How Graphing Calculators and Visual Imagery Contribute to College Algebra Students' Understanding the Concept of Function

• Other Authors: Lane, Rebekah M. (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Education
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-3297

The purpose of this study was to answer the following research questions: • What is the role of graphing calculators in understanding functions? • How does visual imagery contribute to visual and non-visual College Algebra students' understanding of functions? Interviews and document reviews were the data sets used in this study. The data were analyzed by using two theoretical frameworks: O'Callaghan's (1998) translating component for understanding functions and Ruthven's (1990) role of graphing calculator approaches. The investigation utilized the qualitative case study method. The findings of one of the case studies of the two College Algebra students were reported in chapter 4. The findings of the second case study were reported in this chapter. The two participants in this study were presented with mathematical tasks to complete over the course of a semester. Each task was given to the students individually. In order to thoroughly understand the students' responses, task-based interviews were conducted and videotaped. In addition, each participant was interviewed based on his or her response to the mathematical tasks. The tasks captured different types of mathematical functions. These included linear, quadratic, cubic, absolute value, and exponential functions. Furthermore, prior to receiving the tasks, the students' preference for processing mathematical information visually or non-visually were determined using Presmeg's (1985) Mathematical Processing Instrument and Questionnaire. These tools were chosen because they measured how a student preferred to process mathematical information, i.e., visually or non-visually. In this investigation, O'Callaghan's (1998) translating component was present during the completion of linear, quadratic, cubic, absolute value, and exponential functions. One of the participants used the graphing calculator during the completion of all of the mathematical tasks and exhibited Ruthven's (1990) approaches. The other participant used the graphing calculator during the completion of five of the tasks and exhibited Ruthven's (1990) approaches. In addition, one participant relied on visual imagery during the completion of five of the mathematical tasks. The second participant relied on visual imagery during the completion of three of the tasks. === A Dissertation submitted to the Department of Middle and Secondary Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Summer Semester, 2006. === June 5, 2006. === Technology, College Students === Includes bibliographical references. === Leslie Aspinwall, Professor Directing Dissertation; Diana Rice, Outside Committee Member; Maria L. Fernández, Committee Member; Elizabeth Jakubowski, Committee Member.