An examination of college students' reasoning about trigonometric functions with multiple representations
Abstract
The purpose of this study is to examine how individual college students reason through tasks using trigonometric functions and translate among different types of representations of trigonometric functions across various mathematical tasks. I used a qualitative embedded multi-case study for this study. An embedded design is used to study various units within an identifiable case. In this study, the tasks serve as the cases, with each case/task being purposefully designed to begin in a different one of Duval's representation registers (natural language (N), drawings (D), symbolic systems (S), and graphs and mathematical diagrams (G)). Analysis of six participants' work is embedded as sub-units within each of these cases. Data were collected and analyzed under two frameworks, Duval's cognitive approach and Lithner's mathematical reasoning. In this study, the multiple-functional registers N and D were used less often by the participants than the mono-functional registers S and G. However, participants used mainly creative reasoning when employing the multiple-functional registers, N and D. Also, it was likely to see registers S and G used together when registers N and D were employed. Registers S and G were often used with imitative reasoning, although the use of register G contributed to several examples of local and global creative reasoning. Overall, translations among different registers that were based upon creative reasoning were more likely to lead participants to be able to complete given tasks. This study illustrated how college students employed their reasoning during open-ended and unfamiliar tasks, which helped students disclose their reasoning in informal ways without memorizing solutions. The study illustrated some interesting ways in which students were able to creatively use different registers to help them when they became stuck in the register in which they were working. By combining Duval's and Lithners' frameworks together, imitative and creative reasoning were classified in a new approach that could be usefully applied to studies other types of functions in future work.
Degree
Ph.D.
Advisors
Kenney, Purdue University.
Subject Area
Mathematics education
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.