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In this paper we investigate the interpretant signs production during mathematical modelling activities development. The theoretical framework is based on the relationship between mathematical modelling and some elements of the semiotics structured by Charles Sanders Peirce, more specifically in his interpretant theory. This theoretical framework is associated with an empirical research in which modelling activities are developed by students of a Degree in Mathematics in a differential and integral calculus subject. The analysis of the activities follows qualitative research directions and leads us to infer that the students produced different interpretant signs when they developed mathematical modelling activities. In the warm up activity development it was possible to identify immediate interpretant signs, while during the follow up activities the students produced dynamic interpretants and some final interpretants for the extreme function values. In general, the interpretant signs give evidence of how the derivative was being used by the students to decide on the existence of maximum or minimum values of a function obtained when they developed mathematical modeling activities. Resumo Neste artigo investigamos a producao de signos interpretantes no desenvolvimento de atividades de modelagem matematica. O quadro teorico em que se fundamenta nossa pesquisa articula a modelagem matematica na Educacao Matematica e elementos da semiotica estruturada por Charles Sanders Peirce e reconhecida na literatura como semiotica peirceana, com foco na denominada teoria dos signos interpretantes. As argumentacoes teoricas sao associadas a uma pesquisa empirica em que uma sequencia de atividades de modelagem matematica foi desenvolvida com alunos de um curso de licenciatura em matematica na disciplina de calculo diferencial e integral I. A analise das atividades segue encaminhamentos da pesquisa qualitativa e nos leva a inferir que, na sequencia de atividades de modelagem matematica, signos interpretantes imediatos sao mais evidentes na atividade de aquecimento, enquanto interpretantes dinâmicos e interpretantes finais podem ser identificados com mais frequencia nas atividades de acompanhamento. De modo geral, os interpretantes dao indicios de como a derivada foi sendo usada pelos alunos para deliberar sobre a existencia de valor maximo ou valor minimo nos problemas investigados nas atividades de modelagem matematica. Palavras-chave : Educacao matematica, Modelagem matematica, Semiotica peirceana. Keywords : Mathematics education, Mathematical modeling, Peircean semiotics. References ALMEIDA, L. M. W. Um olhar semiotico sobre modelos e modelagem: metaforas como foco de analise. Zetetike. FE-Unicamp , v. 18, numero tematico, p. 387-414, 2010. ALMEIDA, L. M. W. Considerations on the use of mathematics in modeling activities. ZDM , v. 50, p. 19-30, 2018. ALMEIDA, L. M. W.; BRITO, D. S. Atividades de Modelagem Matematica: que sentido os alunos podem lhe atribuir?. Ciencia e Educacao (UNESP ) , 11, 1-16, 2005. ALMEIDA, L. M. W.; SILVA, K. A. P. A Acao dos Signos e o Conhecimento dos Alunos em Atividades de Modelagem Matematica. Boletim de Educacao Matematica , v. 31, n. 57, p. 202-219, abr., 2017. ALMEIDA, L. M. W.; SILVA, K. A. P.; VERONEZ, M. R. D. Sobre a geracao e interpretacao de signos em atividades de modelagem matematica. In : VI SEMINARIO INTERNACIONAL DE PESQUISA EM EDUCACAO MATEMATICA - VI SIPEM, 2015, Pirenopolis. Anais do VI SIPEM . Rio de Janeiro: SBEM, 2015. v. 1. p. 1-12. ARLEBACK, J.; DOERR, H. Moving beyond a single modelling activity. In: Mathematical Modelling in Education Research and Practice . Springer International Publishing, p. 293-303, 2015. ARLEBACK, J.; DOERR, H. Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence. ZDM , v. 50, n. 1-2, p. 187-200, 2018. BOGDAN, R. C.; BIKLEN, S. K. Qualitative research for education : An introduction to theories and methods . New York: Pearson Education, 2003. CARREIRA, S.; BAIOA, A. M. Mathematical modelling with hands-on experimental tasks: On the student’s sense of credibility. ZDM , v. 50, n. 1-2, p. 201-215, 2018. DRIGO, M. O. Comunicacao e cognicao: semiose na mente humana. In: Comunicacao e cognicao : semiose na mente humana. Sulinas, 2007. LESH, R.; CRAMER, K.; DOERR, H.; POST, T.; ZAWOJEWSKI, J. Model Development Sequences. In: Richard Lesh & Helen Doerr, (Eds.), Beyond constructivism : Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Erlbaum, 2003. NOTH, W. Panorama da Semiotica : de Platao a Peirce. Sao Paulo: Annablume, 2008. PEIRCE, C. S. Semiotica e filosofia . Editora Cultrix, 1972. PEIRCE, C. S. Semiotica . 3. ed. Sao Paulo: Perspectiva, 2015. SANTAELLA, L. Semiotica aplicada . Sao Paulo: Thomson Learning, 2012. e3504064

This article aims to structure an approach between Mathematical Modeling and Socio-Education. It initially presents and discusses the concepts of socio-education and Mathematical Modeling, looking for converging points between them.Then, it presents and analyzes modeling activities developed with teenagers who are serving educational measures under enclosed environment inside a Socio-Education Center (CENSE), searching for evidence of interns’ socio-educative learning mediated by these activities. What this analysis indicates is that Socio-Education may be mediated by modeling activities and, in this sense, the activities, while assist students’ learning, also include them in a universe of actions that seek their reintegration into society.

In order to pay attention to the process of learning, when involved in mathematical modelling activities, this text seeks to associate the theoretical aspects of Semiotic Mediation, from the standpoint of Vygotsky, and Intentionality as an attribute to learning. The modelling activity present in the text is derived from a research conducted with students during a course of extension, which will be analyzed by taking elements of the theoretical frameworks mentioned from students' written records and transcripts of conversations that occurred during the activity development. Taking into consideration a classroom environment with modelling activities, we infer that the mediation leads to intentionality and intentionality leads to mediation and it is through the "interaction" of these two elements that the internalization of concepts becomes possible, encouraging learning. Keywords : Mathematical Modelling , Intentionality , Semiotic Mediation . DOI: http://dx.doi.org/10.14244/19827199851 Normal 0 21 false false false PT-BR X-NONE X-NONE