Promoting a set-oriented way of thinking in a U.S. High School discrete mathematics class: a case study

Abstract

In this case study, we investigate one teacher’s implementation of DNR-based combinatorics curriculum in their high school discrete mathematics class. By examining the teacher’s practices in whole-class discussions of two counting problems, we study how they advanced a variety of ways of thinking to support the development of a set-oriented way of thinking about counting. In particular, we find the teacher worked to build shared experience and understanding of mathematical ideas by grounding her teaching in students’ ways of understanding and leveraging students’ intellectual needs. In doing so, the teacher promoted a set-oriented way of thinking through attending to connections between sets of outcomes, counting processes, and formulas in student representations and justifications; elevated solutions employing process pattern generalization; and advanced the beliefs that counting problems can be solved in many ways and entail several types of mathematical activity.