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Artículos

Vol. 11 No. 2 (2008): Julio

THE STUDY OF FUNCTIONAL RELATIONSHIPS AND THE DEVELOPMENT OF THE CONCEPT OF VARIABLE IN 8TH GRADE STUDENTS

Submitted
May 21, 2024
Published
2008-05-08

Abstract

This study analyses the relationship between solving exploratory and investigation tasks involving functional relationships and the development of algebraic thinking in grade 8 students, giving special attention to the way they interpret and use the algebraic language. The methodology, qualitative and interpretative, is based in two case studies of students involved in a teaching unit of 16 classes which included the study of numerical sequences, functions and first degree equations. The data collection involved two interviews (one carried before and the other after the teaching unit), the participant observation of the classes by the teacher, registered in her diary, and gathering of students' written records. The results show that the emphasis in the study of functional relationships based on exploratory and investigation tasks promotes the development of meaning for the algebraic language and the construction of a wider vision regarding the use of symbols.

References

  1. Arcavi, A. (1994), Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
  2. Arcavi, A. (2006). El desarrollo y el uso del sentido de los símbolos. In I. Vale, T. Pimentel, A Barbosa, L. Fonseca, L. Santos & P. Canavarro (Eds.), Números e Algebra na aprendizagem da matemática e na formação de professores (pp. 29-47). Caminha: SEM-SPCE.
  3. Bogdan, R. C., & Biklen, S. K. (1994), Investigação qualitativa em educação. Porto: Porto Editora.
  4. Booth, L. R. (1984). Algebra: Children's strategies and errors. Windsor: Nfer-Nelson.
  5. Booth, L. R. (1988). Children's difficulties in beginning algebra. In A.F. Coxford & A.P. Schulte (Eds.), The ideas of algebra, K-12: 1988 Yearbook (pp. 20-32). Reston, VA: NCTM.
  6. Denzin, N. K., & Lincoln, Y. S. (1994). Introduction: entering the field of qualitative research. in N. K. Denzin, & Y. S. Lincoln (Edits.), Handbook of qualitative research (pp. 1-17). Londres: Sage.
  7. Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Portsmouth, NH: Heinemann.
  8. English, L., & Warren, E. (1998). Introducing the variable through pattern exploration. Mathematics Teacher, 91(1), 166-70.
  9. Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25.
  10. Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Erlbaum.
  11. Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
  12. Küchemann, D. (1981). Algebra. In K.M. Hart (Ed.) Children's understanding of mathematics 11-16 (pp. 102-119). London: Murray.
  13. MacGregor, M., & Stacey, K. (1997). Students' understanding of algebraic notation: 11-15 Educational Studies in Mathematics, 33(1), 1-19.
  14. Matos, A. (2007). Explorando relações funcionais no 8.° ano de escolaridade: Um estudo sobre o desenvolvimento do pensamento algébrico (Dissertação de Mestrado, Universidade de Lisboa, disponível em http://ia.fc.ul.pt).
  15. ME-DGEBS (1991). Programa de Matemática: Plano de organização do ensino-aprendizagen (3. ciclo do ensino básico). Lisboa: Ministério da Educação, Direcção-Geral dos Ensinos Básico e Secundário.
  16. NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA NCTM.
  17. NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  18. Oliveira, H., Segurado, I., Ponte, J. P, & Cunha, M. (1999). Investigações matemáticas na sala de aula: Um projecto colaborativo. [Acedido de http://ia.fc.ul.pt/textos/p 121-131.PDF em 24- 03-2008]
  19. Ponte, J. P. (2002). Investigar a nossa própria prática. In GTI (Org.), Reflectir e investigar sobre a prática profissional (pp. 5-28). Lisboa: APM.
  20. Ponte, J. P. (2004). Problemas e investigaciones en la actividad matemática de los alumnos. In J. Giménez, L. Santos & J. P. da Ponte (Eds.), La actividad matemática en el aula (pp. 25-34). Barcelona: Gráo.
  21. Ponte, J. P. (2006). Estudos de caso em educação matemática, BOLEMA, 25, 105-132.
  22. Ponte, J. P. (2007). Investigations and explorations in the mathematics classroom. ZDM, 39(5-6), 419-430.
  23. Ponte, J. P., Brocardo, J., & Oliveira, H. (2003). Investigações matemáticas na sala de aula. Belo Horizonte: Autêntica.
  24. Rojano, T. (1996). The role of problems and problem solving in the development of algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 55-62). Dordrecht: Kluwer.
  25. Schoenfeld, A. H., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81(6), 420-427.
  26. Sfard, A., & Linchevski, L. (1994). The gains and piftalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228.
  27. Ursini, S., & Trigueros, M. (2001). A model for the uses of variable in elementary algebra. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 327-334). Utrecht: Utrecht University.
  28. Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford & A. P. Schulte (Eds.), The ideas of algebra, K-12 (pp. 8-19). Reston, VA: NCTM.
  29. Yin, R. (1984). Case study research: design and methods. Newbury Park, CA: Sage.

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