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The purpose of this article is to investigate the knowledge related to the concept of function, mobilized by teachers who teach mathematics in Basic Education. Relationships are established with the theoretical and analytical presuppositions of the Mathematical Knowledge for Teaching domains, proposed by Debora Ball and her collaborators, based on the ideas of Lee Shulman. The aim of this study was to identify and analyze constituent aspects of the Content Specific Knowledge and Pedagogical Content Knowledge domains of a group of teachers participating in an extension course at a public university in Sao Paulo in the Education Observatory Program (OBEDUC). Based on a task of professional teacher learning about the concept of function, we have identified and analyzed questions of a task involving the concept of function. The protocols of resolution were taken as data. The methodological structuring is based on a qualitative approach of an interpretative nature. The results showed that the knowledge mobilized by the teachers prioritizes the graphic and tabular representations, promoting the use of softwares and spreadsheets as didactic resources, and also emphasize the presence of ‘letters’, as one of the factors causing difficulties presented by the students of the different levels of Basic Education in the study of functions. Keywords : Concept of function, Teacher’s knowledge, Mathematics education, OBEDUC. Resumo O presente artigo tem como proposito investigar os conhecimentos relativos ao conceito de funcao, mobilizados por professores que ensinam matematica na Educacao Basica. Estabelecem-se relacoes com os pressupostos teoricos e de analise dos dominios do Conhecimento Matematico para o Ensino, propostos por Debora Ball e seus colaboradores, com sustentacao nas ideias de Lee Shulman. Buscou-se identificar e analisar aspectos constituintes dos dominios do Conhecimento Especifico do Conteudo e do Conhecimento Pedagogico de Conteudo de um grupo de professores participantes de um curso de extensao em uma universidade publica de Sao Paulo, no âmbito do programa Observatorio da Educacao (OBEDUC). Tendo como base uma tarefa de aprendizagem profissional docente sobre o conceito de funcao, identificaram-se e analisaram-se questoes de uma tarefa envolvendo o conceito de funcao. Tomaram-se como dados os protocolos de resolucao. A estruturacao metodologica apoia-se em uma abordagem qualitativa de cunho interpretativo. Os resultados mostraram que os conhecimentos mobilizados pelos professores priorizam as representacoes graficas e tabulares, promovendo indicativos de uso de softwares e planilhas como recursos didaticos, e ainda enfatizam a presenca das ‘letras’, como um dos fatores causadores de dificuldades apresentadas pelos estudantes dos diferentes niveis de escolaridade da Educacao Basica, no estudo de funcoes. Palavras-chave : Conceito de funcao, Conhecimentos do professor, Educacao matematica, OBEDUC. References ALRO, H.; SKOVSMOSE, O. Dialogo e aprendizagem em educacao matematica . 2. ed. Belo Horizonte: Autentica, 2010. BALL, D. L.; COHEN, D. K. Developing pratice, developing practioners: toward a pratice-based theory of professional education. In: SYKES, G.; DARLING-HAMMOND, L. (Org.) Teaching as the learning profession : Handbook of policy and practice. San Francisco: Jossey Bass, 1999. p. 3-32. BALL, D.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching: what makes it special? Journal of Teacher Education , v. 59, n. 5, p. 389-407, 2008. BISOGNIN, E.; BISOGNIN, V.; CURY, H. N. Conhecimentos de professores da educacao basica sobre o conceito de funcao. In: ENCONTRO NACIONAL DE EDUCACAO MATEMATICA, 10., 2010, Salvador. Anais... Brasilia: SBEM, 2010. CARNEIRO, V.; FANTINEL, P.; SILVA, R. Funcoes: significados circulantes na formacao de professores. Bolema , Rio Claro (SP), v. 16, n. 19, p.19-39, marco, 2003. CARRILLO, J.  et al. Determining specialised knowledge for mathematics teaching. In: CONGRESS OF EUROPEAN RESEARCH IN MATHEMATICS EDUCATION, 8., 2013, Turquia. Proceedings... Manavgat-Side, Antalya -Turquia: CERME, 2013. CRESWELL, J. W. Projeto de pesquisa: metodos qualitativos, quantitativos e misto. 3. ed. Porto Alegre: Artmed, 2010. FERNANDEZ, S.; FIGUEIRAS, L. Horizon content knowledge: Shaping MKT for a continuous mathematical education. Redimat - Journal of Research in Mathematics Education, Barcelona, v. 3, n. 1, p.7-29, 2014. GARCIA, V. C. Funcao: o professor conhece este conceito? Vidya , Santa Maria, v. 29, n. 2, p. 43-52, 2009. GRAEBER, A.; TIROSH, D. Pedagogical CONTENT KNOWLEDGE - Useful concept or elusive notion? In: SULLIVAN, P. (Org.). Knowledge and beliefs in mathematics teaching and teaching development . Amsterdam, The Netherlands: Sense, 2009. HANSSON, O. Preservice teachers’ view on y = x + 5 and y =  expressed through the utilization of concept maps: a study of the concept of function. In: CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 29. Proceedings... Melbourne, AUS: PME, 2005. v. 3. p. 97-104. HILL, H. C.; ROWAN, B.; BALL, D. L. Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal , Washington D. C., n. 42, p. 371-406, 2005. HOZ, R.; WEIZMAN, G. A revised theorization of the relationship between teachers’ conceptions of mathematics and its teaching, International Journal of Mathematical Education in Science and Technology , Loughborough, v. 39, n. 7, p. 905-924, 2008. HURRELL, D. P. What teachers need to know to teach mathematics: An argument for a reconceptualised model. Australian Journal of Teacher Education , Australia, v. 38, n. 11, 2013. LIMA, L.; PONTES, M. G. de O. A ressignificacao do conceito de funcao na formacao inicial do professor de matematica. In: SEMINARIO INTERNACIONAL DE PESQUISA EM EDUCACAO MATEMATICA, 4., 2009, Brasilia. Anais... Brasilia, UCB, 2009. MOREIRA, P. C.; DAVID, M. M. M. S. O conhecimento matematico do professor: formacao e pratica docente na escola basica. Revista Brasileira de Educacao , Rio de Janeiro, n.28, p.50-61, jan./fev./mar./abr. 2005. PAZUCH, V.; RIBEIRO, A. J. Conhecimento profissional de professores de matematica e o conceito de funcao: uma revisao de literatura. Educacao Matematica Pesquisa , v. 19, n. 1, p. 465-496, 2017. PONTE, J. P. Formacao do professor de matematica: perspectivas atuais. In: PONTE, J. P. (Org.). Praticas profissionais dos professores de matematica . Lisboa: IE/UL, 2014. p. 343-358. REZENDE, W. M. Funcoes reais: uma contribuicao da historia do calculo e das novas tecnologias para o saber pedagogico de conteudo. In: ROQUE, T.; GIRALDO, V. (Org.). O saber do professor de matematica : ultrapassando a dicotomia entre didatica e conteudo. Rio de Janeiro: Ciencia Moderna, 2014. p. 79-106. RIBEIRO, A. J.; CURY, H. N. Algebra para a formacao do professor – explorando conceitos de equacao e de funcao. Belo Horizonte: Autentica, 2015. SANTOS, G. L. D.; BARBOSA, J. C. Como ensinar o conceito de funcao? Educacao Matematica em Revista , Brasilia, v. 22, p. 27-37, 2017. SHULMAN, L. S. Those who understand: Knowledge growth in the teaching. Educational Researcher , Washington, US, v. 15, n. 2, p. 4-14, 1986. SHULMAN, L. S. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review , Cambridge, US, v. 57, n. 1, p. 1-22, 1987. SPEER, N. M.; KING, K. D.; HOWELL, H. Definitions of mathematical knowledge for teaching: using these constructs in research on secondary and college mathematics teachers. Journal of Mathematics Teacher Education , n. 18, p. 105-122, 2015. STEELE, M.; HILLEN, A. F.; SMITH, M. S. Developing mathematical knowledge for teaching in a methods course: the case of function. Journal of Mathematics Teacher Education , v. 16, I. 6, p. 451-483, 2013. STOCKERO, S. L. Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers. Journal of Mathematics Teacher Education , v. 11, p. 373-394, 2008. STYLIANIDES, A. J.; BALL, D. L. Studying the mathematical knowledge needed for teaching: The case of teachers’ knowledge of reasoning and proof. In: AMERICAN EDUCATIONAL RESEARCH ASSOCIATION, 85. Proceedings... San Diego, 2004. TARDIF, M. Saberes docentes e formacao profissional. Petropolis, RJ: Vozes, 2002. TABACH, M.; NACHLIELI, T. Classroom engagement towards using definitions for developing mathematical objects: the case of function. Educational Studies in Mathematics , n. 90, p. 163-187, 2015. THOMAS, M. The role of representation in teacher understanding of function. In: PSYCHOLOGY OF MATHEMATICS EDUCATION, 27., 2003, Honolulu. Proceedings... Honolulu, HI: PME, 2003. v. 4. p. 291-298. TURNER, F.; ROWLAND, T. The knowledge quartet as an organising framework for developing and deepening teachers’ mathematics knowledge. In: ROWLAND, T.; RUTHVEN, K. Mathematical knowledge in teaching . Netherlands: Springer, 2011. p. 195-212. ZUFFI, E. M.; PACCA, J. L. A. O conceito de funcao e sua linguagem para os professores de matematica e de ciencias. Ciencia & Educacao , Bauru (SP), v.8, n. 1, p. 1-12, 2002.

Conhecimentos mobilizados por professores que ensinam matemática e o conceito de função na educação básica