Investigations and explorations as part of the daily work in the classroom
DOI:
https://doi.org/10.18542/amazrecm.v9i18.2019Keywords:
investigations, inquiry teaching, teaching units, tasks, mathematics learningAbstract
This article presents three key elements of teaching units of exploratory nature: (i) the teaching-learning conjecture that frames the development of the unit, (ii) the tasks that compose it; and (iii) the working modes, communication styles and roles or teacher and students. It gives examples of three teaching units of different levels of education that illustrate these elements and their contributions to the learning process. In these teaching units predominate investigation and exploration task teaching that promotes the active involvement of students in their learning. These units also favor working with different types of representations, and the students use their own representations, and progress from there to more formal representations. The structure of classes, with moments of presentation of the task, students autonomous work and collective discussion and synthesis also enhances the involvement of students in their learning and the development of various types of discourse in the classroomReferences
AZEVEDO, A. B. G. O desenvolvimento do raciocínio matemático na aprendizagem das funções: Uma experiência com alunos do ensino secundário, 2009. Dissertação de mestrado, Universidade de Lisboa. Disponível no Repositório da UL.
BISHOP, A.;& GOFFREE, F. Classroom organization and dynamics. In: CHRISTIANSEN, B., HOWSON, A. G. & OTTE, M. (Eds.), Perspectives on mathematics education (pp. 309-365). Dordrecht: D. Reidel, 1986, P. 309-365.
BRANCO, N. O estudo de padrões e regularidades no desenvolvimento do pensamento algébrico, 2008. Dissertação de mestrado, Universidade de Lisboa. Disponível no Repositório da UL.
BRUNER, J. Para uma teoria da educação. Lisboa: Relógio d'Água, 1999.
CARRAHER, D. W.;& SCHLIEMANN, A. D. Early algebra and algebraic reasoning. In: LESTER, F. (Ed.), Second handbook of mathematics teaching and learning. Greenwich, CT: Information Age, 2007, P. 669-705.
CHISTIANSEN, B.;& WALTHER, G. (1986).Task and activity. In: CHRISTIANSEN, B., HOWSON, A. G. &OTTE, M. (Eds.), Perspectives on mathematics education. Dordrecht: D. Reidel, 1986, P. 243-307.
CRAMER, K.; POST, T.;& CURRIER, S. Learning and teaching ratio and proportion: Research implications. In:OWENS, D. T. (Ed.), Research ideas for the classroom: High school mathematics. Reston: NCTM, 1993, p. 159-178.
ENGLISH, L.;& WARREM, E. Introducing the variable through patterns exploration. In: MOSES, B. (Ed.), Algebraic thinking, grades K-12. Reston, VA: National Council of Teachers of Mathematics, 1999, p. 141-145.
FIORENTINI, D.; MIORIM, M. A.;& MIGUEL, A. Contribuição para repensar a educação algébrica elementar. Pro-Posições, 4, n. 1, 1993, 78-90.
HITT, F. Difficulties in the articulation of different representations linked to the concept of function. The Journal of Mathematical Behavior, 17, n. 1, 1998, 123-134.
KAPUT, J. J. (2008). What is algebra? What is algebraic reasoning? In: KAPUT, J. J.;CARRAHER, D. W. &BLANTON, M. L. (Eds.), Algebra in the Early Grades. New York, NY: Routledge, 2008, p. 5-17.
KIEREN, T. Personal knowledge of rational numbers: Its intuitive and formal development. In: HIEBERT, J. & BEHR, M. (Eds.), Number concepts and operations in the middle grades. Reston: NCTM, 1988, p. 162-181.
KISSANE, B. Technology and the curriculum; the case of the graphics calculator. In: THOMAS, M. O. J. (Ed.), Proceedings of Time 2000: An international conference on technology in mathematics education (pp. 60-71). Auckland, New Zealand, 2001, p. 60-71.
MINISTÉRIO DA EDUCAÇÃO. Matemática A – 10.º ano. Lisboa: ME-DES, 2001.
MINISTÉRIO DA EDUCAÇÃO. Programa de Matemática do Ensino Básico. Lisboa: ME-DGIDC, 2007.
NCTM. Princípios e normas para a Matemática escolar. Lisboa: APM, 2007.
PONTE, J. P. Gestão curricular em Matemática. In: GTI (Ed.), O professor e o desenvolvimento curricular. Lisboa: APM, 2005, p. 11-34.
PONTE, J. P., BRANCO, N., & MATOS, A. Álgebra no ensino básico. Lisboa: DGIDC, 2009.
PONTE, J. P.; BROCARDO, J.;& OLIVEIRA, H. Investigações matemáticas na sala de aula. Belo Horizonte: Autêntica, 2003.
QUARESMA, M. (2010). Ordenação e comparação de números racionais em diferentes representações: uma experiência de ensino, 2010. Dissertação de mestrado, Universidade de Lisboa. Disponível no Repositório da UL.
SKOVSMOSE, O. Cenários para investigação. Bolema, 14, 2000, 66-91.
TEIXEIRA, P.; PRECATADO, A.; ALBUQUERQUE, C.; ANTUNES, C.;& NÁPOLES, S. Funções-10º ano de escolaridade. Lisboa: Ministério da Educação, Departamento do Ensino Secundário, 1997.
WEBB, D.; BOSWINKEL, N.;& DEKKER, T. Beneath the tip of the iceberg: Using representations to student understanding. Mathematics Teaching in the Middle School, 14, n. 2, 2008, 110-113.
ZAZKIS, R.;& LILJEDAHL, P.Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 2002, 379-402.
