A Study on the Main Error Types and the Related Remedial Instruction about Solving Problems of Complex Numbers and Complex Plane by the Tenth Graders

• Main Author: 吳銘川
• Other Authors: 宋傳欽
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/33020962791969854516

碩士 === 國立政治大學 === 應用數學研究所 === 97 === The research aims to explore the main error types of first grader’s in a senior high school when solving the unit of complex number and complex plane after the instruction, including the possible reasons of their errors. The course designs of the remedial instructions are followed according to those reasons. At the end of this study, some analyses of the effects of remedial instruction activities are provided. In this study, there are eleven main error types from the first graders when proceeding to do the unit of complex number and complex plane : vague understanding about the definition of complex number; lacking necessary knowledge for the operation rules with the multiplication and division of two radicals; unfamiliar with handling the power of i and sum of the them; constantly making mistakes when doing the fundamental operations of arithmetic with complex number; confusing the meaning or conception concerning the absolute value of complex number under the false ideas existed in junior high about “A negative becomes a positive , and a positive is still a positive ”; not knowing the definition of conjugate complex number or confusing conjugate complex number with the absolute value of complex number; incapable of using the idea of operating the absolute value of complex number; failing to relate complex number to complex plane; inability in plane geometry; unable to construct the concept of complex number; habitual thinking with integer. The primary factors of making the above errors, according to this research, are as follows: ambiguous definition; paradoxical; influenced by instinct; making false analogy; failing to effectively connect complex number with complex plane; lacking prerequisite knowledge. As for the results of this remedial teaching, the rate of blank in students’ answer sheets, regardless of the whole test sheets or individual tests, has obviously decreased; the learners’ rate of accuracy as a whole is mostly higher; the improvement of grades, both in the brilliant group and in the poor group, is significantly improved; the effect of retention, in view of the whole participants’ rate of accuracy, varies insignificantly; more important, the results of students’ post-tests and postponed post-tests are in highly positive correlation. In testing the poor group, we find their retention of learning excellent. The variations of answers in the post-tests and postponed post-tests are not significant. Besides, most learners pay much attention to the contents and materials of employing Power Point and GSP and consider them as useful tools in the remedial teaching. In conclusion, the participants make great progress under this experiment. Therefore, most learners take positive perspectives from the remedial instruction.