Do Secondary School Students’ Strategies in Solving Permutation and Combination Problems Change with Instruction?

Abstract

This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students’ combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo’s research to two groups of students with and without instruction on combinatorics in order to analyse the students’ performances and the strategies used in their solutions, as well as the effect of instruction on the same. We present the results obtained in two permutation and two combination problems (each in the distribution and selection models). Permutation problems were found easier than combination problems, selection problems were found easier after instruction, and the instruction group obtained better results. We found differences in the main strategies used in both groups: enumeration and dividing a problem in parts was more common in the no-instruction group. The instruction group frequently relied on the use of a formula and the product rule.