diferentemente dos outros campos do conhecimento que utilizam a observa??o e a experimenta??o para validar suas verdades. A seguinte disserta??o apresenta um estudo sobre o ensino e a aprendizagem das demonstra??es em Matem?tica, descrevendo um M?dulo de Ensino aplicado em um curso de Teoria dos N?meros oferecido pelo Departamento de Matem?tica da Universidade Federal do Rio Grande do Norte para alunos do Ensino Superior. A disserta??o teve como objetivo propor e testar um M?dulo de Ensino que pudesse servir de modelo para o ensino das demonstra??es matem?ticas. O M?dulo de Ensino consistiu nas seguintes cinco etapas: aplica??o de uma entrevista para determinar o perfil dos alunos e seus conhecimentos pr?vios sobre linguagem matem?tica e t?cnicas de demonstra??o; an?lise de uma s?rie de di?logos utilizando argumentos na linguagem quotidiana; investiga??o e an?lise da estrutura de algumas t?cnicas importantes de demonstra??es; avalia??o escrita e, finalmente, uma entrevista para comprovar os principais resultados do M?dulo de Ensino. A an?lise dos dados obtidos por meio das atividades de sala de aula, avalia??es escritas e entrevistas nos levaram ? conclus?o de que havia uma quantidade significativa de assimila??o do assunto a n?vel de compreens?o relacional, (SKEMP, 1980). Estes instrumentos verificaram que os alunos obtiveram uma melhora consider?vel no uso da linguagem matem?tica e das t?cnicas de demonstra??o apresentadas. Assim, as evidencias levam ? conclus?o que a proposta do M?dulo de Ensino ? um meio eficaz para o ensino/aprendizagem das demonstra??es matem?ticas e, como tal, fornece um guia metodol?gico que pode lan?ar as bases para uma nova abordagem a esse importante tema

This project seeks to determine, to what extent the culture of early Israel (1250-1000 BC) is similar to African cultures, more specifically, to that of the Lemba. However, a comparison between the cultures of early Israel and those of certain African tribes is not the primary objective in this case. This project is neither an anthropological study nor does it intend to mainly focus on the Lemba as such -though this may appear to be the case. This endeavour primarily fits into the ambit of Old Testament Studies. The investigation into the Lemba is meant to be subsidiary to the point of contingence between their culture and Old Testament customs and traditions, and how this information affects the interpretation of the Old Testament and its teaching in Africa. A number of comparisons between the early Israelite religion as reflected in the Old Testament and the Lemba are drawn. Though the qualitative research (inductive approach) is employed in the field work, the greatest part of the data on religious perspectives and practices is mediated by the theory of a phenomenological approach as advocated by Ninian Smart on matters of experience, mythology, ritual, and ethical/judicial dimensions. Therefore, the approach is also deductive. The Lemba is a very specific group with claims about Israelite/Judaic origins. Their early departure from Israel (according to them ca 586 BC) can mean that there are remnants of a very ancient type oflsraelite religion, now valuable when juxtaposed to that of early Israel. This study takes Lemba traditions seriously, but finally does not verify or falsify Lemba claims - but the outcomes in this thesis may take this debate a step further. Their claims make them special and extremely interesting to study from the point of view of oral cultures. Their oral culture is constitutive of their world-view and self-understanding or identity. It incorporates the role of oral traditions, history and historiography and parallels are drawn between orality in early Israelite and Lemba religions. The reciprocity between orality and inscripturation of traditions, yielding valuable information on what may have happened in the developent of traditions in Israel, are also attended to in this project. Nevertheless, this project is primarily a search for the understanding and relevance of the Old Testament in Afiica and is, therefore, a selective and not an exhaustive comparison between the Lemba and early Israel. And so, taking cognisance of the hermeneutic of contextualisation in Africa in particular, a teaching module syllabus for Old Testament Studies is developed, of which the very strands of religion among the Lemba and early Israel are constitutive for teaching Old Testament Studies in present-day African cultures (and perhaps elsewhere). / Biblical and Ancient Studies / D. Litt. et Phil. (Biblical Studies)

This project seeks to determine, to what extent the culture of early Israel (1250-1000 BC) is similar to African cultures, more specifically, to that of the Lemba. However, a comparison between the cultures of early Israel and those of certain African tribes is not the primary objective in this case. This project is neither an anthropological study nor does it intend to mainly focus on the Lemba as such -though this may appear to be the case. This endeavour primarily fits into the ambit of Old Testament Studies. The investigation into the Lemba is meant to be subsidiary to the point of contingence between their culture and Old Testament customs and traditions, and how this information affects the interpretation of the Old Testament and its teaching in Africa. A number of comparisons between the early Israelite religion as reflected in the Old Testament and the Lemba are drawn. Though the qualitative research (inductive approach) is employed in the field work, the greatest part of the data on religious perspectives and practices is mediated by the theory of a phenomenological approach as advocated by Ninian Smart on matters of experience, mythology, ritual, and ethical/judicial dimensions. Therefore, the approach is also deductive. The Lemba is a very specific group with claims about Israelite/Judaic origins. Their early departure from Israel (according to them ca 586 BC) can mean that there are remnants of a very ancient type oflsraelite religion, now valuable when juxtaposed to that of early Israel. This study takes Lemba traditions seriously, but finally does not verify or falsify Lemba claims - but the outcomes in this thesis may take this debate a step further. Their claims make them special and extremely interesting to study from the point of view of oral cultures. Their oral culture is constitutive of their world-view and self-understanding or identity. It incorporates the role of oral traditions, history and historiography and parallels are drawn between orality in early Israelite and Lemba religions. The reciprocity between orality and inscripturation of traditions, yielding valuable information on what may have happened in the developent of traditions in Israel, are also attended to in this project. Nevertheless, this project is primarily a search for the understanding and relevance of the Old Testament in Afiica and is, therefore, a selective and not an exhaustive comparison between the Lemba and early Israel. And so, taking cognisance of the hermeneutic of contextualisation in Africa in particular, a teaching module syllabus for Old Testament Studies is developed, of which the very strands of religion among the Lemba and early Israel are constitutive for teaching Old Testament Studies in present-day African cultures (and perhaps elsewhere). / Biblical and Ancient Studies / D. Litt. et Phil. (Biblical Studies)