政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/73285

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/73285

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/73285

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/73285

Title:	類典型相關分析及其在免試入學上採計成績之研究 A canonical correlation analysis type approach to model a criterion for enrolling high school students
Authors:	卓惠敏 Cho, Hui Min
Contributors:	宋傳欽 Song, Chwan Chin 卓惠敏 Cho, Hui Min
Keywords:	在校學科分數國中基測量尺分數主成份分析類主成份分析典型相關分析類典型相關分析 scores of in-school academic performance scores of the BCTEST for junior high schools principal component analysis principal component analysis type approach canonical correlation analysis canonical correlation analysis type approach
Date:	2014
Issue Date:	2015-02-03 10:24:30 (UTC+8)
Abstract:	實施十二年國民基本教育，目的是為促進學生五育均衡發展，兼顧國中學習品質及日常生活表現。由於各校對成績的評分標準與評分方式皆不相同，因此如何使在校成績採計達到公平性將成為一項重要的問題。戴岑熹(2011) 考慮了國中在校綜合學科分數與基測總分間的相關性，以決定在校各學科的權重。而本研究延伸其概念與方法，將基測各科量尺分數考慮進來，於在校綜合學科分數與基測綜合量尺分數的關聯性最密切的情況下，分析各學科權重的取決方式，希望能找出較理想的模式來代表學生在校三年的整體學習表現與成果，以做為免試升學採計在校成績的參考與依據。本文的研究方法是運用典型相關分析的理論，但因權重的限制條件與傳統典型相關分析的要求不同，因此，便將其命名為「類典型相關分析」。在類典型相關分析中，我們證明了在校各學科分數及基測各科量尺分數的最佳權重，可先透過典型相關分析求得典型相關向量，若有必要的話，使用Rao-Ghangurad 方法加以修正，最後，再將所獲得的非負典型相關向量正規化，即可獲得所要的結果，這是一個求最佳權重向量極便捷的途徑。在實例分析方面，我們發現了一個有趣的現象，即在校學科分數與基測考科量尺分數的最佳權重向量相當接近，即名稱相同的學科與考科幾乎有相同的權重。在比較了幾個權重分配方式不同的在校綜合學科分數後，我們也發現一般學校常用的等加權模式，其表現結果也頗優異。 The purpose of implementing the twelve-year compulsory education is to promote the balanced development of learning in students, taking into account their learning quality and normal daily performances in school. As the evaluation standard and method vary among schools, achieving fairness in calculating in-school grades has become an important issue. Dai (2011) considered the correlations between the scores of in-school academic performance and the total score of the BCTEST for junior high schools, which decided to the weightings of all learning subjects. This study extended his concept and method, and took into account the scale scores of all learning subjects. In the closest case of the weightings of all learning subjects and find out the correlations between the scores of in-school academic performance and the BCTEST, and analyse the weightings of all learning subjects. We hope the study can find a better approach that can not only reflect students’ learning situations and achievements for the three years in school but also provide a reference for the evaluation of entering senior high schools without entrance examinations. The research method in this paper employs the theory of canonical correlation analysis.However, due to that fact that weight restrictions are different from the requirements of canonical correlation analysis, it is named as the canonical correlation analysis type approach. In the canonical correlation analysis type approach, we proved that the optimal weights for school subject score and test subject score scales can be obtained by finding the canonical correlation vectors using canonical correlation analysis. Then the Rao-Ghangurad method can further be used for amending, if needed. Finally, the nonnegative canonical correlation vectors generated would be normalized to get the desired result. It is an extremely convenient way to obtain the optimal weight vector. In the case study, we found an interesting phenomenon as follows: When the optimal weight vectors for school subject score and test subject score scales were very close, subjects and tests of the same name had almost the same weight. After comparing several comprehensive school subject scores of different weight distribution, we also found that the results of the equal weighting model commonly used in schools also showed quite good results.
Reference:	[1] 宋耀廷、周業太、吳佩嶼、林秀珊、曾芬蘭(2010)。高中職入學制度中在校成績採計校正方式之比較。教育科學研究期刊，55(2)，73-113。 [2] 陳柏熹、邱佳民、曾芬蘭(2010)。高中職入學制度中在校成績採計校正方式之比較。教育科學研究期刊，55(2)，115-139。 [3] 周祝瑛(2009)。邁向十二年國民基本教育– 由繁化簡的高中、職免試入學方案。教育資料集刊，第四十二輯–2009 各國中等教育，25-42。 [4] 吳明清(2009)。免費乎？免試乎？十二念國教的政策困境與出路。教育行政論壇，2，49-59。 [5] 楊思偉（2006）。推動十二年國民教育政策之研究。教育研究集刊，52（2），1-31。 [6] 戴岑熹(2011)。高中職及五專免試入學採計國中在校學科分數加權機制之研究。國立政治大學應用數學系碩士論文。 [7] 陳順宇(2004)。多變量分析。臺北市: 華泰書局 [8] 張建邦(1997)。多變量分析。臺北市: 三民書局 [9] 陳耀茂(1999)。多變量解析方法與應用。臺北市: 五南圖書出版 [10] 呂金河(2005)。線性代數導論(第八版)。華泰文化 [11]Anderson, T. W.(1984). An Introduction to Multivariate Statistical Analysis, 2nd ed., New York: John Wiley and Sons, Inc [12]Johnson, R. A. and Wichern, D. W.(2007).Applied Multivariate Statistical Analysis, 6th ed., Prentice Hall International, Inc [13]Hambleton, R. K., and Swaminathan, H. (1985). Item response theory:Principles and 　applications. Boston: Kluwer. [14]Kolman, B. and Hill, D. R.(2005). Introductory linear algebra -An applied first course. Upper Saddle River, N.J.: Pearson Prentice Hall [15]Hair, Black, Babin, and Anderson(2009). Multivariate Data Analysis, 7th ed.
Description:	碩士國立政治大學應用數學系數學教學碩士在職專班 100972017 103
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0100972017
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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