This essay explores the issue of organizing mathematics education by means of syllogism. Two aspects turn out to be particularly significant. One is the syllogistic analysis while the other is the cunning of reason. Thus the exploration is directed towards gathering evidence of their existence and showing by examples their usefulness within mathematics education. The syllogistic analysis and the cunning of reason shed also new light on Chevallard's theory of didactic transposition. According to the latter, each piece of mathematical knowledge used inside school is a didactic transposition of some other knowledge produced outside school, but the theory itself does not indicate any way of transposing, and this empty space can be filled with the former. A weak prototype of syllogism considered here is Freudenthal's change of perspective. Some of the major difficulties in mathematics learning are connected with the inability of performing change of perspective. Consequently, to ease the difficulties becomes a significant issue in mathematics teaching. The syllogistic analysis and the cunning of reason developed in this essay are the contributions to the said issue.

Made available in DSpace on 2014-12-17T15:07:01Z (GMT). No. of bitstreams: 1 JanimaBR_DISSERT.pdf: 4918594 bytes, checksum: 3fe0b9271a1a65af43238c2ded37b3cf (MD5) Previous issue date: 2013-01-25 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This essay aims at investigating the writing proposals of Portuguese textbooks (LDP Livros Did?ticos de Portugu?s) for Middle School (EF Ensino Fundamental), from 6th to 9th grade, from the 70s to 2009. It aims to check, though the discourse reported in the Portuguese Textbook, the control directed to the practice of the teacher and the student to do in the teaching situations. Theoretically, we search for contributions that come from the Discourse Analysis of French filiation, so we can analyze the ideological constructions present in the discourse of the ―LDP‖ more specific lly the control directed to the te cher nd student the users of the book, in writing activities. It started from a corpus of 63 textbooks whereof the following steps were performed: a) mapping of the writing proposals contemplated in the ―LDP‖ of high school; b cutting in the selection of propos l ccording to the rese rch go ls intended (writing proposals of narrative texts). After mapping the writing proposals presented in the ―LDP‖ bout the criteri mentioned bove we re d the writing propos ls to ch rt the quantity of proposals of textual writing productions in each textbook (which usually follows a pattern : 12 chapters and, at the end, the writing proposal. Nevertheless, some books present 2 (two) or more writing proposals at the end of each chapter). We did a cutting in the corpus initi lly constituted 63 ―LDP‖ nd we selected 12 writing proposals of narrative texts presented in the ―LDPs‖ to present wh t we intend to n lyze. Then, we separated these proposals into two groups: 1) activities which present ―instruction guide‖ to be followed by the student; 2) writing activities that allow the student write with no need to follow a text pattern, i.e., which encourage authorship. By means of analyses, it was possible to demonstrate that, in the Basic School, generally, the writing practices concentrate, primarily, on copying activities, reproduction, rewriting and, in more advanced levels, in activities that which start from preset models, asking the students to produce text with similar themes, following the suggested structure. It is about ideals that are supposed to be followed and imitated by the students, depriving them to assume their authorship. In order to insert the student in the world of writing it s necess ry to go beyond the model of c nonic l texts pr ctice th t puts the students f r from the possibility to be ― uthors‖. In contr st to this tendency, we face, nowadays, proposals that prioritize the authorship, the creation of a style / Esta disserta??o tem como objeto de investiga??o as propostas de escrita dos Livros Did?ticos de Portugu s LDP do Ensino Fund ment l EF do 6 o 9 no de 1974 a 2009. Tem o intuito de verificar pelo discurso relatado no Livro Did?tico de Portugu?s o controle direcionado ? pr?tica do professor e ao fazer do aluno em situa??es de ensino. Teoricamente, buscamos contribui??es que adv?m da An?lise do Discurso de filia??o francesa, para que possamos analisar as constru??es ideol?gicas presentes no discurso dos LDP, mais especificamente, o controle direcionado ao professor e ao aluno, usu?rios do livro, nas atividades de escrita. Partiu-se de um corpus de 63 livros did?ticos em que foram realizadas as seguintes etapas: a) mapeamento das propostas de escrita contempladas nos LDP do EF; e b) recorte na sele??o das propostas, de acordo com os prop?sitos da pesquisa pretendidos (propostas de escrita de textos narrativos). Ap?s o mapeamento das propostas de escrita apresentadas nos LDP sobre os crit?rios acima mencionados, fizemos a leitura das propostas de escrita para tabular a quantidade de propostas de produ??es textuais escritas apresentadas em cada Livro Did?tico (que geralmente segue um padr?o: 12 cap?tulos e, ao final, a proposta de escrita. Todavia, alguns livros apresentam 2 (duas) ou mais propostas de escrita ao final de cada cap?tulo). Fizemos um recorte no corpus inicialmente constitu?do (63 LDP) e selecionamos 12 propostas de escrita de textos narrativos apresentados nos LDP para representar o que pretendemos analisar. Em seguida, separamos essas propostas em dois grupos: 1 tivid des que present m ―roteiro de instru??o‖ p r o luno seguir; 2) atividades de escrita que possibilitam ao aluno escrever sem ter que seguir um modelo padr?o de texto, ou seja, que incentivam a autoria. Por meio das an?lises, foi poss?vel demonstrar que, na Escola B?sica, no geral, a pr?tica de escrita concentra-se, prioritariamente, em atividades de c?pia, reprodu??o, reescritura e, em est?gios mais avan?ados, em atividades que partem de modelos preestabelecidos, solicitando aos alunos que produzam textos com temas similares, seguindo a estrutura sugerida. Trata-se de supostos ideais a serem seguidos e imitados pelos alunos, privando-os de assumir sua autoria. Contrariamente a essa tend?ncia, acreditamos que, para inserir o aluno no mundo da escrita, ? preciso ir al?m de modelos can?nicos de texto, pr?tica que distanci os lunos d possibilid de de serem ― utores‖. Em contr p rtid ess tend?ncia, nos deparamos com LDs da contemporaneidade, que apresentam propostas que priorizam a autoria, a cria??o de um estilo