Secondary students’ informal strategies in solving enumeration problems prior to formal combinatorics instruction
DOI:
https://doi.org/10.29408/jel.v11i4.31088Keywords:
combinatorial reasoning, combinatorics, counting principles, enumeration problems, student initial strategiesAbstract
Although enumeration problems are fundamental in combinatorics, little is known about how students intuitively approach such enumeration problems before receiving formal instruction. This exploratory qualitative study investigated the initial strategies employed by twelve-grade students in solving enumeration problems prior to formal instruction on enumeration rules. Fifteen students from a public senior high school in Kerinci, Indonesia, who had not yet learned combinatorics in the curriculum, participated in this study. Data were collected through students’ written responses to three combinatorial problems presented in different real-life contexts and further explored through semi-structured interviews. Only responses demonstrating coherent and interpretable strategy were analyzed. The findings reveal three dominant strategies: listing all possible arrangements, generalizing patterns, and applying the multiplication principle. These findings indicate that students possess intuitive approaches that can serve as a foundation for formal combinatorial reasoning. The study aligns with the Realistic Mathematics Education (RME) perspective, emphasizing the importance of guided reinvention and contextual mathematization, and proposes implications for designing learning trajectories that build on students’ informal reasoning in secondary mathematics education.
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