模糊理論應用於數學學習 : 淡大學生微積分測驗的預測

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 學位論文 > Item 987654321/32872

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题名:	模糊理論應用於數學學習 : 淡大學生微積分測驗的預測
其它题名:	The application of fuzzy theory in mathematics learning : the prediction of calculus exams of TKU students
作者:	蔡典益;Tsai, Dian-yi
贡献者:	淡江大學數學學系碩士班曾琇瑱
关键词:	模糊理論;模糊權重;模糊偏好;數學學習;Fuzzy theory;Fuzzy weight;Fuzzy Preference;Mathematics Learning
日期:	2006
上传时间:	2010-01-11 02:54:04 (UTC+8)
摘要:	近十多年來，由於一窩蜂的辦學熱潮，致使大學數量成倍增長，目前全國已超過一百五十所大專院校，錄取人數也不斷的在攀升。民國九十一年，教育部廢除實行長達四十八年的「大學聯考制度」，轉而全面採用「大學多元入學方案」，這幾年來教育部更為減輕學生的壓力而積極推動教育改革，卻因為課程簡化反而呈現出學生基本學習能力下降的問題。一篇刊載於民國九十四年七月二十八日的中時晚報報導指出,高三教材將多數的微積分課程刪除掉，使得微積分的預備知識不足，與大學數學有關的課程銜接不良，以致於許多學生修習大學微積分時困難重重。本研究針對民國九十三年和九十四年入學之大一新生各發放一問卷調查。在其內容方面, 兩份問卷都包含一些影響學習的因素，讓學生們藉由這些因素來評估和大學微積分期中考成績的關聯及偏好。在分析過程方面,定義適合兩份問卷的模糊偏好關係和整合群體偏好的社會選擇函數。最後應用模糊理論分析傳統問卷, 將每位同學因個人的因素,對於問卷因素選項所產生的不同程度的模糊偏好。透過個體模糊權重,總體模糊權重, 模糊權重數的選定, 和各具不同程度的隸屬函數,來評定其成績的好壞程度(例如:好、普通)。對於沒有明確表明自己所屬的好壞程度的學生,我們運用隸屬度函數和預測其成績的關係,以最大隸屬度來預測其微積分期中考的成績。本研究也進行兩份問卷的設計方式的比較和問卷結果的討論。 Over the past ten years, the number of colleges in Taiwan has multiplied in the light of the boom of running schools. At present, there are over one hundred and fifty colleges, and the number of matriculated students is still increasing. In 2002, the Ministry of Education abolished the Joint College Entrance Examination, which had been implemented for forty-eight years, and turned to thoroughly adopt a diverse entrance policy. In the past years the Ministry of Education had urged to promote the reformation of education in order to relieve students'' pressure arising from the joint entrance examination. However, due to oversimplification of some curriculums, this resulted in the deterioration of students'' learning ability. A report of China Times Express on July 28, 2005 indicated that the calculus part of the third grade senior high mathematics was deleted. This made high school students too insufficient in the preliminary special knowledge to catch up with the level of college mathematics, and calculus learning became difficult when they go to college. In this study, two sets of questionnaire are answered by the freshmen of Tamkang University, class of 2004 and 2005, to identify possible factors, which might affect students'' motivation to study calculus. Based on the identified factors, they are asked to predict the performance of their mid-term calculus examination, and the result obtained compares with the actual scores. The analysis is begun by defining the connection that appropriately conform to fuzzy preference to the two questionnaires, followed by integrating the group preference and the aggregation rule. The conventional questionnaire is then analyzed by applying a fuzzy theory. We assume that each student has different degree of fuzzy preference for the items of the questionnaire on account of their unique personal factors. Through the determination of individual fuzzy weight, total fuzzy weight, and fuzzy weight, qualitative grades (excellent, good, average, bad, and terrible) and the associated membership functions are evaluated. For those who do not express clearly about the level of their grades, the corresponding grades are predicted through the membership function-prediction of grades relation by choosing the maximum of the membership function. A comparison between the designs of the two sets of questionnaire is also made, and the results obtained discussed.
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