KEYWORDSActivity theory; higher education; teaching of differential and integral calculus; Engeström
SUBJECT CLASSIFICATION CODES
B, C, D, D
ABSTRACTIn recent years, changes in the Brazilian economic and social scenario have generated a growing demand for higher education in the country. In response to this new context, the federal government launched in 2007 a programme aiming at expansion of the enrolment to public higher education. In such environment of changes, several proposals have emerged to adapt the Brazilian federal universities to a new reality. Taking this context into account, the focus of our study is on proposals from the Mathematics Department of the Federal University of Minas Gerais. Their aim is to create a new model of teaching practices for the freshman lessons of the Exact Sciences area, which at first were being experimented in special classrooms of students attending their first course on differential and integral calculus. The data were collected from interviews with students and professors from the mathematics department. They were analyzed and systematized using an activity theory approach. We became instigated by a model developed by Engeström in his study on the changes in the Finnish public health system, considering it as a test (testbench) for activity theory in its application to a particular case. Following Engeström's footsteps when developing his research, we arrived at our own model showing the internal tensions in the activity of reformulation of the courses offered by the Department of Mathematics and in the conceptions of teachers that promote -and constraint -the proposals for change.
Resumo A linguagem da Matemática antiga costuma soar hermética àqueles habituados ao simbolismo algébrico com que representamos as ideias da Matemática hoje. Assim, para tornar uma sentença da Matemática clássica mais clara ao leitor atual, é comum reescrevê-la utilizando a notação moderna. No entanto, essa estratégia pode ofuscar algumas características e pressupostos fundamentais da Matemática grega. No caso dos Elementos, para entendermos sua estruturação e suas bases conceituais, precisamos levar em consideração questões teóricas enfrentadas por Euclides. Na passagem da Matemática antiga para a moderna, conceitos fundamentais, como o de número e o de medida, se modificaram; o raciocínio analítico se impôs ao pensamento sintético; e o papel da Matemática na elaboração do conhecimento em geral foi repensado. Por isso, o uso da linguagem algébrica moderna para “traduzir” enunciados contidos nos Elementos pode ocultar essas diferenças e gerar interpretações equivocadas das bases da Matemática clássica e de suas relações com a Matemática atual.
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