Made available in DSpace on 2016-04-27T16:57:20Z (GMT). No. of bitstreams: 1 Edson Rodrigues da Silva.pdf: 2574600 bytes, checksum: fe11256e07c5f09808b243d5f8f0ce49 (MD5) Previous issue date: 2012-10-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to lead students in the 3rd year of high school to construct meaning to the idea of instantaneous rate of change. With this intention, and based on the premises of Didactic Engineering, we elaborated, applied and analyzed a didactic sequence for eight students of a public school in the state of São Paulo. As theoric support, we used the Theory of Didactical Situation (TDS) and the Representation Theory of Semiotics Register. The TDS assisted us in development, tests and analysis of results of didactic sequence, while the Representation Theory of Semiotics Registers emphasized the diversity and articulation of different registers of representation in mathematical activities. The analysis of didactic sequence indicated that teaching students in the 3rd year of high school, through the simultaneous mobilization of records graphing, algebraic and tabular can construct meaning to the idea of rate of change / O presente trabalho tem por objetivo conduzir estudantes do 3º ano do Ensino Médio a construir significado para a ideia de taxa de variação instantânea. Com esse intuito, e fundamentados nos pressupostos da Engenharia Didática, elaboramos, aplicamos e analisamos uma sequência didática para oito alunos de uma escola pública do Estado de São Paulo. Como aporte teórico utilizamos a Teoria das Situações Didáticas (TSD) e a Teoria de Registros de Representação Semiótica. A TSD nos auxiliou na elaboração, experimentação e análise dos resultados da sequência didática, enquanto a Teoria de Registros de Representação Semiótica, enfatizou a diversidade e a articulação de diferentes registros de representação nas atividades matemáticas. A análise da sequência didática apontou que estudantes do 3º ano do Ensino Médio, por meio da mobilização simultânea dos registros de representação gráfica, algébrica e tabular, podem construir significado para a ideia de taxa de variação

It was the purpose of this design study to explore the Geometer’s Sketchpad dynamic mathematics software as a tool to model the derivative in introductory calculus in a manner that would foster a deeper conceptual understanding of the concept – developing domain specific understanding. Sketchpad’s transformation capabilities have been proved useful in the exploration of mathematical concepts by younger learners, college students and professors. The prospect of an open-ended exploration of mathematical concepts motivated the author to pursue the possibility of representing the concept of derivative in dynamic forms. Contemporary CAS studies have predominantly dwelt on static algebraic, graphical and numeric representations and the connections that students are expected to make between them. The dynamic features of Sketchpad and such like software, have not been elaborately examined in so far as they have the potential to bridge the gap between actions, processes and concepts on the one hand and between representations on the other. In this study Sketchpad model-eliciting activities were designed, piloted and revised before a final implementation phase with undergraduate non-math major science students enrolled for an introductory calculus course. Although most of these students had some pre-calculus and calculus background, their performance in the introductory course remained dismal and their grasp of the derivative slippery. The dual meaning of the derivative as the instantaneous rate of change and as the rate of change function was modeled in Sketchpad’s multiple representational capabilities. Six forms of representation were identified: static symbolic, static graphic, static numeric, dynamic graphic, dynamic numeric and occasionally dynamic symbolic. The activities enabled students to establish conceptual links between these representations. Students were able to switch systematically from one form of (foreground or background) representation to another leading to a unique qualitative understanding of the derivative as the invariant concept across the representations. Experimental students scored significantly higher in the posttest than in the pretest. However, in comparison with control group students the experimental students performed significantly better than control students in non-routine problems. A cyclical model of developing a deeper concept image of the derivative is therefore proposed in this study. / Educational Studies / D. Ed. (Education)