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Effect of the Implicit Combinatorial Model on Combinatorial Reasoning in Secondary School Pupils

Carmen Batanero, Virginia Navarro-Pelayo and Juan D. Godino
Educational Studies in Mathematics
Vol. 32, No. 2 (Feb., 1997), pp. 181-199
Published by: Springer
Stable URL: http://www.jstor.org/stable/3482818
Page Count: 19
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Effect of the Implicit Combinatorial Model on Combinatorial Reasoning in Secondary School Pupils
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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.

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