Analysis of mathematical discourse : multiple perspectives

Textbooks have a powerful influence on mathematical education in developing countries like Brazil, where many poorly prepared teachers use them as the only source of information and activities for their teaching. In this context the investigation of the discourse conveyed by mathematics textbooks is very important. As my interest at the present moment is on mathematics education for the undergraduate level, I have chosen the discourse of undergraduate mathematics textbooks as the theme of investigation, giving particular attention to the discourse of Complex Analysis textbooks. In the first two parts of this thesis, I develop the theoretical frameworks necessary to make discourse analysis into an effective educational tool. The philosophical perspectives and analytical tools developed there are expected to be helpful for the discursive investigation of textbooks on other areas of mathematics and other levels of teaching as well. In the third part, I show that, contrary to common expectation, the discourse of Complex Analysis is neither standardized, nor objectively neutral. By applying the theoretical tools developed in the first two parts of this thesis, I demonstrate that this discourse is, globally and locally, permeated by frequent conflicts between logical, heuristic, and rhetorical schemes. The main aim of the discourse analysis I have developed is to give awareness to the teachers that in mathematical discourse heuristic, intuition and rhetoric are necessary complements of logic and, consequently, mathematical discourse cannot be reduced to logical reasoning at all.