| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 104 === This study aims to discuss the learning situation for students in higher vocational school in the unit of “basic definition of trigonometric function and trigonometric function of generalized triangle”, summarize their types of errors and analyze the possible causes of errors.
The researchers self-compile the test for “basic definition of trigonometric function and trigonometric function of generalized triangle”, including 6 themes and totally 12 items. The samples were selected from 118 students of Grade 3 in a public vocational high school in Taichung City, and the types of errors were analyzed according to the situation of item answering in the test. Eleven students were selected for non-structural interview. This study then summarized the common types of errors in students as well as the possible causes of errors. The results are as follows:
I. Types of errors:
1. Being unclear about the definitions of 6 trigonometric functions.
2. Being unclear about the connection between length of side and angle in trigonometric function.
3. Being unfamiliar with the proportional relation of length of side in special angles.
4. Being unfamiliar with the basic relationship between trigonometric functions.
5. Being unclear about the positive and negative situations of trigonometric function of generalized triangle in 4 quadrants.
6. Errors of fraction and radical sign patterns in calculation.
7. Errors during the transformation from trigonometric function of generalized triangle to trigonometric function of acute triangle.
8. Being unclear about the concept of coterminal angle.
9. Misunderstanding of subject meaning or misuse of data.
10. Errors in the concepts of the points of rectangular coordinate in 4 quadrants.
II. Causes of errors:
1. Remembering the basic definition of trigonometric function wrongly.
2. Failure in judging hypotenuse, adjacent side and opposite side in a correct manner.
3. Weakness in reading ability causes the failure in mastering the text symbols and subject meaning clearly, thus the subject meaning is misunderstood.
4. Having no idea of the proportional relation of length of side in special angles.
5. Insufficiency in logical reasoning ability and failure in connecting the contents learned in the past.
6. Due to insufficiency in calculative ability, errors may easily occur during the handling fraction and radical sign pattern in complex calculation.
7. Solving the problems on the basis of wrong prior knowledge.
Based on the results, the findings are expected to provide teachers with the basis for the improvement of teaching, so as to enhance students’ learning effectiveness in learning this unit and provide reference for teachers’ teaching and future studies.
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