Graduation Year

2005

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Secondary Education

Major Professor

Denisse R. Thompson, Ph.D

Committee Member

Jeffrey D. Kromrey, Ph.D

Committee Member

James A. White, Ph.D

Committee Member

Fredric J. Zerla, Ph.D

Keywords

Calculus, Graphing calculator

Abstract

This study examined the effects of using graphing calculators with a numerical approach designed by the researcher on students learning of limits and derivatives in an Applied Calculus course at a community college. The purposes of this study were to investigate the following: (1) students achievement in solving limit problems (Skills, Concepts, and Applications) with a numerical approach compared to that of students who solved limit problems with a traditional approach (primarily an algebraic approach); and (2) students achievement in solving derivative problems (Skills, Concepts, and Applications) with a numerical approach compared to that of students who solved derivative problems with a traditional approach (primarily an algebraic approach).

Students (n = 93) in all four daytime sections of an Applied Calculus course in a community college participated in the study during the spring 2005 semester. One of two MWF sections and one of two TR sections served as the treatment groups; the other two sections served as the control groups. Two instructors other than the researcher participated in the study. Instructor A taught one treatment group (a TR section) and one control group (a MWF section); instructor B taught one treatment group (a MWF section) and one control group (a TR section).

Dependent variables were achievement to solve skill, concept, and application limit problems and skill, concept, and application derivative problems, measured by two teacher-made tests. A pretest administered on the first day of class determined that no significant difference existed between the groups on prerequisite algebra skills. Separate ANCOVA tests were conducted on the skill, concept, and application portions of each of the limit and derivative exams.

Data analyses revealed the following: (1) there was no significant difference found on the skill portion of the limit topic (unit 1 exam) due to instruction or to instructor; (2) there was a significant difference found on the concept portion of the limit topic due to instruction and to instructor; (3) there was a significant difference found on the application portion of the limit topic due to instruction but not due to instructor; (4) the interaction effects between instructor and instruction were not significant on the skill, concept, and application portions of the limit topic; (5) there was a significant difference found on the skill portion of the derivative topic (unit 2 exam) due to instruction but not due to instructor; (6) there was a significant difference found on the concept portion of the derivative topic due to instruction and to instructor; (7) there was a significant difference found on the application portion of the derivative topic due to instruction but not due to instructor; and (8) the interaction effects between instructor and instruction were not significant on the skill, concept, and application portions of the derivative topic. All significant differences were in favor of the treatment group.

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