Made available in DSpace on 2016-04-27T16:58:54Z (GMT). No. of bitstreams: 1 Marcio Antonio da Silva.pdf: 1192509 bytes, checksum: 39ebed9fcc448c228302818663cb0429 (MD5) Previous issue date: 2009-06-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work focus on the Mathematics Curricula for the Brazilian Ensino Médio, analyzing the criteria used in order to select and organize contents, once official orientations, as well as much of the research already carried out in our country, do not focus explicitly on what the guiding fundaments for selecting mathematic themes would be. The research is methodologically characterized as a theoretical essay, once we aim, using the argumentation, through the theoretical support, at the idea that it is necessary to search for criteria to select and organize mathematical contents to Ensino Médio, and they should take into consideration cultural features and the objectives of each community in order to fulfill the objectives of a school that aims equality through social transformation and, at the same time, valuing scientific knowledge built through many civilizations throughout the history of Humankind. In order to accomplish that, we look at Philosophy of Mathematics so we can understand how certain tendencies and conceptions about some concepts and the Mathematics itself can be explained; we think about William Doll Jr s work and his curricular criteria in a post-modern perspective; we use the concept of Critical Mathematical Education, following Skovsmose and we analyze the social and cultural factors of a curriculum. As far as the work organization is concerned, we emphasize the importance of breaking with the linear paradigm, which is still present in the Mathematics curricula, building a disposition based on net ideas. We resume our ideas through eight propositions concerning what the criteria to select and organize a critical and post-modern curricula would be: richness, recursion, relations, rigor, reflection, reality, responsibility and resignification. Finally, throughout our studies, we have concluded that Mathematics Curricula for Ensino Médio must present this science in its main plenitude, with all its research areas, reflecting that the inefficiency of certain contents in real situations do not make them less important, which is different from what has been currently done, as far as we are concerned, once Mathematics is divided and presented in an incomplete way. This creates an opportunity only for students who will keep on their studies in Educação Superior to study Mathematics in its richness and interconnections / Essa tese trata dos Currículos de Matemática no Ensino Médio brasileiro buscando reflexões sobre critérios para escolha e organização de conteúdos, pois as orientações oficiais e grande parte das pesquisas já realizadas em nosso país não enfocam explicitamente quais seriam os fundamentos norteadores para selecionar temas matemáticos. A pesquisa é metodologicamente caracterizada como um ensaio teórico, pois buscamos com a argumentação, através do aporte teórico apresentado, a defesa da asserção de que é necessário buscar critérios para escolha e organização de conteúdos matemáticos para o Ensino Médio e que estes devem levar em conta características culturais e os objetivos próprios de cada comunidade, para atender aos objetivos de uma escola comprometida com a busca pela igualdade, por meio da transformação social e, ao mesmo tempo, valorizando os conhecimentos científicos construídos por várias civilizações, ao longo da história da humanidade. Para isso, olhamos para a Filosofia da Matemática com a intenção de compreendermos como certas tendências e concepções sobre conceitos e sobre a própria Matemática podem ser explicadas, refletimos sobre o trabalho de William Doll Jr. e seus critérios curriculares em uma perspectiva pós-moderna, nos apropriamos do conceito de Educação Matemática Crítica, segundo Skovsmose e analisamos os fatores sociais e culturais de um currículo. No aspecto organizacional, enfatizamos a importância de quebrar o paradigma linear, ainda presente nos currículos de Matemática, construindo uma disposição pautada na ideia de rede. Sintetizamos nossas reflexões por meio de oito proposições a respeito de quais seriam os critérios para escolha e organização de um currículo crítico e pós-moderno: riqueza, recursão, relações, rigor, reflexão, realidade, responsabilidade e ressignificação. Finalmente, em decorrência dos nossos estudos, concluímos que os Currículos de Matemática para o Ensino Médio devem apresentar esta ciência na sua plenitude, com todos os seus campos de pesquisa e variedade de eixos articuladores, mostrando que a inaplicabilidade de alguns conteúdos em situações reais não diminui a importância dos mesmos, diferente do que atualmente é feito, ao nosso ver, seccionando a Matemática e apresentando-a de maneira incompleta, proporcionando, apenas aos alunos que seguirão seus estudos na Educação Superior, a oportunidade de vê-la e estudá-la na riqueza de suas interconexões

The era of high stakes testing often puts pressure on teachers and administrators to deemphasize creative activities not perceived as directly related to improving test scores. Alternatively, the authors propose that using environmental text is essential for encouraging overall learning competencies in general and reading/writing/ and mathematical achievement in particular. The authors propose that using real estate booklets can be helpful in generating learning activities in literacy, social studies, and mathematics. In addition, integrating music and art comfortably accompanies strategies presented. Real estate booklets are colorful, rich in content, and readily available at no expense.

Multicultural countries such as England have recognised the need to multiculturalise their mathematics curricula to cater for the needs of all ethnic/cultural groups, to encourage racial harmony and have pupils of a specific culture learn about, and accord respect to, another culture (Duncan, 1986;Dyson, 1986; Gilbert, 1984). However, in South Africa, a multicultural country with its large Black majority, such an approach has not been given the necessary attention. Laridon (1990) has criticised the way in which curriculum development in mathematics is conducted in South Africa. He describes it as a "top-down" approach and based on input from non-representative samples of teachers and not taking into account the needs of all cultural groups in South Africa. He criticises the manner in which topics are added to or removed from the syllabus and calls this "syllabus tinkering". With a number of, mostly English medium, schools opening their doors to all races, it is possible that certain cultural groups are at a disadvantage when compared with others if modifications to the syllabus, to accommodate their needs, are not made. This study is a small scale case-study, conducted at Woolhope Secondary, a predominantly Indian school, but with a significant number of Black pupils (approximately 25%). The study focusses on the need for a multicultural approach to mathematics curriculum design. The views of the senior mathematics pupils and mathematics teachers are considered in this regard, and together with the relevant literature, broad guidelines for a multicultural mathematics curriculum design in South Africa are suggested.

I identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on creative uses of mathematics and an increased emphasis on verbalizations, reasoning and conceptualization as opposed to numerical and computational skills. With tools provided by a qualitative textual analysis of several Swedish curricula from the past from which I trace a shift of focus from the classical towards the conceptual aspects of mathematical knowledge, I examine the common research framework for discussing mathematical knowledge in terms of the procedural and the conceptual. I investigate whether the shift towards a conceptual approach to mathematical knowledge has occurred and how this presumed shift reveals itself. A close reading and comparison of the historical guidance documents' purpose descriptions and grading criteria concerning the mathematics subject is carried out. Commentary materials for the various course plans are examined. Here I conclude that a shift has occurred during the last decades in the mathematics curricula that may have severely affected the mathematical education in schools. I argue that this shift needs to be acknowledged in order to halt a tendency that seems to gravitate towards a decreasing mathematical competency among the Swedish students.

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This case study analyzed the roles development and implementation have had in the Eighth-grade Algebra I policy and the California High School Exit Exam policy. From a political, economical, and historical perspective, the intended purposes of many education policies have been distorted due to implementation. By investigating national and California education policies, this case study describes the roles development and implementation have had education policies. In addition, this case study found that the state of education in California is reliant on many mitigating factors affecting education policy development and implementation: Budget cuts, achievement gaps particularly with children of color, and teacher qualification issues. However, systemic education reform requires policy makers to juggle their political affiliations and the needs of students to create policies that improve curriculum, improve student achievement, and supports teachers and administrators. When policy makers do not utilize informed constituencies to assist in policy development, mandates such as the Eighth-grade Algebra I policy are created. Well developed and researched education policies like the California High School Exit Exam, which took about six years to develop before it was implemented in California, was successful because it involved collaboration of various interest groups, educators, local education agencies, and school administrators. Policy makers must learn to work in collaboration with its constituency to develop policies that empower schools to sustain and extend greater individualization on one hand, and broaden community interest on the other. The future of California schools in regard to the Race to the Top policies remain to be seen, but if policy makers rely on the informed voices of education researchers, constituents who are willing to put students' needs before their own political conquests, school administrators, teachers, parents, and students, then California's school will have a future of systemic reform that will be bright.

Quelle est la nature des mathématiques enseignées dans les classes de l’enseignement secondaire? Dans quelle mesure l’enseignement des compétences n’handicape-t-il pas l’accès à des mathématiques telles qu’en rêvent les enseignants ?Ce qu’on enseigne a les caractéristiques d’un texte, d’une forme scripturale qui présente des différences avec la forme orale d’une société qui ne connaît pas l’écriture. Il apparaît que la formulation des définitions présente un outil performant pour cette analyse. Les investigations empiriques dévoilent, à travers quatre tensions, les difficultés qu’ont les enseignants à faire entrer leurs élèves dans l’apprentissage d’une théorie mathématique. L’analyse des différentes manières de valider ce qu’ils enseignent conduit à montrer dans quelle situation problématique se trouve l’enseignement des mathématiques aujourd’hui. Un remède serait l’apprentissage de la compétence idiomatique.<p><p><p><p>What is the nature of the Mathematics which are taught in secondary education classes (pupils from 12 to 18 years old)? How far does it impair learning mathematics like teachers dream them ?The taught matter shows the features of a text, of a scriptural form showing up differences with the oral form of a society without writing. The formulation of definitions appears to be a powerful tool to perform this analysis. Empirical investigations reveal through four tensions, how hardly the teachers bring their pupils into the learning of a mathematical theory. The analysis of the various ways to validate what they teach leads to show in what serious difficulties is today the teaching of mathematics. A remedy could be the learning of idiomatic competence.<p> / Doctorat en Sciences Psychologiques et de l'éducation / info:eu-repo/semantics/nonPublished

In this study, senior certificate (standard 10) pupils' attainment of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum was investigated. With regard to the attainment of the cognitive objectives and aims, senior certificate pupils' performance in their mathematics examination, in terms of three broad categories of cognitive abilities (lower level, middle level and higher level mathematical abilities) was analysed and examined. As no norms (criteria) for mathematical attainment in respect of these three categories of cognitive abilities could be identified, these norms had to be firstly developed by the researcher. However, suitable standardised scales were identified and administered to determine senior certificate pupils' attainment of the affective aims and objectives (attitude towards and interest in mathematics). Besides the quantitative analysis, qualitative assessments of senior certificate pupils' attainment of the cognitive and affective aims and objectives were also made using information obtained, by way of a questionnaire, from teachers of senior certificate mathematics classes. The main findings that emerged from this investigation were: * The senior certificate pupils are attaining the desired proficiency levels in the cognitive objectives and aims of the senior certificate mathematics curriculum. However, these pupils are not adequately attaining the affective aims and objectives of the mathematics curriculum. * Qualitative information elicited from senior certificate teachers of mathematics tends to support the above findings which were obtained from the quantitative analysis. * There is a need for curriculum development in certain areas of the senior certificate mathematics curriculum, particularly in Euclidean geometry, for standard grade pupils. In terms of the general findings, certain recommendations were also formulated. In several ways, the present research is a pioneering effort in evaluating the efficacy of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum. It is hoped that this study will serve as a catalyst for future research. / Curriculum and Instructional Studies / D. Ed. (Didactics)

In this study, senior certificate (standard 10) pupils' attainment of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum was investigated. With regard to the attainment of the cognitive objectives and aims, senior certificate pupils' performance in their mathematics examination, in terms of three broad categories of cognitive abilities (lower level, middle level and higher level mathematical abilities) was analysed and examined. As no norms (criteria) for mathematical attainment in respect of these three categories of cognitive abilities could be identified, these norms had to be firstly developed by the researcher. However, suitable standardised scales were identified and administered to determine senior certificate pupils' attainment of the affective aims and objectives (attitude towards and interest in mathematics). Besides the quantitative analysis, qualitative assessments of senior certificate pupils' attainment of the cognitive and affective aims and objectives were also made using information obtained, by way of a questionnaire, from teachers of senior certificate mathematics classes. The main findings that emerged from this investigation were: * The senior certificate pupils are attaining the desired proficiency levels in the cognitive objectives and aims of the senior certificate mathematics curriculum. However, these pupils are not adequately attaining the affective aims and objectives of the mathematics curriculum. * Qualitative information elicited from senior certificate teachers of mathematics tends to support the above findings which were obtained from the quantitative analysis. * There is a need for curriculum development in certain areas of the senior certificate mathematics curriculum, particularly in Euclidean geometry, for standard grade pupils. In terms of the general findings, certain recommendations were also formulated. In several ways, the present research is a pioneering effort in evaluating the efficacy of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum. It is hoped that this study will serve as a catalyst for future research. / Curriculum and Instructional Studies / D. Ed. (Didactics)