Improving awareness about the meaning of the principle of mathematical induction

Authors

  • Annalisa Cusi Università di Modena e Reggio Emilia, Italia
  • Nicolina A. Malara Università di Modena e Reggio Emilia, Italia

DOI:

https://doi.org/10.30827/pna.v4i1.6170

Keywords:

Learning and teaching with understanding, Methods of teaching, Principle of mathematical induction, Proof in mathematics, Teachers' training

Abstract

This work is based on our conviction that it is possible to minimize difficulties students face in learning the principle of mathematical induction by means of clarifying its logical aspects. Based on previous research and theory, we designed a method of fostering students’ understanding of the principle. We present results that support the effectiveness of our method with teachers in training who are not specializing in mathematics.

Fomentar la conciencia sobre el significado del principio de inducción matemática

Este trabajo está basado en nuestra convicción de que es posible minimizar las dificultades de los alumnos cuando se enfrentan al aprendizaje del principio de inducción matemática mediante la clarificación de sus aspectos lógicos. Basándonos en la investigación y teoría previas, diseñamos un método para fomentar la comprensión del principio por los alumnos. Presentamos resultados que respaldan la efectividad de nuestro método con profesores en formación no especializados en matemáticas.

Handle: http://hdl.handle.net/10481/3507

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Author Biography

Annalisa Cusi, Università di Modena e Reggio Emilia, Italia

Código ORCID

References

Avital, S., & Libeskind, S. (1978). Mathematical induction in the classroom: Didactical and mathematical issues. Educational Studies in Mathematics, 9(4), 429-438.

Ernest, P. (1984). Mathematical induction: A pedagogical discussion. Educational Studies in Mathematics, 15(2), 173-189.

Fishbein, E., & Engel, I. (1989). Psychological difficulties in understanding the principle of mathematical induction. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 276-282). Paris: PME.

Harel, G. (2001). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 185-212). Norwood, NJ: Ablex Publishing.

Malara, N. A. (2002). La dimostrazione in ambito aritmetico, quale spazio nella scuola secondaria? In N. A. Malara (Ed.), Educazione matematica e sviluppo sociale: esperienze nel mondo e prospettive (pp. 129-166). Soveria Mannelli, Italy: Rubettino.

Ron, G., & Dreyfus, T. (2004). The use of models in teaching proof by mathematical induction. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 113-120). Bergen, Norway: Bergen University College.

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Published

2011-09-01

Issue

Section

Articles