學習表現為教育社會學中的重要議題，其中城鄉間的學習表現差距受到重視。過去研究認為家庭背景與地區的教育資源是影響學生學習表現的主要因素，然而這些研究缺乏班級因素與同儕效果的分析。因此本研究使用台灣教育長期追蹤資料庫（Taiwan Education Panel Survey, TEPS）在2001年與2003年的國中生樣本，以階層線性模型（Hierarchical Linear Modeling, HLM）分析國一班級同儕學習投入對國三數學表現的影響，學習投入以學生為課業所付出的時間為指標。分析結果發現：(1)學生數學表現的總變異中有24%來自班級因素的影響，76%為學生因素。(2)國三數學表現、個人學習投入與班級同儕學習投入有城鄉差距。(3)在控制其他變項下，個人學習投入、班級同儕學習投入對數學表現有正向效果。(4)班級所在地區的都市化程度透過班級同儕學習投入間接影響國三數學表現。 / Academic performance has been an important topic of research on educational sociology for a long time, while urban-rural differences have been already well documented in literatures. In the past, the literature indicated that the key factors to affecting academic performance are family background and the educational resources. But these researches have ignored the factors of class level and peer effects. In this study, the data are from Taiwan Education Panel Survey (TEPS) in 2001 and 2003, use Hierarchical Linear Modeling (HLM) to assess how peer engagement affects junior high students’ mathematics performance. The time students spend in studying is an index of engagement. The main finding are: (1) This research model accounts for 76% of the variation in student level and for 24% of the class variation in class level with regard to mathematical performance. (2) Students in the urban and rural city show a differences in their mathematics performance, student’s own engagement and peer engagement. (3) When controlling variables, student’s own engagement and peer engagement have positive effect on mathematics performance. (4) Urbanization levels indirectly affect mathematics performance through peer engagement.

近年來隨著網路學習的發展，能夠透過網路輔以學習者進行線上合作閱讀學習的合作數位閱讀標註系統興起，並已發展出多媒體的標註模式，不但可以由學生自己針對閱讀文本進行合作閱讀標註，更可以在閱讀文本上進行標註互動討論，具有提昇閱讀理解成效的效益。而數學應用問題的閱讀理解，影響學習者對於數學應用問題的解題甚巨，但是長久以來並無好的提升數學應用問題閱讀理解策略。本研究比較採用合作數位閱讀標註系統及使用傳統同儕面對面合作學習數學應用問題的實驗組與控制組學習者，在解決數學應用問題的學習成效及學習動機上是否具有顯著差異。此外，亦探討場地獨立/場地依賴型不同認知風格及高/低不同學習能力的學習者，採用上述兩種不同學習方法進行數學應用問題學習之學習成效與學習動機是否具有顯著的差異，最後探討實驗學習者使用此合作式數位閱讀標註系統輔以數學應用問題學習之學習滿意度。 研究結果發現：（1）採用合作式數位閱讀標註系統輔以進行數學一元一次方程式應用問題學習，在學習成效與學習動機上均顯著優於傳統同儕面對面合作學習數學一元一次方程式應用問題；（2）採用合作式數位閱讀標註系統以及傳統同儕面對面合作學習輔以進行數學一元一次方程式應用問題學習的實驗組與控制組學習者，在回歸到一般學習後，實驗組在學習成效上仍顯著優於控制組學習者；（3）無論是場地獨立或場地相依認知風格學習者，採用合作式數位閱讀標註系統輔以進行數學一元一次方程式應用問題的標註學習後，在學習動機上均顯著優於採用傳統同儕面對面合作學習輔以進行數學一元一次方程式應用問題學習的控制組學習者；（4）無論是高低不同能力學習者，採用合作式數位閱讀標註系統輔以進行數學一元一次方程式應用問題的標註學習後，在學習動機上均顯著優於採用傳統同儕面對面合作學習輔以進行數學一元一次方程式應用問題學習的控制組學習者；（5）實驗組場地獨立學習者在使用合作式數位閱讀標註系統後的學習動機優於場地相依學習者；（6）實驗組高學習能力學習者在使用合作式數位閱讀標註系統後的學習動機優於低能力學習者。 綜合以上，本研究所提出採用合作數位閱讀標註系統輔以數學應用問題閱讀理解的學習模式，具有提升學習動機與閱讀理解成效的效益，可推廣至解決更複雜數學單元之閱讀理解，甚至發展為創新數學教學之翻轉教學模式。 / Along with the development of web-based learning in past years, cooperative digital reading annotation systems, which could assist learners in online cooperative reading learning through the Internet, are emerged. Besides, multimedia annotation models are also developed for students, aiming at the reading texts, proceeding cooperative reading annotation as well as annotation interactive discussion on the reading texts. It presents the benefit to enhance the reading comprehension efficiency. The reading comprehension of mathematical application problems would largely affect learners’ mathematical application problem solving. However, there has not been a good strategy to enhance the reading comprehension of mathematical application problems. In comparison with the experimental group and the control group, which respectively apply the cooperative digital reading annotation system and traditional peers’ face-to-face cooperative learning to solve mathematical application problems, the differences in the learning outcome and learning motivation are discussed in this study. Furthermore, learners with field independent/field dependent cognitive styles and high/low learning abilities are preceded above two different learning approaches for learning mathematical application problems to discuss the differences in the learning outcome and learning motivation. Finally, learners learning mathematical application problems with the cooperative digital reading annotation system in the experiment are discussed the learning satisfaction. The research findings are summarized as below. (1) Learners applying the cooperative digital reading annotation system to learn the mathematical application problems in linear equation with one unknown present better learning outcome and learning motivation than those using traditional peers’ face-to-face cooperative learning for the mathematical application problems in linear equation with one unknown. (2) The experimental group, applying the cooperative digital reading annotation system to learn mathematical application problems in linear equation with one unknown, still outperforms the experimental group, using traditional peers’ face-to-face cooperative learning, on the learning outcome after return to general learning. (3) Learners with either field independent or field dependent cognitive style present significant better learning motivation, after learning mathematical application problems in linear equation with one unknown with the cooperative digital reading annotation system, than those applying traditional peers’ face-to-face cooperative learning. (4) Learners with either high or low ability show remarkably better learning motivation, after learning mathematical application problems in linear equation with one unknown with the cooperative digital reading annotation system, than those using traditional peers’ face-to-face cooperative learning. (5) Field independent learners in the experimental group present better learning motivation than field dependent learners after using the cooperative digital reading annotation system. (6) Learners with high learning ability in the experimental group reveal better learning motivation than those with low ability after using the cooperative digital reading annotation system. In sum, the learning model for the reading comprehension of mathematical application problems with the cooperative digital reading annotation system proposed in this study could enhance the benefits of learning motivation and reading comprehension. It could be promoted to solve the reading comprehension of more complicated mathematical units and even to become the flipped teaching model for innovative mathematics teaching.

University of Macau / Faculty of Education

本論文係研究和發展平行疊代法（PARALLEL ITERATIVE METHOD ）以解決數學規劃（ MATHEMATICAL PROGRAMMING）中之互補問題（COMPLEMENTA-RITY PROBLEM）。互補問 題源自解決國防軍事、工程經濟及管理科學等領域之應用，而由於近年來各種超級或 平行電腦不斷地創新，使得發展平行演算法以充分並有效地應用超級或平行電腦來解 決大型科學計算的問題日趨重要。 在本篇論文中，我們分別探討線性互補問題以及非線性互補問題。首先我們發展出一 半非同步（SEMI-ASYNCHRONOUS ）法來解決線性互補問題，此法之特性在於其能大幅 地減低因同步法所造成處理機閒置（IDLING）之冗額成本（OVERHEAD）；同時，也放 寬了非同步法對問題所加諸之限制，因而擴大了半非同步法所能應用之範圍。我們也 建立了有關該法收斂性（CONVERGENCE ）之理論根據。此外，線性互補問題之探討， 實為進一步研究非線性互補問題之基礎。 其次，我們提出一個整體性之架構，探討平行牛頓法（NEWTON METHOD ）及其各種變 型（VARIATIONS）來解決各種非線性互補問題，比較並研究各種方法的特性、限制及 執行效率。 然後，針對上述各種演算法，我們在教育部電算中心之IBM ３０９０上發展並模擬各 該法之平行運算，經由廣泛地實驗測試，以獲得具體之數值結果，來檢驗其效率，並 比較研究各法之適用性與優劣。最後，我們也提出一些相關之問題，以供未來後續研 究之參考。

本論文目的在分析臺灣學生學習成就評量資料庫(TASA)之新移民子女學習成就、心理、背景特質表現，及與本土子女進行比較。研究中自描述新移民族群的歷史演變、發展、可能遭遇困境與相關的研究中，進而，再搭配現行既有評量架構，以決定針對國小(四、六年級)新移民子女之數學成就、性別、家庭結構、家庭語言環境、家庭社經地位、家人、自我教育期望、親子關係、學校適應、學習策略、學習偏好、能力歸因、數學能力自我概念、內在動機、家庭作業、課業補習、課外活動等十多項心理、背景特質進行分析，而在詮釋其理論、實徵研究基礎後，運用測量不變性、多元潛在迴歸分析等技術以進行本研究各項議題之探討，希冀能就分析結果，提供未來研究之參考。 綜整分析後，可發現以下幾點結論： 一、在針對數學成就進行族群間之比較時，研究中在單向度假設與Rasch模式適配度檢定符合下，進而於排除顯著差異試題功能測量指標後，是運用多元潛在迴歸分析以進行本土與新移民子女數學成就之比較，分析結果顯示，在國小六年級內，並未存在顯著的族群差異，但是於國小四年級中，則是以本土子女的表現平均優於新移民子女，其差異效果為0.36，約屬Cohen(1992)認為介於中等至小的效果量，而接續於分析是否存在其它因素影響時，分析結果是顯示在先天消極的族群因素外，族群間家庭社經地位的不均衡才是真正影響之主因。 二、有關族群間之心理與背景特質比較方面，研究中在經採用測量不變性以確立工具品質，並伴隨著卡方獨立性考驗、獨立樣本t檢定之運用後，其分析結果大致顯示出新移民子女是較本土子女，在家中手足數僅有1位、位居老大或獨子女、繼親家庭與身處雙語環境等現況具有相對的多數，但是在學生認知家人、自我教育期望、親子關係、學校適應、學習策略運用、學習偏好以至課業補習、課外活動時間分派等，整體而言，則多是未具顯著的差異或屬Cohen(1992)所認為小的差異效果量範圍內。另一方面，研究中更突顯出的是族群間家庭社經地位的不平衡，確實占有極大的比重，是具備Cohen認為之中等至小的差異效果。 三、在分析心理、背景特質與數學成就關聯時，研究中在經採多元潛在迴歸分析後，其結果大致顯示：就族群與變項間之交互作用而言，國小四年級學生所認知之自我教育期望、內在動機等，相較於新移民子女，是對本土子女之數學成就有較高的影響力，但是國小六年級學生的家中手足數、家庭社經地位、記憶、控制策略運用與外控能力歸因的認知上，則是相對在新移民子女之數學成就上有較深厚的影響，而至於其它變項之分析，則多未存在族群的差異。進而，在排除族群的干擾，僅就各特質與數學成就關聯之主要效果而言，研究結果顯示除性別、家庭子女的出生序、家庭作業與課業補習分派時間等，存在不顯著或僅部份年級具備顯著效果外，其餘特質皆能符合本研究理論所預測之傾向，大致是以具備過多家中手足數或持過度的外控數學能力歸因者，是會對學生數學成就產生負面的影響，而其餘如來自完整家庭、身處主流語言環境、具備高家庭社經地位、教育期望、和諧親子關係、良好學校適應與擁有高度學習策略、偏好、動機等，則皆能正向的影響數學成就。 最後，研究中是就新移民子女定義、抽樣架構、測量指標等面向，提出對新移民子女學習成長資料庫之建立及與其它實務、研究之建議。 / The purpose of this study is to analyze neo-immigrant children’s achievement, performance in psychological traits and compare these with native children. Starting from the description of development, challenge and related researches of immigrant children in the past, we found the assessment frame of Taiwan Assessment of Student Achievement (TASA) just corresponded to the purpose we expect. Therefore, based on TASA , we decided to analyze the status and performance of neo-immigrant children in math, gender, family structure, language environment, socio-economic status, parents and self expectation, parents-children relationship, school adjustment, learning strategy, learning preference, ability attribution, academic self-concept, intrinsic motivation, time assignment of homework, school cramming, and extracurricular activity etc. Following the support of the theoretical and empirical evidences, we used the technique of measurement invariance and multiple latent regression to discover the different topics in the thesis. In sum, some conclusions are proposed. 1. In the comparison of math achievement between neo-immigrant and native children, we use the technique of multiple latent regression to test the difference after exclusion some items with significant differential item functioning. The result indicates that there is no significant difference between these two races in the sixth grade, but in the fourth grade the native children perform better than neo-immigrant children. The effect size is 0.36, and it is between medium and small degree according to Cohen(1992)’s opinion. Depended on this result, several following analyses are implemented. It shows the inequality of family socio-economic status between races is the main cause instead of the race people belong to. 2. In the comparison of psychological traits between neo-immigrant and native children, we not only use the technique of measurement invariance to ensure the qualities of assessment tools but also adopt chi-square test and independent samples t-test to examine the differences. The results indicate that the neo-immigrant children have more chances belonging to the categories of being eldest among siblings or only one child in his family, living in step-parents family, and involvement in bilingual environment. But there is almost no or just little difference between the two races in the perception of parent and self expectation, parents-children relationship, school adjustment, learning strategy application, learning preference, and the time assignment of school cramming and extracurricular activity. Besides, we found the inequality of family socio-economic status between races is the most different. The effect sizes range approximately from small to medium degree according to Cohen(1992)’s opinion. 3. In this study, we used the technique of multiple latent regression to analyze the relationship between different psychological traits and math achievement. The results indicate that as far as the interaction effects are concerned, the perception of self expectation and intrinsic motivation has greater impacts on native children’s math achievement than neo-immigrant’s in the fourth grade, but in the sixth grade the family size, family socio-economic status, the usage of memorization and control strategy, external ability attribution have greater impacts on neo-immigrant children’s math achievement than native children’s. Besides, there are no interaction effects on the remaining variables. Furthermore, as far as the main effect is concerned, the result shows that except no or just little relationship between gender, birth order, the time assignment of homework, school cramming and math achievement, the remaining variables have the similar relationships toward math achievement as we expect. That is that having too many siblings, external attribution of math ability may have negative influence on students’ achievement, but students who belong to intact family, involve in the mainstream of language environment, have higher family socio-economic status, and perceive better parent and self expectation, parents-children relationship, school adjustment etc. may have positive influence on their math achievement. Finally, some suggestions about the definition of neo-immigrant children, the way of sampling and qualities of measurement indicators are proposed. We expect they may do a greater help in the construct of the database of Prospect of Neo-Immigrant Children Learning and future usage.

University of Macau / Faculty of Education

University of Macau / Faculty of Education

University of Macau / Faculty of Education

University of Macau / Faculty of Education

University of Macau / Faculty of Education