Cálculo diferencial e integral nos livros didáticos: uma análise do ponto de vista da organização praxeológica - Mateus, Pedro (2007)
This research aims at analysing and better understanding how currently the concepts of Differential and Integral Calculus are dealt with in some available text-books. The discussion is related with Differential and Integral Calculus because we consider them as a branch of mathematics with enormous contribuition for scientifical and technological progress in our society. The research focuses on text-books analysis because of their outstanding role on teacher s activities in classroom of Differential and Integral Calculus on one hand, and they are source of knowledge for pupil, on another hand. The work is based in the hypotheses that some interfering factors in teaching and learning Differential and Integral Calculus are directly related to the way the text-books of Calculus are organized in didactical and matehmatical terms. Analysing this praxeological organization of text-books may strengthen understanding the causes of difficulties in teaching and learning Differential and Integral Calculus in classroom and may create a sound base to use them correctly and with some initiative. The research question is: what do the available text-books suggest to build the concepts and strategies for teaching and learning Differential and Integral Calculus? The theoritical framework was based on Registers of Semiotic Representation Theory of Duval (2003), the Anthropological Theory of Didactics of Chevallard (1999) and the Theory of Didactical Situations in Mathematics of Brousseau (1970-1990). The first theory served to evaluate the joint degree of registers of semiotic representation used in selected text-books, the second theory was used to analyze the types of tasks, techniques and technological and theoritical discourse whic justifies them. The third theory was used to evaluate the contexts set to expose the mathematical content. The results point out that the joint degree of registers of semiotic representation is weak, because there is preference to use algebric registers and their treatments instead of promoting articulation with conversions of registers; more posed activities are on practical-technical bloc than balancing with technological-theoritical bloc; formal exposition of content is predominant one, instead of taking the contextualization as a thread of ideas to get the formalization