PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Student Conceptions Of Trigonometric Identities Through Apos Theory
Page: 1167
This preliminary study attempts to describe an initial genetic decomposition of a trigonometric identity for college students. Scant research exists into the concepts found in trigonometry. Thus, little is known about how students actually understand a trigonometric identity. Following the guidelines of APOS theory, an initial genetic decomposition for a trigonometric identity was proposed. According to this decomposition, students with action conceptions can verify identities explicitly using step-by-step manipulations while students holding a process conception are able to visualize steps to demonstrate that the identity is true. Having an object conception means students recognize the truth of the equality without verification and are able to then use the identity to verify other identities. After observing students in task-based interviews, needed modifications to the genetic decomposition became apparent. For example, students’ conceptions of the function argument appeared to influence the verification process.