Graduation Year

2015

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Curriculum and Instruction

Major Professor

Denisse Thompson, Ph.D.

Co-Major Professor

Janet Richards, Ph.D.

Committee Member

Samuel Eskelson, Ed.D.

Committee Member

Yiping Lou, Ph.D.

Committee Member

Ruthmae Sears, Ph.D.

Keywords

functions, mathematics teaching, statistics, technology use, trigonometry

Abstract

Nowadays, technology plays a fundamental role in education, in general, and in mathematics education in particular. The graphing calculator has been an important technological tool in mathematics classrooms since its invention and introduction in 1985 by Casio. As graphing calculators provided so many uses, their contribution to the teaching and learning process has been investigated by many researchers who have shown the use of such technology can have a significant effect on improving mathematics teaching and learning.

Investigating the impact of graphing calculators on student learning is important. It is also essential to research teachers’ perspectives on how using graphing calculators in mathematics determines how such use affects their teaching and learning. However, there are few studies on this issue. Therefore, this dissertation study may fill the gap in the literature in terms of examining high school mathematics teachers’ perspectives when they teach a precalculus course with technology integrated in the curriculum materials.

In this study, I analyzed eleven teachers’ perspectives about using graphing calculator technology in a precalculus course, titled Functions, Statistics, and Trigonometry (FST). This study was a descriptive intrinsic case study in which I analyzed teachers’ perspectives about how they use graphing calculators in the FST course, specifically about their teaching and students’ learning with available graphing calculator technology. Additionally, I explored teachers' perspectives about the issues they face when using the available technology and for what topics teachers frequently used it. I used mixed methods to examine eleven mathematics teachers’ perspectives about their teaching, students’ learning, and issues that arise when they use graphing calculator technology. In the quantitative part of the study, I created an Index of Teachers’ Initial Perceived Attitude and Experience Level and an Index of Teachers’ Use of Graphing Calculators to measure teachers’ perspectives on technology use at the beginning and end of the school year, respectively. In the qualitative inquiry, I analyzed teachers’ responses to semi-structured interview questions by using thematic analysis.

The results of this study showed eight of the eleven mathematics teachers’ students used graphing calculators with Computer Algebra System (CAS) capability loaned by The University of Chicago School Mathematics Project (UCSMP). Five teachers had a high initial perceived attitude and experience level and the other six teachers had a medium level. All teachers reported that helping students learn to use a symbolic manipulator was equally or less important than to use a graphing calculator. The themes (1) Teachers’ use of graphing calculators, (2) Teachers’ opinions about students’ use of graphing calculators, and (3) Teachers’ issues with graphing calculator technology were created to explain teachers’ responses to interview questions related to their graphing calculator perspectives throughout the year.

Teachers typically used graphing calculators almost every day for such purposes as exploring mathematics, solving problems, and checking work. Some teachers reported the benefits of using graphing calculators in terms of instruction were focusing on the concepts and showing additional solution approaches. Teachers who wanted their students to be able to do some work without graphing calculators used no calculator tests or questions on which graphing calculators were not allowed as part of their assessment process. Teachers mentioned the need for a manual showing the steps for using graphing calculators with CAS.

Teachers’ opinions about students’ use of graphing calculators included that students generally liked them. Teachers reported graphing calculators positively affected students’ learning because students were able to find the answers for problems and have better visualization opportunities. However, teachers reported some meaning was missing and students’ arithmetic skills were negatively affected because of the presence of graphing calculators. Additionally, five teachers indicated their students relied on the graphing calculators too much. The most common issue teachers had relative to graphing calculator technology was the liability issue of the graphing calculators sent by UCSMP for students to loan. Teachers were responsible for those loaned graphing calculators. Additionally, cheating, using features that minimized the mathematics, and not being familiar with the type of graphing calculators loaned from UCSMP were other issues teachers reported. Teachers’ graphing calculator use was demonstrated based on the index of teachers’ use of graphing calculators. Seven teachers were high in terms of their use of graphing calculators at the end of the school year and four teachers had a medium use of graphing calculators.

For implications of this study, mathematics teacher educators can use the results to improve professional development programs for teachers. They might create workshops based on teachers’ perspectives and their initial perceived attitude and experience level. Additionally, textbook developers can create more exploration activities with graphing calculators, especially with CAS.

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