Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic
DOI:
https://doi.org/10.48489/quadrante.23878Keywords:
combinatorics, mathematical modelling, secondary school, study and research paths, modelling praxeologiesAbstract
This paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks’ problem situation. We consider students’ construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the relationships used to characterise the types of padlocks. Second, we analyse how students simulate and validate these elementary combinatorial models before generalising them to explore other systems beyond padlocks.
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