PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2013
Denver, Colorado
Developing Facility with Sets of Outcomes by Solving Smaller, Simpler Counting Problems
Page: 1-323
Combinatorial enumeration has a variety of important applications, but there is much evidence indicating that students struggle with solving counting problems. In this paper, the use of the problem-solving strategy of solving smaller, similar problems is tied to students’ facility with sets of outcomes. Drawing upon student data from semi-structured interviews in which post- secondary students solved counting problems, evidence is given for how numerical reduction of parameters can allow for a more concrete grasp of outcomes. The case is made that the strategy is particularly useful within combinatorics, and avenues for further research are discussed.