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Artículos

Vol. 15 No. 2 (2012): Julio

MULTIPLE REPRESENTATIONS: A CONTRIBUTION FOR THE LEARNING OF THE CONCEPT OF FUNCTION

  • Jael Miriam Andrade
  • Manuel Joaquim Saraiva
Submitted
July 14, 2023
Published
2012-07-01

Abstract

This article presents a study focused on the understanding of
the concept of function by students of 10th grade. It studies the connections that students establish among the various
representations of a function, mobilizing and linking his concepts definition and image of a function, when solving
problem-solving tasks, exploratory and investigative tasks and using the graphing calculator, oriented by the teacher.
It also studies the importance of multiple representations for the development of the learning of the concept of function. It aims to identify and understand, also, the difficulties that students manifest in the learning of functions, knowing better the connections made by students between the various representations of functions considered.

It follows the theory defined by Duval (register of semiotic representation) and the cognitive theory of Vinner (concept image and concept definition). Students worked in classes of mathematics in an environment of problem solving, exploratory and investigative tasks and using the graphing calculator. The research methodology adopted is a qualitative and interpretative. Data collection included an initial questionnaire, reports written by students in classrooms throughout the didactic unit "functions" and an interview with a couple of students after the apprentice. The results indicate that the coordination that students make between the various registers of representation of a function and of different functions allows them to achieve different perspectives of a function. The cognitive paradox of mathematical understanding was highlighted by the students through the coordination that they made of the records of semiotic representations (natural language, algebraic, tabular and graphic), which allowed them to stop confusing the mathematical object function with its representation, and also achieve a strong convergence of the concept image to the concept definition of function.

References

  1. Abalos, G., Ordóñez, A. (2009). El comportamiento periódico en la relación de una función y sus derivadas: significados a partir de la variación. Revista Latinoamericana de Investigación en Matemática Educativa, 12 (1), 7-28.
  2. Abrantes, A., Serrazina, L. & Oliveira, I. (1999). A Matemática na Educação Básica. Lisboa: Ministério da Educação - Departamento da Educação Básica.
  3. Andrade, J. (2009). Aprendizagens e dificuldades de alunos do 10° ano no estudo das Funções. Dissertação de Mestrado. Covilhã: UBI.
  4. Berger, M. (2010). A semiotic view of mathematical activity with a computer algebra system. Revista Latinoamericana de Investigación en Matemática Educativa, 13 (2), 159-186.
  5. Bogdan, R. C., & Biklen, S. K. (1994). Investigação qualitativa em educação. Porto: Porto Editora.
  6. Brocardo J. (2001). As Investigações na aula de Matemática: Um projecto curricular no 8° ano (Tese de doutoramento, Universidade de Lisboa).
  7. Castillo, S. (2008). Propuesta pedagógica basada en el constructivismo para el uso óptimo de las TIC en la enseñanza y el aprendizaje de la matemática. Revista Latinoamericana de Investigación en Matemática Educativa, 11 (2), 171-194.
  8. Chazan, D., Yerushalmy, M. (2003). On Appreciating the Cognitive Complexity of School Algebra: Research on Algebra Learning and Directions of Curricular Change. In Kilpatrick,
  9. J., Martin, W., Schifter, D. (Eds.), A Research Companion to Principles and Standards for School Mathematics. Reston, VA: NCTM.
  10. D'Amore, B. (2006). Objetos, significados, representaciones semióticas y sentido. Revista Latinoamericana de Investigación en Matemática Educativa, 9 (Extra 1), 177-196.
  11. Saraiva, M. (2001). O conhecimento e o desenvolvimento profissional dos professores de matemática. Tese de doutoramento. Lisboa: Universidade de Lisboa.
  12. Saraiva, M. J. & Teixeira, A. M. (2009). Secondary school students' understanding of function via exploratory and investigative tasks. Quaderni di Ricerca in Didattica, Supplemento nº 4 al n" 19, pp. 74-83. Itália: Palermo. (ISSN on-line 1592-4424).
  13. Slavit, D. (1997). An alternative route to the reification of function. Educational Studies in Mathematics, 33, 259-281.
  14. Teixeira, A. (2005), Tarefas de investigação matemática no curriculo do 7° ano do 3º ciclo do ensino básico. Dissertação de Mestrado. Covilhã: UBI
  15. Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14:3, 293-305.
  16. Zachariades, T., Christou, C. & Papageorgiou, E. (2001). The Difficulties and Reasoning of Undergraduate Mathematics Students in the Identification of Functions. Proceedings in the 10th ICME Conference, Crete, Greece: University of Athens.

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