Research on Error Patterns of Trigonometric Functions of Senior High Vocational Students by Different Curricular Standards

• Main Authors: Fang-chuan Lin, 林芳全
• Other Authors: Chien-chung Huang
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/01122847402427871157

碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 100 === This paper focused on exploring if senior high vocational students by different curricular standards would perform differently in solving trigonometric functions. It also aimedto analyze the error patterns and to further understand the possible reasons that lead to making mistakes. All samples in the research were randomly selected from the vocational high school where the researcher teaches, and were divided into two groups which separately include 76 participants : one group is high school year 2 suitable for 99 provisional curricular standards while the other is high school year 3 suitable for 95 temporary curricular standards. The research adopted both qualitative and quantitative methods. After the participants completed the self-developed instrument assessment involved in trigonometric functions, 24 participants were selected for each error patterns to have semi-structured interviews. We conducted a quantitative analysis with SPSS 19, and the statistics included mean, standard deviation, the hit rate, the defect rate, and the blank rate. With the analyses and interviews, we get the results as follows: A、Of different curricular standards, the test results among juniors and seniors: (A) The questions with over 50 percent of the hit rate were 65 percent. The fact reflected that all the samples study trigonometric functions to certain degree. (B) The average of the seniors is higher than juniors. The fact reflected that the seniors performed better in solving trigonometric functions than juniors. (C) The standard deviation of the seniors was higher than juniors. The fact reflected that the level difference of the seniors is higher than the juniors. (D) Based on the research on defect rate and blank rate, we found that the juniors have more misconception of errors than the seniors. B、The error patterns in trigonometric functions were 17 in total: （A）the cognitive errors in the acute angle trigonometric function （B）the cognitive errors in standard position angle （C）the cognitive error in generalized angle’s definition of trigonometric function （D）the unclear cognition in the trigonometric function of emphasis angle （E）the difficulty in transforming generalized angle to acute angle （F）the unclear cognition in the definition of conterminous angle （G）the cognitive error in basic trigonometric identity （H）the unclear cognition in the conversion rules of measurement of angle （I）the errors due to the lack of graphical concept （J）the unclear cognition of sine rule （K）the unclear cognition of sector radius, arc length and central angle （L）the misunderstanding of the meaning of the questions （M）the errors due to the unskillful computational capabilities （N）carelessness led to errors （O）the errors due to self-constructing the relation between sides and angles （P）incorrectly judging the negative or positive of trigonometric function in each quadrant （Q）the lack of prior knowledge other than trigonometric functions C、Of different curricular standards, the causes of the errors in solving trigonometric functions （A）the cognitive error in the definition of trigonometric functions （B）the disability to draw the correct graphics （C）the deficiency and misusage of prior knowledge （D）the misunderstanding of the meaning of the questions （E）carelessness （F）miscalculation （G）being confused with the relations of functions or units （H）answering questions by intuition with incorrect concepts （I）the lack of logic inference （J）guessing the answer It is our hope that this research can contribute to a better understanding of the senior high vocational students’ study in the trigonometric functions, and further provide better instruction for future teaching.