This paper presents a methodological proposal for the teaching of exponential function, resulting from the application of a didactic sequence involving exponential function, where evidence of learning and the consolidation and application of mathematical concepts in problem solving were identified and analyzed. The Didactic Engineering of Michèle Artigue (1988) was used as a research methodology. As theoretical contributions that guided and enabled the development of the research, we chose the use of Mathematical Investigation in the classroom; Didactic Sequence in the conception of Zabala (1999); the Articulated Units of Conceptual Reconstruction proposed by Cabral (2017) and assumptions of Vygotsky's theory. A didactic sequence composed of five UARC's was elaborated to work the exponential function, with a view to minimizing the difficulties naturally imposed by the content to be explained. Microgenetic analysis of verbal interactions between teacher and students was used to analyze the results of the application. The results show that the students participating in the experiment showed evidence of learning, recorded during the process, and began to have a good understanding of the concepts and properties related to the topic, in addition to a good performance in carrying out the activities, facts that corroborate the potential of the didactic sequence proposed herein.

O presente texto analisa as determinações mais amplas que constituíram os embates presentes no campo da educação que permearam a publicação do Manifesto dos Pioneiros da Educação Nova no cenário marcado pelas disputas entre liberais e católicos. Objetiva situar os distanciamentos e aproximações entre os dois grupos que apesar das diferenças existentes, defendiam a ordem regida pelo capital. Tomamos como parâmetros de nossas análises, além do Manifesto dos Pioneiros da Educação Nova, os trabalhos de Saviani (2008), Xavier (2002), Lemme (2005) Azevedo (1976), Nagle (1974), entre outros.

(2005). Esse referencial serviu de suporte para elaboração do roteiro de observação e para a aplicação do questionário Assim, busca-se responder o problema colocado a partir da análise da percepção daqueles que encontram-se no "chão da escola". Afinal, não basta que se constituam em meros executores de projetos oficiais e responder burocraticamente pela escola ou pelo sistema educacional. Palavras-chave: Educação Integral. Rondônia. Politecnia. MATERIALIZATION THE FORMS OF EDUCATION POLICIES IN INTEGRAL RONDÔNIAABSTRACT This article aims to examine ways of materialization of Integral Education policies in the Basic Education of the State of Rondônia. This is an important issue, to the extent that needs to be answered without mystifications or speculation. Therefore , this work seeks the historical link between the design of comprehensive education and the concept of polytechnic. To achieve this objective we direct the documentary and literature about the concept of integral education , as well as data collection during the meeting of coordinators and directors of public school network Rondonia between 19 and 21 October 2015, in which it applied a open questionnaire to 24 engineers and 24 directors, totaling 48 professionals working daily in schools that offer the More Education Program. The theoretical framework was made by means of a theoretical option rooted in authors such as Marx (2003), Marx; Engles (1992;2007 ), Maciel (2013, Alves (2006) and Mészáros (2005). This reference served as support for the preparation of observation guidelines and the questionnaire therefore seeks to answer the problem posed from the perception of the analysis of those who are on the "ground school". After all, it is not enough to constitute mere executors of official projects and respond bureaucratically by the school or the educational system.