Abstract
Elementary combinatorial problems may be classified into three different combinatorial models (selection, partition and distribution). The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. When building the questionnaire, we also considered the combinatorial operation and the nature of elements as task variables. The analysis of variance of the answers from 720 14–15 year-old pupils showed the influence of the implicit combinatorial model on problem difficulty and the interaction of all the factors with instruction. Qualitative analysis also revealed the dependence of error types on task variables. Consequently, the implicit combinatorial model should be considered as a didactic variable in organising elementary combinatorics teaching.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Batanero, C., Godino, J. D. and Navarro-Pelayo, V.: 1994, Razonamiento combinatorio. Síntesis, Madrid.
Batanero, C., Godino, J. D. and Navarro-Pelayo, V.: 1995, ‘The use of implicative and correspondence analysis for assessing pupils' combinatorial reasoning’, in R. Gras (Ed), Actes du colloque méthodes d'analyses statistiques multidimensionnelles en Didactique des Mathematiques. IRMAR, Rennes, pp. 245–256.
Brennan, R. L.: 1983, Elements of Generalizability Theory, ACT Publications, Iowa.
Dubois, J. G.: 1984, ‘Une systematique des configurations combinatoires simples’. Educational Studies in Mathematics 15(1), 37–57.
Fischbein, E., Pampu, L. and Minzat, I.: 1970, ‘Effect of Age and Instruction on Combinatorial Ability in Children’, British Journal of Educational Psychology 40, 261–270.
Fischbein, E.: 1975, The Intuitive Sources of Probabilistic Thinking in Children, Reidel, Dordrecht.
Fischbein, E. and Gazit, A.: 1988, ‘The Combinatorial Solving Capacity in Children and Adolescents’, Zentralblatt für Didaktitk der Mathematik 5, 193–198.
Gras, R. and Larher, A.: 1992, ‘L'implication statistique, une nouvelle méthode d'analyse des données’, Mathématiques, Informatique et Sciences Humaines 120, 5–31.
Green, D. R.: 1981, Probability Concepts in School Pupils Aged 11–16 Years. Ph. D. Thesis. Loughborough University of Technology (U.K.).
Greenacre, M. J.: 1984, Theory and Application of Correspondence Analysis, Academic Press, London.
Hadar, N. and Hadass, R.: 1981, ‘The road to solving a combinatorial problem is strewn wih pitfalls’.Educational Studies in Mathematics 12, 435–443.
Kaput, J. N.: 1970, ‘Combinatorial Analysis and School Mathematics’, Educational Studies in Mathematics 3, 111–127.
Piaget, J. and Inhelder, B.: 1951, La genèse de l'idee de hasard chez l'enfant, Presses Universitaires de France, Paris.
Rights and permissions
About this article
Cite this article
Batanero, C., Navarro-Pelayo, V. & Godino, J.D. Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics 32, 181–199 (1997). https://doi.org/10.1023/A:1002954428327
Issue date:
DOI: https://doi.org/10.1023/A:1002954428327