A descriptive study of level three advanced mathematics students' conceptual understanding of the roots of polynomial functions

Windsor, Annette Mary (1997) A descriptive study of level three advanced mathematics students' conceptual understanding of the roots of polynomial functions. Masters thesis, Memorial University of Newfoundland.

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Abstract

The purpose of this descriptive study was to investigate level III advanced mathematics students' understanding of the roots of polynomial functions as a result of an integrated approach with the graphing calculator. It examined the students' ability to work with the symbolic, tabular, and graphic representations of polynomial functions in their quest to identify its roots. It also explored what students had to say about the graphing calculator and its features and their reaction to its inclusion in the learning process. -- One class of thirty one students of Mathematics 3201 participated in the study. Each student completed a manual of thirteen activities designed specifically for the TI-82 graphing calculator to address the curricular objectives for the polynomial unit. Students were required to formulate a written definition for the root of a polynomial function, at the beginning and conclusion of the study. All were interviewed as many as five times and all wrote a final unit test and questionnaire. -- After the integrated approach with the graphing calculator, students were able to formulate and articulate a coherent explanation of the root of a polynomial function. Additionally, many could also provide significant detail regarding the different aspects of a root and demonstrated a reasonable degree of proficiency with polynomial functions expressed symbolically, graphically, and in tabular form. -- Most students responded positively to the integration of the graphing calculator and learned to use it efficiently and effectively by the time the study concluded. It proved to be most popular in a supportive role to verify work and to provide insight so busy work could be kept at a minimum. It helped most students appreciate that the graph of a polynomial function was integrally connected to the algebra they had learned in past courses. -- Not all students, however, were pleased with the frequent use of the calculator. Some felt that it detracted from their ability to master the algebraic procedures that were paramount in "real" mathematics.

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