Study on Error Types of Conic Sections Made by Vocational High School Students in Changhua Area

• Main Authors: Min-Chih Lo, 羅敏志
• Other Authors: 賈明益
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/21918808624708550527

碩士 === 國立中興大學 === 應用數學系所 === 101 === The purpose of the study aims to discuss the error types of conic sections which national vocational high students have and to analyze the cause of the errors when they solve the conic problems, hoping to provide teachers with reference that can assist their remedial instructions and improve their teaching skills. The methods of the study are to use self-designed conic sections tests to investigate and analyze the error types which students have and to interview them to understand their thoughts when they solve the problems in the tests and the cause of errors. The subjects are seventy-seven sophomores of certain vocational high school in Changhua County. The steps are three. First, pretest the students. Second, based on the test results, use SPSS to do reliability analysis, and meanwhile construct items validity. Finally, let the students take a formal test. It is concluded that among four themes, the average error rate or the average blank rate in circle problems is the highest. According to the test results, error types and the cause of errors are as follows. 1.Error types： (1)guessing answers based on the problems or the messages when solving problems. (2)errors in algebraic calculations. (3)formula mistakes or the errors of using improper formulas. (4)the errors due to the confusion of canonical equation, especially about ellipse and hyperbola. (5)errors in connecting focal length of parabola with canonical equation. (6)confusion in the relation between semi-major axis length, semi-minor axis length or semi-transverse axis length, semi-conjugate axis and their half focal length. (7)errors in judging the graphs of parabola, ellipse and hyperbola. (8)errors because of carelessness in understanding questions,writing the wrong numbers,or reading numbers. (9)misunderstanding about the directrix and axis of symmetry of parabola. (10)confusion of focus,vertex and center. (11)confusion in the number of the focus of parabola, ellipse and hyperbola. (12)putting coordinates into the equations to seek unknown number. 2. The cause of errors： (1)unclear concepts about the definitions,formulas,and terms related to various conic sections. (2)misconcept of linear equation. (3)confusion of the characteristics of various conic sections,making errors in relating and inferring. (4)carelessness or negligence. (5)insufficient computation or miscalculation. (6)insufficient prior knowledge. (7)interactive interruptions of new knowledge and old experience. (8)inference based on nothing. At last, based on the findings, I propose four recommendations to math instructions and three suggestions to the further research in the future.