PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
An unexpected outcome: Students’ focus on order in the Multiplication Principle
Page: 715
In an effort to better understand students’ understanding of the multiplication principle, which is a fundamental aspect of combinatorial enumeration, we had two undergraduate students engage in reinvention of a statement of the principle during an eight-session teaching experiment. In this presentation, we report on the students’ unexpected attention to the order in which they complete stages of counting process in a counting problem. We suggest that an early experience with a particular problem prompted them to think about order, and this way of thinking persisted throughout the experiment. The students’ reasoning about order sheds light on ways in which students may think about order and about the nature of multiplication in counting. We conclude with potential implications and directions for further research.