In 1981 the author submitted that "many of the (then) more recent school syllabuses remain disjointed and give expression still to a school mathematics course as step-by-step progression through a list of disparate topics". The position has not changed. It is not yet generally accepted that there can no longer be an accepted body of mathematical knowledge that needs to be taught. The rapid development of new technology and the introduction of the microcomputer should enable the 'modern' mathematics of the early 1960's to enhance the mathematical experiences of pupils in a practical and comprehensible way and prompt a new style of teaching and learning mathematics. There is, however, a fundamental core of mathematics which must inevitably find a place in the school mathematics curriculum. In Part I of the thesis the emphasis is on a method of presentation of certain key topics which illustrate the basic pattern of a group structure. Former complications at school level of putting plane geometry on a logical footing have to be avoided. The use of complex numbers highlights significant and sometimes rather difficult geometrical ideas. In Part 11 the author attempts to show how some of these ideas may be presented to extend the basic pattern to that of linear algebra. The work culminates in Part III with the use of linear complex algebra to present more vividly the symmetries of the Platonic solids. The author anticipates the realistic presentation of the aesthetic side of 3-dimensional geometry and takes a look at its possible presentation through the medium of the microcomputer. At this early stage of the development of the ideas to be discussed, there can be no formal testing of the results by quantitative analysis. Evaluation of the viability of the proposals will be qualitative and the comments of 'critical academic friends' will be included. The originality demanded of a piece of research goes beyond the exposition. Here it will consist of new insights into ideas appropriate to senior pupils in schools and a rewriting of existing material often thought to be beyond their scope. The work is supported by suggested lesson sequences, transcripts of recorded presentations, and examples of students' work. Subsequent development must face the question of assessment and evaluation at sixth-form level of the proposed new style of teaching mathematics. The author makes some suggestions in the concluding chapter.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-09-27T18:31:21Z No. of bitstreams: 1 tatianegoncalvesmoraes.pdf: 3568679 bytes, checksum: c76f3116a9ab930c37e5db6d547b89d9 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-09-28T14:11:51Z (GMT) No. of bitstreams: 1 tatianegoncalvesmoraes.pdf: 3568679 bytes, checksum: c76f3116a9ab930c37e5db6d547b89d9 (MD5) / Made available in DSpace on 2017-09-28T14:11:51Z (GMT). No. of bitstreams: 1 tatianegoncalvesmoraes.pdf: 3568679 bytes, checksum: c76f3116a9ab930c37e5db6d547b89d9 (MD5) Previous issue date: 2017-02-21 / A presente dissertação foi desenvolvida como parte de nossos trabalhos no âmbito do Mestrado Profissional em Gestão e Avaliação da Educação (PPGP) da Universidade Federal de Juiz de Fora (UFJF). O caso de gestão discute de que forma o Centro de Políticas Públicas e Avaliação da Educação da Universidade Federal de Juiz de Fora (CAEd/UFJF), contratado pela Secretaria de Educação do Estado de Goiás, pode contribuir para, com base nas análises estatísticas e pedagógicas de itens de matemática do 3º ano do ensino médio, por ele realizadas, fornecer aos profissionais da educação goiana recomendações para que estes empreendam esforços no intuito de fortalecer os pontos fortes e corrigir possíveis fragilidades no ensino de Matemática. Em termos metodológicos, o estudo do desempenho dos alunos nos itens de Matemática é aqui realizado com base nos percentuais de acerto corrigidos dos itens e controlados pelo índice socioeconômico da população avaliada. Dessa forma, elencamos como tema desta dissertação a avaliação em larga escala; como objeto, os dados estatísticos do teste aplicado pelo Sistema de Avaliação Educacional do Estado de Goiás (SAEGO), em 2014; e, como plano de ação, uma sugestão para a reestruturação do boletim pedagógico, tendo como meta a implementação de um mapa de aprendizagem de Matemática para o Ensino Médio. / This dissertation has been developed as part of our work in the Mestrado Profissional em Gestão e Avaliação da Educação (PPGP, or Professional Master´s Course on Educational Management and Evaluation), of the Universidade Federal de Juiz de Fora (UFJF, Federal University of Juiz de Fora). The management study case discusses how the Centro de Políticas Públicas e Avaliação da Educação of the Universidade Federal de Juiz de Fora (CAEd/UFJF, Center for Public Policy and Educational Evaluation), as an institution hired by the Goiás State Secretary of Education, can contribute for providing to Goiás education professionals recommendations able to make them improve even more eventual strengths and correct weaknesses in Mathematics teaching, based on statistical and pedagogical analyses done on High School 3rdgrade Mathematics items. Methodologically, the study of student performance is carried out on the basis of right answer percentages controlled by student socioeconomic status. The theme of the dissertation is thereby large-scale evaluation; its study object is the statistical data of the 2014 test applied by the Sistema de Avaliação Educacional do Estado de Goiás (SAEGO, Goiás State Educational Evaluation System), in 2014; and its action plan is a suggestion for restructuring the pedagogical bulletin, with the aim of implementing a High School Mathematics learning map.

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