Abstract
This study reports on combinatorial reasoning to solve problems. We observed the mathematical thinking of students aged 14–16 and study the variation of the students’ combinatorial reasoning in terms of activity levels in a process of emergent modelling . We interpret student reasoning with the focus on stages of attention and describe the results in a framework of long-term mathematical thinking. 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 for 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 of combinatorial reasoning , stimulating students to create a relational network of knowledge.
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Coenen, T., Hof, F., Verhoef, N. (2018). Combinatorial Reasoning to Solve Problems. In: Hart, E., Sandefur, J. (eds) Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70308-4_5
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DOI: https://doi.org/10.1007/978-3-319-70308-4_5
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