Combinatorial reasoning to solve problems

This study reports combinatorial reasoning to solve problems. We observed the mathematical thinking of students aged 14-16. We study the variation of the students’ solution strategies in the context of emergent modelling. The results show that the students are tempted to begin the problem solving process on the highest level and otherwise have difficulties transitioning from a lower to a higher level of activities. Qualitative analysis revealed some students’ preference of the use of formulas, while at the same time other students showed more insight by their systematic approach of the problems, leading to better results. We advocate matching emergent modelling with teaching combinatorial reasoning, stimulating students to create a relational network of knowledge