The effects of graphing calculators on secondary students' understanding of the inverse trigonometric functions.

摘要

The purpose of this study was to determine if using the graphing calculator in trigonometry enhanced high school students' understanding of the inverse trigonometric functions. The sample for this study consisted of 58 male students, ages 16 to 18, enrolled in a trigonometry course at an all male, private high school in southern Louisiana. The sample was equally divided into two groups: the graphing calculator group which used the graphing calculator with teacher instruction on the topic, and the noncalculator group which received instruction on the topic without the use of the graphing calculator. The researcher and classroom teacher provided instruction on the topic.; All students took a pretest on concepts related to elementary functions. The pretest was used as a covariate in this study. All students took a posttest on the inverse trigonometric functions. The posttest was separated into two parts: Part 1 consisted of questions related to the fundamental nature of the inverse trigonometric functions, and Part 2 consisted of application and extension questions related to this topic. Additionally, three instructional sessions of each group were videotaped for discerning differences in students' problem-solving approaches and types of students' questions.; ANCOVA results indicated that students using the graphing calculator performed better than students not using graphing calculators on application and extension problems. Significant results also indicated that students using the graphing calculator achieved overall higher posttest scores than students not using the graphing calculator. Results were not found to be significant in terms of students' basic understanding of the inverse trigonometric functions. Analysis of the qualitative data indicated several major differences in problem-solving approaches between the two groups. Also, differences between the two groups were found in the types of questions and concerns generated when studying this topic.; This study confirmed at the high school level what has been reported in the research for other grade levels and other topics: the graphing calculator is a highly effective tool in helping high school students understand more complex functions. It is an invaluable tool in helping mathematics students to become flexible and resourceful problem solvers.