The Error Patterns of Functions of Undergraduate Students

• Main Authors: SHEN, GUAN-TING, 沈冠廷
• Other Authors: HUANG, CHIEN-CHUNG
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/m25f8p

碩士 === 國立臺南大學 === 應用數學系碩士班 === 107 === The purpose of this Research was to investigate function concepts of undergraduate students and various representations of the function. Moreover,by generalizing their error patterns and analyzing the possible reasons for making mistakes in order to know students’ difficult part in learning function concepts. This study took a survey research approach with 51 students from an engineering college in Tainan,Taiwan as the study subjects. A self-developed instrument “function concepts and its various representations test” was used to gather data about undergraduate students. Then,thirteen students were picked and then interviewed. By comparing the contents of the interviews,the researcher sorted the pattern of error and the cause of the error. The research results are as followings: First,the overall average performance of the undergraduate students was low. Among them, Dimensions（3）one-to-one,one-to-many,many-to-one,one-to-none was the best indication, but Dimensions（2）Domain,Codomain,Range was the worst indication. Second,the responses patterns of error of were summarized in the following: （1） The error pattern of function definition . （2） The error pattern of function correspondence. （3） The error pattern of function corresponding rule. （4） The error pattern of function representation concept. （5） The error pattern of function definition and function representation error link （6） The error pattern of lack of prior knowledge. （7） The error pattern of algebraic calculation. （8） The error pattern of ignore conditions Third,the reasons for the mistakes made by undergraduate students were summarized as the following five possible causes: （1） Lack of perfect function concepts （2） Learning and solving the mathematic problems as machine （3） Negatively intuitive guess （4） Lack of ability to do Mathematical derivation （5） Lack of ability to check errors.