Leveraging a Categorization Activity to Facilitate Productive Generalizing Activity and Combinatorial Thinking

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes, topics, and mathematical practices that distinguish discrete mathematics. We then present potential benefits of focusing on discrete mathematics topics for mathematics education; in particular, we discuss the accessibility of topics in discrete mathematics, the connection to mathematical processes and affect, and the relevance of discrete mathematics in our current society. We also emphasize discrete mathematics from an international perspective, highlighting studies from the US, Italy, France, Chile, and Germany, which are across all school levels–primary, middle, and secondary school, and with some implications for post-secondary education. We particularly discuss discrete topics including number theory, combinatorics, iteration and recursion, graph theory, and discrete games and puzzles; we describe and situate these topics within literature. We also suggest the additional topics of game theory and the mathematics of fairness that we hope to see addressed in future studies.

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Leveraging a Categorization Activity to Facilitate Productive Generalizing Activity and Combinatorial Thinking

Cited by 7 publications

References 39 publications

Using an Actor-Oriented Perspective to Explore an Undergraduate Student’s Repeated Reference to a Particular Counting Problem

Using an Actor-Oriented Perspective to Explore an Undergraduate Student’s Repeated Reference to a Particular Counting Problem

Two students’ mathematical thinking and activity across representational registers in a combinatorial setting

Teaching and learning discrete mathematics

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