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A importância do conhecimento do conteúdo matemático na prática letiva de uma professora
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Palavras-chave

Modelação da prática. Cognições. Conhecimento matemático para o ensino.

Como Citar

RIBEIRO, Carlos Miguel. A importância do conhecimento do conteúdo matemático na prática letiva de uma professora: discutindo um modelo de análise. Zetetike, Campinas, SP, v. 19, n. 1, p. 71–102, 2011. DOI: 10.20396/zet.v19i35.8646646. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646646. Acesso em: 10 maio. 2024.

Resumo

A prática lectiva é potenciada e condicionada por um conjunto de dimensões entre as quais se encontram as cognições do professor (objectivos, crenças e conhecimentos). Todas estas cognições do professor interferem directamente no processo de ensino, porém, quando leccionamos uma aula de matemática os conhecimentos do professor, face aos conteúdos, sua natureza e forma como os pode tornar perceptíveis para os alunos assumem um papel de relevo, pois, se o professor não for possuidor de um sólido e consistente Mathematical Knowledge for Teaching, as possíveis lacunas que possua transparecem nas oportunidades de aprender que efectiva aos seus alunos.
Este artigo apresenta um modelo de análise da prática lectiva, evidenciado através da prática de uma professora do 1.º Ciclo, discutindo as relações entre as componentes de tal modelo num episódio em que a professora tem por objectivo (declarado a posteriori) consolidar a interpretação/”inferência” de dados a partir de um pictograma anteriormente elaborado. Após a apresentação teórica do modelo, e uma sua concretização no episódio referido, discutem-se algumas potencialidades da realização deste tipo de análise e discussão na formação inicial e/ou contínua de professores de forma a trazer para as discussões aspectos matemáticos e do seu ensino e não se focarem apenas questões de natureza educativa em geral.

Palavras-chave

 

The importance of mathematical content knowledge to a teacher’s practice: discussing a model for analysis

Abstract

Teacher practice depends on a set of dimensions, including teachers’ cognitions (goals, beliefs and knowledge). They all have a direct interference with the teaching process, but, when teaching mathematics, teacher knowledge concerning the content, as well as its nature and how a teacher can make it understandable for students, play an important role in practice. If a teacher does not have solid and consistent mathematical knowledge for teaching, the gaps he/she may present will be reflected in students’ learning.
This paper presents a model to analyze teaching practice, through an example from a primary school teacher’s practice. The relationships between the dimensions of such model are discussed in an episode in which the teacher  explicitly intended to consolidate the interpretation/inference of data from a previously elaborated pictogram. After presenting the model theoretically and in practice, some potentialities of this kind of analysis in teacher education are discussed. This is a way of focusing (and showing teachers) mathematical aspects of their practice, rather that just issues of educational nature in general.

Keywords

Modeling teacher practice; cognitions; mathematical knowledge for teaching.

https://doi.org/10.20396/zet.v19i35.8646646
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Referências

AGUIRRE, J.; SPEER, N. Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behavior, Nova York, v. 18, n. 3, p. 327-356, 2000.

BALL, D. What mathematical knowledge is needed for teaching mathematics. Washington, DC: U.S. Department of Education, Secretary’s Mathematics Summit., 6 fev. 2003. Disponível em: http://www-personal.umich.edu/~dball/presentations/index.html. Acesso em: 10 maio 2008.

BALL, D. L.; BASS, H. Toward a practice-based theory of mathematical knowledge for teaching. In: DAVIS, B.; SIMMT, E. (Ed.). Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group. Edmonton, AB: CMESG/GCEDM, 2003. p. 3-14.

BALL, D.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching: What makes it special? Journal of Teacher Education, Thousand Oaks, v.59, n.5, p.389-407, 2008.

BATURO, A. R.; WARREN, E. A.; COOPER, T. J. Queensland Numeracy Research and Development Project fi nal report: Teachers enhancing numeracy. Camberra, ACT: Department of Education, Science and Training, 2004.

BRENDEFUR, J.; FRYKHOLM, J. Promoting mathematical communication in the classroom: Two preservice teachers’ conceptions and practices. Journal of Mathematics Teacher Education, Nova York, v.3, p.125-153, 2000.

CARRILLO, J. et al. Análisis de secuencias de aprendizaje matemático desde la perspectiva de la gestión de la participación. Enseñanza de las Ciencias, Barcelona, v. 26, n.1, p. 67-76, 2008.

CHARMAZ, K. Grounded theory: Objectivist and construtivist methods. In: DENZIN, N. K.; LINCOLN, Y. (Ed.). The handbook of qualitative research. Nova York: Sage Publications, 2000. v. 2. p. 509-535.

CLIMENT, N. El desarrollo profesional del maestro de Primaria respecto de la enseñanza de la matemática. Un estudio de caso. 2005. (PhD Dissertation) — Universidad de Huelva. Michigan: Proquest Michigan University, 2005. Disponível em: www.proquest.co.uk. Acesso em: 15 abr. 2008.

COBB, P.; MCCLAIN, K. Guiding inquiry-based math learning. In: SAWYER, R. K. (Ed.). The Cambridge handbook of the learning sciences. New York, NY: Cambridge University Press, 2006. p. 171-185

ELBERS, E. Classroom interactions as refl ection: learning and teaching mathematics in a community of inquiry. Educational Studies in Mathematics, Nova York, v.54, p. 77-99. 2003.

ELLIS, V. Taking subject knowledge seriously: from professional knowledge recipes to complex conceptualizations of teacher development. The Curriculum Journal, Londres, v.18, n.4, p.447- 462, 2007.

ERNEST, P. The knowledge, beliefs and attitudes of mathematics teacher: a model. Journal of Education for Teaching, Londres, v.15, n.1, p.13-33, 1989.

HIEBERT, J. et al. Making sense: Teaching and Learning mathematics with understanding. Portsmouth, NH: Heinemann, 1997.

HILL, H. C.; BALL, D.; SCHILLING, S. Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specifi c knowledge of students. Journal for Research in Mathematics Education, Reston, v.39, n.4, p.372-400, 2008.

HILL, H.; ROWAN, B.; BALL, D. L. Effects of teachers’ mathematics knowledge for teaching on student achievement. American Education Research Journal, Thousand Oaks, v.42, n.2, p.371- 406, 2005.

KELLY, G. A. Theory of personality: the psychology of personal constructs. New York: Routledge, 1963.

LAMPERT, M. When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Education Research Journal, Thousand Oaks, v.27, n.1, p.29-63, 1990.

MONTEIRO, R.; CARRILLO, J.; AGUADED, S. Emergent theorizations in modelling the teaching of two science teachers. Research in Science Education, Nova York, v.38, n.3, p.301-319, 2008.

NATIONAL COUNCIL OF TEACHER OF MATHEMATICS [NCTM]. Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM, 1989.

PAJARES, F. Teacher’s beliefs and educational research: cleaning up a messy construct. Review of Educational Research, Thousand Oaks, v.62 n. 39, p. 307-332, 1992.

PARK, S.; OLIVER, J. S. Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Sciences Education, Nova York, v.38, p.261–284, 2008.

PONTE, J. P. et al. Programa de Matemática do Ensino Básico. Lisboa: Ministério da Educação – DGIDC, 2007.

PRESTAGE, S.; PERKS, P. Developing teacher knowledge using a tool for creating tasks for the classroom. Journal of Mathematics Teacher Education, Nova York, v.10, p.381-390, 2007.

RIBEIRO, C. M. From modeling the teacher practice to the establishment of relations between the teacher actions and cognitions. In: JOUBERT, M. (Ed.). Proceedings of the British Society for Research into Learning Mathematics — British Society for Research into Learning Mathematics, London, v. 28, n. 3, p. 102-107, 2008.

RIBEIRO, C. M. Conhecimento matemático para Ensinar: uma experiência de formação de professores no caso da multiplicação de decimais. Bolema, Rio Claro, v. 22, n. 34, p. 1-26, 2009a.

RIBEIRO, C. M. Possíveis contributos da elaboração de um modelo da prática lectiva para a formação de professores. In: FERREIRA, H. et al. (Org.). Actas do X Congresso da Sociedade Portuguesa de Ciências da Educação – investigar, avaliar, descentralizar. Bragança: SPCE; IPB, 2009b.

RIBEIRO, C. M. Sequência de acções, crenças e conhecimentos num episódio de apresentação do conteúdo: analisando a prática da professora Maria. In: SEMINÁRIO DE INVESTIGAÇÃO EM EDUCAÇÃO MATEMÁTICA (SIEM), 20., setembro 2009, Viana do Castelo. Actas... Braga: Centro de Investigação em Educação (CIEd), Instituto de Educação da Universidade do Minho, 2009c. p. 119-130.

RIBEIRO, C. M.; CARRILLO, J.; MONTEIRO, R. Uma perspectiva cognitiva para a análise de uma aula de matemática do 1.º ciclo: um modelo de apresentação de conteúdo tendo como recurso o desenho no quadro. In: LUENGO, R.; ALFONSO, B.; BLANCO, L. J. (Ed.). Investigación en Educación Matemática XII. Badajoz: Sociedad Extremeña de Educación Matemática “Ventura Reyes Prósper”; Sociedad Española de Investigación en Educación Matemática (SEIEM), 2008. p. 545-555.

RIBEIRO, C. M.; CARRILLO, J.; MONTEIRO, R. Cognições do professor numa aula de matemática. Paper presented at the VI Congreso Iberoamericano de Educación Matemática (VI CIBEM), Puerto Montt, Chile, 2009a.

RIBEIRO, C. M.; CARRILLO, J.; MONTEIRO, R. ¿De qué nos informan los objetivos del profesor sobre su práctica?: Análisis y infl uencia en la práctica de una maestra. In: SIMPOSIO DE LA SEIEM, INVESTIGACIÓN EN EDUCACIÓN MATEMÁTICA, 13., setembro 2009, Santander. Actas… . Santander: SEIEM; Universidade de Cantabria, 2009b. p.415-423

RIBEIRO, C. M.; MARTINS, C. The impact of a Professional Development Program in Teacher’s Practice. In: NOVOTNÁ, J.; MORAOVÁ, H. (Ed.) Proceedings of International Symposium Elementary Maths Teaching (SEMT 09), Praga, República Checa: Charles University, Faculty of Education, 2009a. p. 212-219.

RIBEIRO, C. M.; MARTINS, C. O trabalho colaborativo como promotor de desenvolvimento profi ssional: perspectivas de formandos e formadores do PFCM. In: ENCONTRO NACIONAL DE PROFESSORES DE MATEMÁTICA – PROFMAT, 25., 2009, Viana do Castelo. Actas... APM, 2009b.

RIBEIRO, C. M.; MENDES, O. Mudar as práticas no 1.º ciclo. Perspectivas de uma professora. In: SEMINÁRIO DE INVESTIGAÇÃO EM EDUCAÇÃO MATEMÁTICA (SIEM), 18., Local. Actas...– Ilha Terceira: SEM-SPCE, 2007.

RIBEIRO, C. M.; MONTEIRO, R.; CARRILLO, J. Professional knowledge in an improvisation episode: the importance of a cognitive model. In: DURAND-GUERRIER, V.; SOURYLAVERGNE, S.; ARZARELLO, F. (Ed.), Proceedings of the 6th Conference of the European Society for Research in Mathematics Education (CERME6). Lyon: ERME, 2009. p. 2030-2039. Disponível em: http://www.inrp.fr/editions/editions-electroniques/cerme6/working-group-10. Acesso em: 02 jul. 2009

ROCHELLE, J. Choosing and using video equipment for data collection. In: KELLY, A.; LECH, R. (Ed.). Handbook of research design in mathematics and science education. Londres: Lawrence Erlbaum Associates Publishers, 2000. p.709-732.

ROWLAND, T. The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, Nova York, v. 69, p.149-163, 2008.

SAXE, G. Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Lawrence Erlbaum Associates, 1991.

SCHANK, R. C.; ABELSON, R. P. Scripts, plans, goals, and understanding: An inquiry into the human knowledge structures. Hillsdale: Lawrence Erlbaum Associates, 1977.

SCHOENFELD, A. H. On modeling teaching. Issues in Education, Charlotte, North Carolina, v. 4, n.1, p. 149–162, 1998a.

SCHOENFELD, A. H. Toward a theory of teaching-in-context. Issues in Education, Charlotte, North Carolina, v.4, n.1, p.1-94, 1998b.

SCHOENFELD, A. H. Models of the teaching process. Journal of Mathematical Behaviour, Nova York, v. 18, n. 3, p. 243–261, 2000.

SCHOENFELD, A. H.; MINISTRELL, J.; ZEE, E. V. The detailed analysis of an established teacher’s non-traditional lesson. Journal of Mathematical Behavior, Nova York, v.18, n.3, p. 281–325, 2000.

SCHÖN, D. The refl ective practitioner: How professionals think in action. Nova York: Basic Books, Inc., Publishers, 1983.

SCHÖN, D. Educating the refl ective practitioner: Toward a new design for teaching and learning in the professions. San Francisco, CA: Jossey Bass, 1987.

SERRAZINA, L. Teacher’s professional development in a period of radical change in primary mathematics education in Portugal. 1998. p. 812 Tese (Doutorado) — Universidade de Londres. Associação de Professores de Matemática, Lisboa, 1998.

SERRAZINA, L. A Formação contínua de professores em matemática: o conhecimento e a supervisão em sala de aula e a sua infl uência na alteração das práticas. International Journal for Studies in Mathematics Education, São Paulo, v.2, n.1, 1-23, 2010.

SHERIN, M. G.; SHERIN, B. L.; MADANES, R. Exploring diverse accounts of teacher knowledge. Journal of Mathematical Behavior, Nova York, v.18, n. 3, p. 357-375, 2000.

SHULMAN, L. Those who understand: Knowledge growth in teaching. Educational Researcher, Thousand Oaks, v.15, n.2, p.4-14, 1986.

STAR, J. R.; STRICKLAND, S. K. Learning to observe: using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, Nova York, v.11, n.2, p.107-125, 2008.

STRAUSS, A.; CORBIN, J. Grounded theory in practice. Thousand Oaks, CA: Sage Publications, 1997.

STRAUSS, A.;CORBIN, J. Basics of qualitative research: Techniques and procedures for developing grounded theory. Londres: Sage Publications, 1998.

TAYLOR, M. Encouraging professional growth and mathematics reform through collegial interaction. In: RUBENSTEIN, R.; BRIGHT, G. (Ed.). Sixty-sixth Yearbook do NCTM: Perspectives on the teaching of mathematics. Reston, The National Council of Teachers of Mathematics, 2004. p. 219-228.

THOMPSON, A. The relationship of teacher’s conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, Nova York, v.15, p.105-127, 1984.

THOMPSON, A. Teachers beliefs and conceptions: A synthesis of the research. In: GROWS D. A. (Ed.). Handbook of research on mathematics teaching and learning. Nova York: Macmillan, 1992. p. 127-146.

TICHÁ, M.; HOŠPESOVÁ, A. Qualifi ed pedagogical refl ection as a way to improve mathematics education. Journal of Mathematics Teacher Education, Nova York, v.9, p.129-156, 2006.

WILKINS, J. L. M. The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, Nova York, p.139-164, 2008.

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