Leveraging Specific Contexts and Outcomes to Generalize in Combinatorial Settings

2018

International audience; Generalization is a fundamental aspect of mathematics, and it is a practice with which undergraduate students should engage and gain fluency. It is important for students in combinatorial settings to be able to generalize, but combinatorics lends itself to engagement with specific examples, concrete outcomes, and particular contexts. In this paper, we seek to inform the nature of generalization in combinatorial settings by demonstrating ways in which students leverage specific, concrete settings to engage in generalizing activity in combinatorics. We provide two data examples that highlight ways in which concrete and specific ideas can be leveraged to help students d…