高級中學經營效率之四篇實證研究：評估方法及數位學習之附加角色

Four Essays on Evaluating Efficiencies of the Selected High Schools: Evaluation Method and Additional Role of Innovative Teaching via Digital Mobile E-Learning

郭福祥(FU-HSIANG KUO)

指導教授 ： 李麗華 ； 劉祥熹

朝陽科技大學/資訊學院/資訊管理系/博士(2020年)

摘要

本文研究目的旨在評估臺灣高級中學有引進行動數位學習（mobile digital e-learning）之學校經營效率，並以資料包絡分析法(data envelopment analysis, DEA)進行估計學校管理之經營效率，且運用Tobin regression model (TRM)與Bootstrap truncated regression (BTR)找出行動數位學習效率對學校經營效率之影響效果。本文進一步引用data mining methodology (DMM)之CRISP-DM模型透過不同學校經營效率值與行動數位學習的代表性因素之關連性資訊或訊息，以發現不同學校屬性/特性，並依此不同學校屬性/特性，以DEA共同邊界模式(DEA meta-frontier model)分別評估一般高中學校與職業高中學校進行估計學校管理之經營效率及其受行動數位學習之影響效果。為了達成此目的，本文採用四篇實證論文進行研究，並將其每一篇實證結論分別描述如下：
第一篇實證結果(第二章)，依DEA模式評估學校效率並以Tobit迴歸模型(TRM)分析行動數位學習對學校經營效率的影響。本研究以DEA模型分析2013年至2015年期間，共有七所學校的整體總技術效率(TE)值為1，四所學校的整體TE值為1。相反，有五所學校的TE值未達到1，且有一所學校的TE值呈現下降，則為公立麗山高級中學。純技術效率(PTE)的值為1時，其結果表明學校的資源可以得到有效運用，從2013年到2015年，共有五所學校的PTE值為1，相對而言，顯示共四所學校的PTE值未達到1時，則表示資源為未有效運用則需要改進。整體規模效率(SE)是指學校是否需要擴大或縮小規模以實現效率，2013年至2015年，共有4所學校的SE效率值為1，其表示這些學校不需要更改學校規模。整體而言，研究顯示這些有效率的學校位置都位於台北市或新北市。本研究運用Tobit迴歸模型分析之實證結果顯示其學校規模、師生比例、平版電腦數量、技術教師比例、平板電腦相關的設備總支出、學校屬性(公立與私立)及學校屬性(高中與高職)等會影響學校管理的效率。為了提高學生學習的效率及提升學校的經營管理效率，首先有必要增加學校的規模、平板電腦的數量和技術教師的人數。通常技術教師比例的提高將吸引更多的學生參加學校的行動學習行列。當技術教師比例的數量與平板電腦的數量相對於學校教師總數的增加時，就可以提高學校的經營管理效率。但是，應該注意的是，由於相關設備的成本增加，與平板電腦相關的設備總費用對學校管理效率呈現負向且影響很小。結果還表明，學校屬性(公立與私立)及學校屬性(高中與高職)對學校經營效率均呈現有影響。因此，在選擇用於行動學習的設備時，其學校屬性也必須考慮進去。
第二篇實證分析結果(第三章)，除以DEA模式評估學校效率外並進一步運用BTR方法探討分析行動數位學習對學校經營效率的影響。我們發現(1)採用DEA模式可進行評估導入數位行動學習之學校經營效率。(2)本文進一步找出數位行動學習對學校經營效率的因素與效果，因此本文採用BTR (bootstrap truncated regression)迴歸模型進行分析，結果顯示，學校規模、師生比例、平版電腦數量、技術教師比例、平板電腦相關的設備總支出、學校位置、學校屬性(公立與私立)及學校屬性(高中與高職)等會影響學校管理的效率，其研究結果顯示確實可以影響或提高學校經營效率。值得注意的是，通過BTR方法，所有估計係數的顯著性水準平均為1％或5％。結果發現，BTR方法的結果優於TRM方法。
第三篇實證分析結果(第四章)引用data mining methodology (DMM)之CRISP-DM模型透過不同學校經營效率與代表數位學習的代表性因素之關連性資訊或訊息，做為學校特性/屬性之發掘。經研究發現在2013年至2015年間，學校規模是學校人數在1400-3000之間、師生比例為7.4 %到8.0 %之間、平板電腦數量大約是1200-3000台、數位學習諮詢技術教師的比例為8%-16%及設備費用範圍為15佰萬-30佰萬在此範圍內則學校導入數位行動學習將可以提高學校管理效率。在實際結果驗證中，我們發現有引入行動數位學習的一般高中學校經營效率比高職高中學校經營效率較好，且公立高中學校經營效率也比私立高中學校更有能力實施數位行動學習之效果，而學校位置在北方比其他地方好。這些研究結果，亦可為教育機構制訂臺灣高中行動數位學習策略與政策提供參考。
根據學校管理效率值(TE)，本研究進一步將其效率值區分為高效率、中效率及低效率等三個效率群組，以比較學校效率之學校特徵或屬性的差異。在高效率群(TE = 1)共有四間，這些學校分別為台北第一女中學，復興高中與麗山高中，我們發現這些學校都是公立高中，另一所是私立高職則為莊敬高職，且這些高效率的學校位於台灣北部。中效率群(TE = 0.85-0.99)僅為一所學校為公立陽明高中且位於北部地區。低效率體(TE <0.85)有四所學校，分別為公立中崙高中與私立及人高中學均位於台灣北部地區。另外公立羅東高中與花蓮農業及工業職業學校則位於台灣東部地區。其結果總體來說，我們發現公立高中學校比私立高中學校呈現更有經營管理效率，並且顯示學校位置位於北部地區的學校比其他地區得到更好的經營管理效率，也顯示行動學習會影響學校的經營管理效率。
第四篇實證分析結果(第五章)，本研究考量不同屬性與特性下，而運用DEA meta-frontier進行學校經營效率評估，並進一步採用Bootstrap truncated regression (BTR)模型找出數位學習因子是否影響學校經營效率，由於研究顯示，一般高中與職業高中有不同的生產邊界，不能直接合並來評估其技術效率，因此採用meta-frontier模式進行學校效率評估。其結果顯示透過比較群組生產技術效率(GP-TE)時，我們發現職業高中(0.941)優於一般高中(0.930)，又兩群組(GP-TE)值小於1，也顯示更多的平均輸入因子浪費導致一般高中組的效率或管理效率降低。比較共同生產技術效率(MP-TE)效率時，我們發現職業高中學校(0.785)優於一般高中(0.765)。應該注意的是，MP-TE效率值的差異表明兩個學校群體的技術效率值在共同邊界上確實存在顯著差異。此外，我們進一步比較技術差距比例(TGR)或共同技術比例(MTR)時，根據三年平均TGR或MTR，一般高中學校(0.950)優於職業高中學校(0.843)。其中一般高中學校之TGR或MTR的平均值接近1，這意味著在當前輸入水平下，TGR或MTR的產量或服務水平約為最大潛力。反之，平均TGR或MTR相對較低時，這意味著一般高中學校與職業高中學校的現有技術並不接近共同技術邊界，代表在管理技能或操作流程上還有更大的改進空間。因此當政府機構針對不同的教育群體(特徵/屬性)制定學校運營效率的政策時，更要考慮教學方法與教育方向。
另一方面我們還進一步採用BTR模型方法評估數位學習因子是否影響學校經營效率(MP-TE)。在實際操作中，我們發現師生比例、平板電腦數量、技術教師比例、平板電腦相關的設備總支出及學校位置等均呈現顯著效果，特別是數位行動學習之知識教學或諮詢技術教師的數量和平板電腦數量等均呈現會影響學校經營管理效率(MP-TE)且有著重要作用。我們的實證結果進一步證明並發現學校規模與學校屬性(公立與私立)對學校經營效率(MP-TE)不具有顯著性效果，乃由於近年來出生率低，學生人數開始減少，政府實施移動電子學習與學校屬性(公立與私立)之學校無關。最後期望本文研究結果可為教育部門在制定促進數位移動電子學習的政策和法規時提供參考。
最後，本研究期望這四篇論文的實證結果與發現，在制訂台灣地區高級中學數位行動學習的發展策略與政策以提升或推廣數位行動學習時，也可為高級中學與教育相關當局提供參考。

關鍵字

資料包絡分析法 ； Tobit迴歸模型 ； 拔靴法迴歸模型 ； 資料探勘 ； 共同邊界模式 ； 行動數位學習

並列摘要

This study aims to evaluate the operational efficiency of school management using the data envelopment analysis (DEA) model and explore the impact of mobile e-learning on the operational efficiency of high schools in Taiwan. We cannot assume that senior and vocational high schools have the same know-how or technical level. This study applies the DEA meta-frontier model to measure school’s management efficiencies and determine whether implementing mobile e-learning improves the school management efficiency, and then examine whether mobile e-learning can affect schools’ operational efficiencies using the Tobin regression model (TRM) and Bootstrap truncated regression (BTR). We further utilize data mining methodology (DMM), such as CRISP-DM, to mine school characteristics/attributes from information or messages about the relationships between school management efficiencies (scores) and the representative factors of mobile e-learning. To fulfill the research purpose, this study summarizes four essays to satisfy the research objectives.
In the first essay (Chapter 2), we apply DEA model to evaluate the operational efficiency and use the Tobin regression model (TRM) method to analyze the effect of mobile e-learning on the operational efficiency of high school in Taiwan. The result of the efficiency analysis shows that seven schools have an overall total technical efficiency (TE) value of 1, with four schools having an overall TE value of 1 for the period 2013–2015. Conversely, five schools failed to reach a TE value of 1, with only one school showing a decline in TE which is the Taipei Municipal Zhong-Lun Senior High School. The pure technical efficiency (PTE) reaches a value of 1; this result shows that the schools’ resources can be used effectively. Five schools have an overall PTE value of 1 from 2013 to 2015. In contrast, four schools failed to reach the PTE value of 1. Scale efficiency refers to whether the schools need to either expand or reduce their scales to achieve efficiency. Four schools have an overall scale efficiency (SE) value of 1 from 2013 to 2015; schools which do not need to change their school size. Other four schools achieve a SE value of 1. Overall, research shows that these efficient schools, all of which are located in Taipei City or New Taipei City. In this study, we utilized TRM model analysis to determine whether the results support the notion that school size, teacher-student ratio, number of tablet PCs, technical teacher ratio, total equipment expenses associated with tablet PCs, and the senior high vs. vocational-high attribute are important factors that affect school management efficiency. To increase the effectiveness of student learning and enhance the school’s operational efficiency, it was necessary to first add school size, the number of tablets, and the number of technical teachers. Generally, an increase in the technical–teacher ratio will attract more school students to participate in schools’ mobile e-learning programs. When the ratio of the number of technicians acting as consultants tablet computer knowledge, to the total number of teachers in school increases, which can increase the school’s operational efficiency. However, it should be noted that total equipment expenses associated with tablets have a small negative influence on school management efficiency, because of increasing costs of related equipment. The results also show that school attributes, and high- and vocational-school attributes have a significant impact on an operational efficiency. Thus, the degree of a school’s operational efficiency must be considered when choosing attributes such as equipment, teaching quality, management decisions, etc., for mobile e-learning.
In the second essay researches (Chapter 3), we still apply DEA model to evaluate the operational efficiency and use the Bootstrap truncated regression (BTR) method to analyze the operational efficiency of high school in Taiwan. (1) We find that the DEA model can be used to evaluate the operational efficiency which introducing mobile e-learning in schools. (2) The imported mobile e-learning factors can affect the operational efficiency of school management by the Bootstrap truncated regression (BTR). The results also show that school size, teacher-student ratio, numbers of tablet computers, technical–teacher ratios, total equipment expenses associated with tablets, school location, school attributes, and high- and vocational-school attributes are the main factors affecting school management efficiency. The research results show that the introducing mobile e-learning in schools can indeed affect or improve the efficiency of school operations. It is worth noting that all the estimated coefficients are significant at the 1% or 5% significant level by the BTR method. It finds that the results from BTR method are better than the TRM method.
In the third essay (Chapter 4), the results of DMM model indicate that during the years 2013-2015 the schools with the total number of students (P_1) in schools about 1400-3000 persons, the teacher-student ratio (P_2) between 7.4 %-8.0 %, the tablet PC numbers (P_3) about 1200-3000 units, the technical teacher ratio of mobile e-learning (P_4) is about 8%-16% and the total equipment expenses associated with tablet PC (P_5) about the range of 1.5-3.0 Million NTD could obtain higher operational efficiency of school management through innovative teaching via mobile e-learning.
Now, based on the ranks of school management efficiency, we further divide into three efficiency groups to compare the efficiencies to detect their school characteristic and attributes: high, medium and low groups. The high-efficiency group (TE = 1), these schools are Taipei First Girls Senior High School, Fu-Xing Senior High School, and Li-Shan Senior High School, all of which are public high schools, and the other private high school, which is Juan-Jing Vocational High School. These highly efficient schools are located in northern Taiwan. The medium- efficiency group (TE = 0.85-0.99) is made up of only one public Yang-Ming Senior High School in northern Taiwan. The low-efficiency group (TE < 0.85) has four schools, the public Zhong-Lun Senior High School and the private Chi-Jen Senior High School are located in northern Taiwan. The public Lo-Tung Senior High School and the public Hua-Lien Agricultural and Industrial Vocational Senior High School are located in eastern Taiwan. In general, we also found that public high schools are more efficient than private high schools and that schools are better managed in the north than in other areas because they enable mobile e-learning, the effects of which are related to school operation and management.
In the fourth essay (Chapter 5), this study further utilizes the DEA meta-frontier model to assess school management efficiency at different know-how levels and examine whether mobile e-learning effects on school operational efficiency using the BTR model. Comparing the average group technical efficiency scores (GP-TE) for each group, we find that vocational high schools (0.941) are more efficient than senior high schools (0.803). This means that more wastage of the input factors resulted in the senior high school group having lower operational efficiency than the other two groups. Comparing the average MP-TE values for each group, we find that vocational high schools (0.785) are more efficient than senior high schools (0.765). It should be noted that the difference in MP-TE scores indicates that the technical efficiency values of the two school groups have significant differences in the common frontier. Additionally, we compare the TGR or MTR values for each group. According to their three-year average TGR or MTR values, senior high schools (0.950) are more efficient than vocational high schools (0.837). The average TGR or MTR value is close to 1 for senior high schools, which means that they produce or serve the approximate maximum potential output at the current input level. A low average TGR or MTR value means that the prior operations of vocational high schools are not close to the frontier of meta-technical possibilities. There is more room for improvement in management skills or operational processes. Additional, when governmental agencies formulate policies for improving the operational efficiency of schools at the different levels (characteristics/attributes) of education, they need more consider education methods and directions.
It is worth noting that, in our study, the MP-TE values are lower than the GP-TE values for schools with the different characteristics/attributes such as senior high schools and vocational high schools. There is sufficient evidence to show that the technical efficiency values of any two school groups had significant differences in the common frontier. Additionally, we cannot treat school groups at different technology levels as the same group when calculating their respective efficiency values.
Moreover, in this study, we examine whether mobile e-learning could affect schools’ operational efficiency using the BTR method. Based on our empirical results, we find that the teacher-student ratio, number of tablet PCs, technical teacher ratios, total equipment expenses associated with tablets, and school location are the main factors affecting school management efficiency. Our empirical results further justify that school size and the public-private school attribute are not significant for school management. The results also indicate that to increase students’ learning effectiveness and therefore enhance schools’ operational efficiency, it is necessary to first increase school size as well as the number of tablet PCs and technical teachers. Moreover, the results show that the total equipment expenses associated with tablet PCs have a small negative influence on school management efficiency. The results of this research can used as a reference for educational authorities when formulating policies and regulations to promote mobile e-learning.
These research and findings of the above four essays can also become a reference for educational authorities when formulating strategies and policies for promoting digital mobile e-learning in the high school of Taiwan area.

並列關鍵字

Data Envelopment Analysis (DEA) ； Tobit Regression Method (TRM) ； Bootstrap Truncated Regression (BTR) ； Data Mining Methodology (DMM) ； DEA Meta-Frontier ； Mobile E-Learning

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