PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Does a Statement of Whether Order Matters in Counting Problems Affect Students’ Strategies?
Page: 1-69
Counting problems ask students to compute the number of ways a certain set of requirements can be satisfied, and they are important in such mathematical subjects as probability, combinatorics, and abstract algebra, among others. Students are often taught to solve counting problems by looking for specific clues to help categorize the problems and identify solution strategies. In this study, we investigate how the wording of certain counting problems, specifically whether or not “order matters,” affects students' solution strategies. In particular, we gave students questions involving explicit statements as to whether or not order matters, some of which were intentionally misleading, and questions that do not contain such an explicit statement. Data was collected in the form of written responses and student interviews. The results show that many students do, in fact, rely heavily on such explicit statements about whether order matters, even when such statements are misleading.