PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Examining Students’ Combinatorial Thinking Through Reinvention Of Basic Counting Formulas
Page: 169
Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in students’ thinking, we engaged a pair of undergraduate students in a ten-session teaching experiment. The students successfully reinvented four basic counting formulas, but their work revealed a number of unexpected issues concerning justification in counting. In this paper, we describe the students’ successful reinvention of the four counting formulas, we critically examine their combinatorial reasoning in terms of Lockwood's (2013) initial model of students' combinatorial thinking, and we offer several directions for further research.