PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
The simple life: An exploration of student reasoning in verifying trigonometric identities
Page: 1050
Reasoning used by students as they verify trigonometric identities has not been investigated. Through analyzing students’ spoken explanations of their thought processes in clinical interviews, this current study explores why students choose certain expressions to begin manipulating and why certain manipulations or substitutions are performed as they verify the purported identity. Preliminary findings suggest that students may use beliefs about mathematics to inform and monitor their decisions, namely, the belief that mathematical answers are results of a simplification process. Thus, students spoke of the flow of verification problems in terms of a simplifying process. This belief may be imported from a cultural belief that being simpler is better and more desired; thus, mathematical tasks could validate the imported belief and in turn strengthen the belief about mathematics as simplification. To support this possibility, this paper will share student comments. Implications for instructional practice will also be suggested.