大型資料庫的建制與分析逐漸成為一種教育研究趨勢，本研究即以PISA 2003資料庫為例，亟欲驗證期望價值論裡的構念和成就之結構關係，因此，由測量模式出發，擬運用探索性因素探索研究工具的信效度，以作為結構方程模式驗證結構關係模式之基礎，並驗證期望價值論下之動機二成分模式。本研究主要研究目的為驗證期望價值論的數學效用性價值、數學自我概念與成就之結構關係，且數學效用性價值是正向直接影響數學成就，並且會經由數學自我概念而間接影響數學成就，並為使本研究所建立的理論模型具有模型穩定之證據，將有效樣本隨機分為建模樣本與驗證樣本，進行模型的交叉驗證。研究樣本為香港十五歲學生，有效樣本為4437人。研究結果顯示：測量模式方面，顯示數學效用性價值以及數學自我概念具有良好的信效度；數學效用性價值以及數學自我概念為學習動機的二成分；結構模式方面，顯示數學效用性價值是正向影響數學成就，且數學效用性價值會經由數學自我概念對數學成就有間接影響，亦即數學自我概念扮演數學效用性價值及數學成就之中介變項。因此，本研究之理論假設獲得實徵資料的支持。

在統計學上，我們常使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩變數間線性關係的強度，同時也表達出關係之方向。傳統之相關係數所處理的資料都是明確的實數值，但是當資料是模糊數時，並不適合使用傳統的方法來計算模糊相關係數。而本研究探討區間模糊樣本資料值求得模糊相關係數，首先將區間型模糊資料分為離散型和連續型，提出區間模糊相關係數定義，並提出廣義誤差公式，將相關係數作合理的調整，使所求的出相關係數更加精確。在第三章我們以影響數學成就評量的因素，作實證研究分析，得出合理的分析。而此相關係數定義和廣義誤差公式也能應用在兩資料值為實數或其中一筆資料值為實數的情況，可以解釋更多在實務上所發生的相關現象。 / In the statistic research, we usually express the magnitude of linear relation between two variables by means of Pearson’s Correlation Coefficient, which is also used to convey the direction of such relation. Traditionally, correlation coefficient deals with data which consist of specific real numbers. But when the data are composed of fuzzy numbers, it is not feasible to use this traditional approach to figure out the fuzzy correlation coefficient. The present study investigates the fuzzy samples of interval data to find out the fuzzy correlation coefficient. First, we categorize the fuzzy interval data into two types: discrete and continuous. Second, we define fuzzy correlation with interval data and propose broad formulas of error in order to adjust the coefficient more reasonably and deal with it more accurately. In Chapter Three, we conduct empirical research by the factor which affects the evaluation of mathematical achievement to acquire reasonable analysis. By doing so, broad definition of coefficient and formulas of error can also be applied to the conditions of either both values of the data are real number or one value of the data is real number, and can explain more related practical phenomenon.

本研究運用PISA 2003資料庫為例，說明數學焦慮之認知與情意，如何影響學生數學內在動機、自我概念與成就的機制。本研究的研究對象，為香港十五歲學生，並採取整列剔除法（listwise deletion）刪除作答不全的缺失值與極端值，共計取得有效樣本為4,397人，其中男生2,168位，女生2,229位。研究結果顯示：第一、數學焦慮之認知與情意模式獲得驗證；第二、數學焦慮之認知與情意除了直接影響數學成就之外，還能經由數學內在動機與自我概念，對數學成就產生間接影響。 / The purpose of the present study was to assess the influence of mathematics anxiety (including the cognitive and affective dimensions), mathematics intrinsic motivation, and mathematics self-concept on mathematics achievement. Participants were 4,397 9th-grade students from Hong Kong who attended PISA 2003 study. The results of confirmatory factor analyses supported the theoretical distinction between cognitive and affective dimensions of mathematics anxiety. The analysis of structural equation modeling confirmed that the cognitive and affective dimensions of mathematics anxiety can predict mathematics achievement through the mediating effect of mathematics intrinsic motivation and mathematics self-concept.

本研究目的，在利用PISA 2003資料庫為例，分辨數學自我概念、自我效能與數學成就關係之模式的建構。本研究選香港為研究對象，以參加PISA 2003的4402名香港的15歲學生為樣本來進行本研究。本研究運用探索性因素分析(EFA)檢視自我概念與自我效能之測量指標的信效度。分析結果顯示，「自我概念」與「自我效能」的測量模式的建構達良好的信效度。另一研究結果顯示，學生數學自我概念對數學成就之間沒有直接的影響效果，但會透過數學自我效能此中介變項，而產生對數學成就的間接影響效果。此外，在雙交叉驗證方面，顯示研究二組樣本具有交叉效度，研究模式之接受性均相當高。 / The purpose of this study was to examine the relationship among self-concept, self-efficacy, and performance in mathematics. The PISA 2003 Hong Kong data was used as an example. There were 4402 15-year-old participants in this survey. Explore factor analysis was used to identify the good measurement models of self-concept and self-efficacy in PISA 2003. The results showed that the measurement models had high reliability and validity. The other result showed self concept had no direct effects on the mathematics achievement. But under the mediation of the mediator, such as self-efficacy, there was indirect effect on the mathematics achievement. Analysis also showed that the two sets of samples have presented cross validity, the research model is highly acceptable.

本論文從教育社會學角度探討造成數學成就性別差異現象的成因，以班級的性別環境為研究脈絡，研究影響國中女生數學成就的可能原因。假設數學成就的性別差異是受到後天學習歷程影響，班級環境中隱含的性別刻板印象為其中一個重要社會文化影響因素。透過比較國一到國三階段女生班和一般男女合班女生數學成就的異同，嘗試找出造成數學成就性別差異現象的成因，是否與班級性別環境、師生的性別刻板印象等因素有關。利用階層線性模式（Hierarchical Linear Models，HLM）統計方法，分析資料取自由中央研究院、教育部和國科會共同規劃的全國性長期的調查計畫：「台灣教育長期追蹤資料庫」（Taiwan Education Panel Survey，簡稱TEPS）。研究結果發現女生班、數學老師性別及班級學業氣氛等因素對於國中女生數學成就有顯著影響力，但進一步考慮學校公私別變項之後，女生班的影響力即消失。 / The main purpose of this study is to assess the magnitude of individual and contextual influences to explain gender differences in math achievements. Adopting the hierarchical linear model analysis to determine whether or not statistically significant differences between the mathematical achievements of 7th grade students who attend all-girls classes compared with those who attend coeducational classes at the same time, and their academic performance after two years. The result shows that there are three factors that have significant influences on girls’ math achievement in junior high schools, which are the single-sex classes, female math teachers and the academic climate of each class. However, if private schools are taken into consideration, the significant influence of the gender composition of classes will disappear.

為瞭解國民中小學學生學習電腦相關行為及現況,本研究以台北市國民中學三年級學生1251人及國小六年級學生1201人為研究對象,經運用電腦經驗調查表.認知需求量表.數學焦慮量表.電腦態度量表及電腦素養測驗卷等研究工具,獲得所需的資料,再以chi-square考驗.皮爾遜積差相關. t-test.典型相關.多元(逐步)迴歸及因徑分析等方法進行統計分析,結果 有以下幾點發現: 一. 國民中小學學生電腦經驗.電腦資源.電腦態度與電腦素養現況方面 1. 國中與國小學生之電腦經驗有顯著的差異存在. 2. 國中與國小學生之電腦資源部份有顯著的差異. 3. 國中與國小男女學生之電腦經驗部份有顯著的差異存在. 4. 國中與國小男女學生之電腦資源部份有顯著的差異存在. 5. 國中學生與國小學生在電腦焦慮與電腦有用性兩電腦態度上有顯著差異. 6. 國民中小學男學生之電腦態度(焦慮與自信)顯著較女生好. 7. 國中學生之電腦素養(軟硬體.應用與影響.操作.倫理)顯著較國中學生佳. 8. 國民中小學男學生之電腦素養(軟硬體.應用與影響.操作)顯著較女生佳. 二. 影響國中小學生電腦態度方面 1. 電腦經驗與國中小學生之電腦態度有顯著之正相關. 2. 電腦資源與國中小學生之電腦態度有顯著之正相關. 3.認知需求與國中小學生之電腦態度有顯著之正相關. 4. 數學焦慮與國中小學生之電腦態度有顯著之相關. 5. 數學成就與國中小學生之電腦態度有顯著之正相關. 6. 認知需求.每星期使用電腦的時間.每星期閱讀電腦書籍及雜誌的.家中電腦週邊設備的情形.自己或與他人共同使用電腦以及是否有電腦學前經驗等六個變項對國中小學生之電腦態度有顯著的預測效果,預測解釋力為32%. 三. 影響國中小學生電腦素養方面 1. 電腦經驗與國中小學生之電腦素養有顯著之正相關. 2. 電腦資源與國中小學生之電腦素養有顯著之正相關. 3. 認知需求與國中小學生之電腦素養有顯著之正相關. 4. 數學焦慮與國中小學生之電腦素養有顯著之相關. 5. 數學成就與國中小學生之電腦素養有顯著之正相關. 6. 每星期閱讀電腦書籍及雜誌的時間.家中電腦週邊設備的情形.自己或與他人共同使用電腦.電腦焦慮.電腦自信以及電腦喜歡等六個變項對國中小學生之電腦素養有顯著的預測效果,預測解釋力約為52%.四.整合模式分析方面1. 國中學生之電腦經驗與電腦資源對其電腦素養之影響,主要是來自直接效果的影響(經驗:57.32%;資源:73.31%), 而認知需求對電腦素養之影響主要是透過電腦態度間接效果的影響(89.06%).2. 電腦經驗與電腦資源對國小學生電腦素養之影響, 來自間接效果的影響約佔(經驗: 67.55%;資源:52.32%),認知需求對國小電腦素養的影響主要是透過電腦態度的間接效果,佔61.29%. With the expansion of computer technology, it is important to prepare individuals for success in our increasingly computerized society. Therefore,factors that impact decisions regarding attitude and literacy of computer should be expored. Several factors should be considered: (1) individual characteristics, (2) computer experience, (3) computer resource, (4) cognitiveneed, (5) mathematics anxiety, and (6) mathematics achievement. The purposes of this study were : (1) To find out the situation of information education in junior secondaryand primary school at present; (2) To find out the situation of the computer attitude and literacy in junior secondary and primary school students at present; (3) To examine the relationship and effects toward computer attitudes and literacy of many factors. 1251 junior secondary and 1201 primary school students were measured by (1)individual characteristics and computer experience questionnare, (2) Cognitive Need Scale , (3) Mathematics Anxiety Scale , (4) Computer Attitude Scale, and(5) Computer Literacy Test. The mainly statistical methods are chi-square, pearson product moment correlation, t-test, canonical correlation analysis, multiple(stepwise) regression analysis and path analysis. The results of the analysis of data indicated the following : (1) There were significant sex and school level differences of attitude and literacy toward computer. Boys were better than girls. Primary school students were better than junior secondary school; (2) There were significant correlations between computer experience, computer resource, cognitive need, mathematics anxiety, mathematics achievement, and computer attitude; (3) There were significant correlations between computer experience, computer resource, cognitive need, mathematics anxiety, mathematics achievement, and computer literacy; (4) Computer experience, computer resourse, cognitive need and computer attitude were significant predictors for computer literacy. Computer attitude was the best significant predictor. Recommendations were made for information education , school , family,educational organization and future additional research , to improve the attitude and literacy toward computer of junior secondary and primary school students.

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.