Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 15 No. 3 (2012): Noviembre

PATTERN TASKS: THINKING PROCESSES USED BY 6TH GRADE STUDENTS

Submitted
July 14, 2023
Published
2011-11-07

Abstract

This paper gives a description of an ongoing study focused on pattern exploration and generalization tasks, analysing the performance of fifty-four 6th grade students when solving this type of tasks. The main goal is to understand the strategies they use, difficulties that emerge from students’ work and ascertain the role played by visualization in their reasoning. Results so far indicate that, in general, students tend to use numeric instead of visual approaches. They also tend to use incorrect strategies when attempting to generalize, the most common being an incorrect use of direct proportion.

References

  1. Amaro. G., Cardoso, F. e Reis, P. (1994). Terceiro Estudo Internacional de Matemática e Ciências, Relatório Internacional, Desempenho de alunos em Matemática e Ciências: 7.º e 8.º anos. Lisboa, Portugal: Instituto de Inovação Educacional.
  2. Becker, J. & Rivera, F. (2005). Generalization strategies of beginning high school algebra students. In H. Chick & J.L. Vincent (Eds.), Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). Melbourne, Australia: University of Melbourne.
  3. Creswell, J. (2003). Research Design: Qualitative, Quantitative and Mixed Approaches. Newbury Park, CA: Sage
  4. Departamento do Ensino Básico (DEB). (2001). Currículo Nacional do Ensino Básico. Competências Essenciais. Lisboa: Editorial do Ministério da Educação.
  5. Devlin, K. (2002). Matemática: A ciência dos padrões. Porto, Portugal: Porto Editora.
  6. Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.) Proceedings of the 15th International Conference of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 33-48). Genova, Italy: University of Genova.
  7. García Cruz, J. A. & Martinón, A. (1997). Actions and Invariant Schemata in Linear Generalizing Problems. In E. Pehkonen (Ed.) Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 289-296). Lahti, Finland: University of Helsinki.
  8. Gardner, H. (1993). Multiple Intelligences: The Theory in Practice. New York, USA: Basic Books.
  9. GAVE (2004). Resultados do Estudo Internacional PISA 2003. Lisboa, Portugal: Ministério da Educação. Gabinete de Avaliação Educacional.
  10. Goldenberg, E. P. (1996). “Habits of Mind” as an organizer for the curriculum. Journal of Education 178(1), 13-34.
  11. Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In L. Puig & A. Gutiérrez (Eds.). Proceedings of the 20th International Conference of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 3-19). Valencia, Spain: University of Valencia.
  12. Healy, L. & Hoyles, C. (1996). Seeing, doing and expressing: An evaluation of task sequences for supporting algebraic thinking. In L. Puig & A. Gutierrez (Eds.). Proceedings of the 20th International Conference of the International Group for the Psychology of Mathematics Education. (Vol. 3, pp. 67-74). Valencia, Spain: University of Valencia
  13. Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. Chicago, USA: University of Chicago Press
  14. Mason, J., Johnston-Wilder, S. & Graham, A. (2005). Developing Thinking in Algebra. London, England: Sage
  15. ME-DGIDC (2007). Programa de Matemática do Ensino Básico. Lisboa: Ministério da Educação, Departamento de educação Básica
  16. Moses, B. (1982). Visualisation: A Different Approach to Problem Solving. School Science and Mathematics 82(2),141-147
  17. NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
  18. Noss, R., Healy, L. & Hoyles, C. (1997). The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic. Educational Studies in Mathematics 33(2), 203-33. DOI: 10.1023/A:1002943821419
  19. Orton, A. & Orton, J. (1999). Pattern and the approach to algebra. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics(pp. 104-120). London, England: Cassel.
  20. Palarea, M. & Socas, M. (1998). Operational and conceptual abilities in the learning of algebraic language. A case study. In A. Olivier & K. Newstead (Eds.). Proceedings of the 22th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 3, pp. 327-334). Stellenbosch, South Africa: University of Stellenbosch.
  21. Pólya, G. (1945). How to solve it. Princeton, USA: Princeton University Press
  22. Presmeg, N. (1986). Visualization and mathematical giftedness. Educational Studies in Mathematics 17(3), 297-311.
  23. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology. In: A. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 205–235). Dordrecht, Netherlands: Sense Publishers.
  24. Ramalho, G. (1994). As nossas crianças e a Matemática: caracterização da participação dos alunos portugueses no “Second International Assessment of Educational Progress”. Lisboa, Portugal: Departamento de Programação e Gestão Financeira.
  25. Sasman, M., Olivier, A. & Linchevski, L. (1999). Factors influencing students’ generalization thinking processes. In O. Zaslavski (Ed.). Proceedings of the 23rd International Conference of the International Group for the Psychology of Mathematics Education. (Vol. 4, pp. 161-168). Haifa, Israel: University of Haifa.
  26. Schoenfeld, A. & Arcavi, A. (1999). Variables, expressions, and equations. In B. Moses (Ed.), Algebraic thinking, grades K-12 (pp. 150-156). Reston, VA: National Council of Teachers of Mathematics
  27. Shama, G. & Dreyfus, T. (1994). Visual, algebraic and mixed strategies in visually presented linear programming problems. Educational Studies in Mathematics 26, 45-70. DOI: 10.1007/ BF01273300
  28. Stacey, K. (1989). Finding and Using Patterns in Linear Generalising Problems. Educational Studies in Mathematics 20(2), 147-164. DOI: 10.1007/BF00579460
  29. Steen, L. (1990). On the shoulders of giants: New approaches to numeracy. Washington, DC: National Academy Press.
  30. Tall, D. (1991). (Ed). Advanced Mathematical Thinking. London, England: Kluwer Academic Publishers.
  31. Thornton, S. (2001). A Picture is Worth a Thousand Words. In A. Rogerson (Ed.), New ideas in mathematics education: Proceedings of the International Conference of the Mathematics Education into the 21st Century Project (pp. 251-256). Retrieved from http://math.unipa.it/ ~grim/AThornton251.PDF
  32. Vale, I. e Pimentel, T. (2005). Padrões: um tema transversal do currículo. Educação e Matemática 85,14-20
  33. Vale, I., Palhares, P., Cabrita, I. e Borralho, A. (2006). Os padrões no ensino aprendizagem da Álgebra. In I. Vale, T. Pimentel, A. Barbosa, L. Fonseca, L. Santos, P. Canavarro (Orgs.), Números e Álgebra na aprendizagem da matemática e na formação de professores (pp. 193- 211). Lisboa, Portugal: Secção de educação Matemática da Sociedade Portuguesa de Ciências da Educação.
  34. Zazkis, R & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational studies in mathematics 49(3), 379-402.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 > >> 

You may also start an advanced similarity search for this article.