Contributions of the MiGen software in introducing algebraic concepts

Authors

  • Fernando de Mello Trevisani Paulista State University
  • Marcus Vinicius Maltempi Paulista State University

DOI:

https://doi.org/10.17533/udea.unipluri.19816

Keywords:

mathematical generalization, mathematical patterns

Abstract

The goal of this article is to show some contributions of the MiGen software to the process of introduction to algebra to basic education students from a Brazilian public school. The MiGen features that enhance the development of algebraic thinking are first highlighted. Then we describe an activity carried out with eight seventh graders who provided us with information for our research. We conclude that the MiGen software inhibited the counting process due to its dynamic way of presenting figural patterns on the computer, by stimulating the development of generalization processes, and it also helped to develop the idea of algebraic expressions as providers of general answers to the proposed activities.

|Abstract
= 164 veces | PDF (ESPAÑOL (ESPAÑA))
= 79 veces|

Downloads

Download data is not yet available.

Author Biographies

Fernando de Mello Trevisani, Paulista State University

Master in Mathematics Education, with the degree work «Strategies for the generalization of mathematical patterns», presented to the Institute of Geosciences and Exact Sciences at the Río Claro Campus, São Paulo, Paulista State University (UNESP), Brazil. Supervisor: Dr. Marcus Vinicius Maltempi. Teacher of mathematics in basic and higher education. Coordinator and pedagogical advisor in the use of technologies in education.

 

Marcus Vinicius Maltempi, Paulista State University

Professor at the Department of Statistics, Applied Mathematics and Computing (DEMAC), and of the postgraduate program in Mathematics Education of the Institute of Geosciences and Exact Sciences, Paulista State University (UNESP), Brazil. Miembro del Grupo Research in Informatics, Other Media and Mathematics Education (GPIMEM).

References

Barbosa, Ana Cristina Coelho (2010). A resolução de problemas que envolvem a generalização de padrões em contexto visuais: um estudo longitudinal com alunos do 2.o ciclo do ensino básico.Tesis de doctorado. Braga: Universidade do Minho.

Becker, Joanne Rossi y Rivera, Ferdinand (2005). «Generalization strategies of beginning high school álgebra students». En: chick, Helen L. y Vincent, Jill L. (Eds.). Proceedings of the 29.rd Conference of the International Group for the Psychology of Mathematics Education, pp.121-128. Melbourne: PME.

Bicudo, Maria Aparecida Viggiani (2004). «Pesquisa qualitativa e pesquisa qualitativa segundo a abordagem fenomenológica». En: borbA, Marcelo de Carvalho Borba y Araújo, Jussara de Loiola (Orgs.). Pesquisa qualitativa em educação matemática, pp. 101-114. Belo Horizonte: Autêntica.

Borralho, António et al. (2007). «Os padrões no ensino e aprendizagem da álgebra». En: Vale, Isabel et al. (Eds.). Números e Álgebra, pp. 193-211. Lisboa: SEM-SPCE.

Caraça, Bento de Jesus (1984). Conceitos fundamentais da matemática. Sá da Costa: Lisboa.

Geraniou, Eirini et al. (2009). «Towards a constructionist approach to mathematical generalisation». En: Research in Mathematics Education, Vol. 11, N.o 1, pp. 75-76. Londres: Institute of Education (IOE), University of London.

Geraniou, Eirini et al. (2011). «Student’s justification strategies on the equivalence of quase-algebraic expressions». En: International Conference on Psychology of Mathematics Education. Ankara: Turquía.

Kaput, James J. (1999). «Teaching and learning a new algebra». En: Fennema, Elizabeth y RomberG, Thomas A. (Eds.). Mathematics classrooms that promote understanding, pp. 133-155. Mahwah: Erlbaum.

Lannin, John (2005). «Generalization and justification: the challenge of introducing algebraic reasoning through patterning activities». En: Mathematical Thinking and Learning, Vol. 7, N.o 3, pp. 231-258. Philadelphia: Taylor & Francis.

Lannin, John, Barker, David y Townsend, Brian (2006). «Algebraic generalization strategies: factors influencing student strategy selection». En: Mathematics Education Research Journal, Vol. 18, N.o 3. pp. 3-28. New York: Springer.

NCTM (2000). Principles and Standards for School Mathematics. Reston: NCTM.

Noss, Richard et al. (2009). «Developing a Microworld to Support Mathematical Generalisation». En:tzekAki, Marianna, Kaldrimidou, Maria y Sakonidis, Haralambos (Eds.).Proceedings of the 33.rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 49-56. Te-salónica, Grecia: PME.

Noss, Richard et al. (2012). «The design of a system to support exploratory learning of algebraic generalization». En: Computers & Education,Vol. 59, N.o1, pp. 63-81. Reino Unido: Elsevier.

Sasman, Marlene, Olivier, Alwyn y Linchevski, Liora (1999). «Developing a Microworld to Support Mathematical Generalisation». En: Zaslavsky, orit(ed.). Proceedings of the 23.rd International Conference for Psychology of Mathematics Education, Vol. 4,pp. 161-168. Haifa, Israel: PME.

Secretáriada Educação (2010). Currículo do Estado de São Paulo: matemática e suas tecnologias. São Paulo, Brasil: SEE.

Stacey, Kaye (1989). «Finding and using patterns in linear generalising problems». En: Educational Studies in Mathematics, Vol. 20, N.o 2, pp. 147-164. Holanda: Springer.

Vale, Isabel y Pimentel, Teresa (2005). «Padrões: um tema transversal no currículo». En: Revista Educação e Matemática, Vol. 85, pp. 14-20. Brasil: Asso-ciação de Professores de Matemática (APM).

Published

2014-06-24

How to Cite

de Mello Trevisani, F., & Vinicius Maltempi, M. (2014). Contributions of the MiGen software in introducing algebraic concepts. Uni-Pluriversidad, 14(1), 63–69. https://doi.org/10.17533/udea.unipluri.19816

Issue

Section

RESEARCH REPORTS AND UNPUBLISHED ESSAYS