MEDSED / Department of Maths, Science and Technology Education

The low grades that students score in some statistical units in Kenyan universities is of great concern and has evoked research interest in the teaching of some of the units and the students’ learning of the statistical content. The aim of the study was to investigate the difficulties undergraduate students experience in the learning of bivariate normal distribution in a Kenyan university. The research also aimed to answer the following research questions on the difficulties undergraduate students encounter in the learning of bivariate normal distribution. The first research question was based on the reasons why students find learning of bivariate normal distribution difficult and the second research question was to find the reasons why students experience such difficulties in learning bivariate normal distribution. The target population for this study included lecturers teaching statistics in the university, and second- and third- year students enrolled or who have previously completed the probability and statistics III unit, where the bivariate normal distribution content is covered. In selecting students for the study, the simple random sampling technique was employed while convenient sampling was used to select lecturers who participated in the study. A mixed methods design was adopted for this study where both quantitative and qualitative data was collected. A total of 175 students and six lecturers participated in this research study. All students who participated in the study did a bivariate normal distribution test (Appendix 1) designed by the researcher and then filled in a questionnaire (Appendix 2). The lecturers who participated in the study filled in an open-ended questionnaire (Appendix 3). The results showed that undergraduate students have difficulties in learning bivariate normal distribution. This is because most of them could neither state the bivariate normal distribution nor solve any of the application questions on the content. The students find it difficult to learn and comprehend the bivariate normal distribution equation with its many parameters and constants of the two random independent variables. The results also showed that students could not state the normal distribution equation nor could they solve questions on the normal distribution, which forms the foundational knowledge required for effective learning of the bivariate normal distribution content. ii Based on the results, the study recommended that emphasis should be placed on the basic and foundational knowledge of the normal distribution content and its applications before teaching bivariate normal distribution in probability and statistics III. In addition, it is recommended that all students should be involved in the learning of basic content to enable them to understand all parameters and constants in the equations and their applications. The study also recommends that lecturers revise the foundational knowledge and content related to the bivariate normal distribution before introducing and teaching the bivariate normal distribution content. This study also recommends that the university should consider a change of curriculum by teaching the bivariate normal distribution, as an introductory course to the unit under the multivariate distributions in statistics, in third year of the students’ studies. ; ; / Mathematics Education / M. Sc. (Mathematics Education)

Orientador: Marcia Regina Ferreira de Brito / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-09T00:27:57Z (GMT). No. of bitstreams: 1 Souza_MariaAliceVeigaFerreirade_D.pdf: 1847772 bytes, checksum: 0a22f8b1eba3a0b2f2b39867f9a8ccff (MD5) Previous issue date: 2007 / Resumo: A presente pesquisa explorou as relações entre o desempenho no ENADE 2005, o desempenho no EGRAF e o raciocínio dedutivo de 141 estudantes ingressantes e concluintes da Ciência da Computação quando envolvidos em atividades que exploraram o pensar matemático. Os instrumentos foram o exame do ENADE, o exame do EGRAF e o teste psicológico GfRLD. Além disso, doze desses sujeitos foram submetidos a uma testagem individual de alguns componentes da habilidade matemática e a representação mental, além das variáveis estudadas para os 141 estudantes. Para a habilidade e a representação foram utilizados cinco problemas da série XIX-B de Krutetskii e uma entrevista semi-estruturada. Durante a aplicação do teste de Krutetskii, os doze estudantes foram solicitados a pensar em voz alta. Foram feitas anotações complementando informações não captadas via gravação de voz e imagem. Os principais resultados mostraram que nove dos doze estudantes foram considerados mais habilidosos e apresentaram uma tendência para representar os problemas de maneira proposicional. Essa representação sempre que usada por estudantes que dominavam os elementos do problema e suas relações levavamnos ao sucesso em suas soluções. Os desempenhos desses estudantes no ENADE não indicaram estar associados ao fato de serem ingressantes ou concluintes, mas relacionados ao desempenho em nível acadêmico. O raciocínio dedutivo diferiu significativamente entre estudantes concluintes e ingressantes e, dentre os bem e mal sucedidos em atividades acadêmicas. De uma maneira geral, os 141 estudantes tenderam a apresentar associação entre os desempenhos do ENADE e os do EGRAF, que avaliam as inteligências fluido-cristalizadas e cristalizadas, respectivamente / Abstract: he present research explored the relations between the performance in ENADE 2005, the performance in EGRAF and the deductive reasoning of 141 Freshman and Senior students of the Computer Science course when involved in tasks that explored the mathematic thinking. The instruments were the ENADE exam, the EGRAF exam and the psychological test GfRLD. In addition, twelve of those students were submitted to an individual test of some mathematical ability components and the mental representation, over there the variables studied for the 141 students. For the ability and the representation five of Krutetskii's serie XIX- B series problems and a semi structurated interview were used. During the application of the Krutetskii's test, the twelve students were invited to think out loud. Notes were made to complement information not captured by the voice and image videotape. The main results showed that nine out of twelve students were considered more skilful and presented a tendency to represent the problems in a propositional way. This representation when used by students that dominated the elements of the problem and its relations took them to success in their solutions. Those students' performances in ENADE indicated no association with the fact that they were Freshmen or Senior students, but they were related with the level academic performance. The deductive reasoning differed significantly between Freshmen and Senior students and, between well and bad succeeded in academic tasks. In general, the 141 students tended to present association between ENADE performance and EGRAF performance, that evaluate the fluid-crystallized and crystallized intelligences, respectively / Doutorado / Psicologia, Desenvolvimento Humano e Educação / Doutor em Educação

University of Macau / Faculty of Education

CAPES / Este trabalho traz um relato a respeito da Hipótese de Riemann, com o objetivo de tornar os conceitos referentes a esse problema acessíveis ao professor da educação básica, que pretenda abordá-los em sala de aula quando tratar de conteúdos a ele relacionados. A pesquisa foi inteira bibliográfica, apoiada em sua grande parte em textos de História da Matemática, tornando este trabalho divulgador dos problemas que ocupam parte das pesquisas matemáticas deste século, em especial da Hipótese de Riemann. / This study presents a report about the Riemann Hypothesis, leaving the underlying concepts behind this problem more accessible to a high school teacher. The literature review was based mainly on History of Mathematics texts. This research aims to study significant topics of mathematical research throughout this century, particularly to popularize the Riemann Hypothesis.