本研究透過「教學信念量表」的施測，選取「傳統取向」與「進步取向」教學信念的中年級國小數學教師各20名，在四種學生數學表現情境下，進行教學處理的訪問，以探討教師教學信念對教學處理的關係。 結果顯示，當面對一個程度較差的學生表現出錯誤解答時，「進步取向」教師較常用「提示思考」類型的教學處理，而「傳統取向」教師較常用「示範觀察」類型的教學處理；當學生表現錯誤解答時，「傳統取向」教師對程度較好的學生較常用「提示思考」類型的教學處理，而對程度較差的學生使用「示範觀察」類型的教學處理；當學生以非標準步驟獲得正確解答時，兩種教學信念的教師多採用「接納了解」類型的教學處理；進一步地探討，發現「傳統取向」教師較常使用教師講解策略，而「進步取向」教師則較常提供同僚討論的機會；在訪談中，皆請教師描述其進行教學處理的理由，從理由的分析，本研究建議兩種教學信念的教師，對各種教學處理的觀點及功能有不同的認知，而導致教學處理偏好的差異。

本文主題是討論二階自伴隨線性方程式和離散型非線性波方程式的振盪行為，主要的工作在於找出使得該方程式所有非零解振盪的充份條件。 / The major topic in this thesis is that of oscillatory behaviors for difference equations, including self-adjoint second order linear equation and the discrete version of nonlinear wave equation. Our work is to give sufficient conditions such that every nontrivial solution of the equations oscillates.

傳統上，時間數列的型態分類與認定的分析方法，一般都應用在定態的隨機過程。雖然單根檢定的方法用來檢定一時間數列是否定態的判定，一直被計量經濟學家所重視。但由於近幾年來非直線性時間數列越來越受到重視與研究，以傳統的單根檢定法來分析已無法顯出其數列的特性，甚至許多時候會導致對其數列辨識準確度穩健性的喪失，所以結構轉變的檢定先行於單根檢定，對於非線型時間數列來說是非常重要的。 　　鑑於此，本文嘗試模擬5組非線性的時間數列資料，用平均值估計信賴區間之方法和模糊熵分類方法，以事前的觀點用我們所定義的分類標準客觀的來認定其結構轉變的區間。我們也舉出匯率的實際例子以我們所提出的方法加以探討認定，找出其高低匯率時期及轉型期。 / Traditionally, the analysis methods of pattern classification and recognition for time series generally apply to the stationary process. Tests for unit roots used to test whether the time series is stationary has always been looked upon by the statisticians econometrics. Because there have been much more research on the nonlinear time series in recent years, the tests for unit roots can't tell the features of time series and even result in the lost of robustness for the identification precision of the time series. 　　Because of this fact, this article tries to simulate four sets of nonlinear time series data, using both the method for estimating confidence interval based on the mean and the one for fuzzy classification to recognize the structure change period objectively with the classification standards we define in the perspective view. We also take the exchange rate as an example and recognize it using method to find out the high and low exchange period and it's structure change period.

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。

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.

本研究在探討新北市九年級的學生在七、八年級的數學課程內容上，有哪些解題上的差異(參考本文第一章第三節名詞解釋)。依據民國97年教育部修訂之九年一貫課程綱要數學能力指標，設計15題計算題，並隨機抽樣新北市五所學校九年級學生進行施測，經統計答題結果並輸入統計軟體TESTER for Windows 2.0版與SPSS 15.0中文版，得出結論歸納如以下五點： 一、不同的性別，在解題能力上，男生的答題表現明顯優於女生的只有在以下三個部份：關於價格打折的折數比例概念、複雜的乘法公式計算，以及空間圖形概念，其餘的部分沒有顯著差異。整體而言，男生的解題能力只比女生略好一點點，但並未發現有顯著的差異。 二、看起來計算複雜的題目，若需要善用解題技巧(特別是乘法公式)才容易解的出來，學生的答題表現會相當的不好。 三、解方程式的題目，學生的答題表現較佳，特別是二元一次聯立方程式的題目，會比一元一次方程式和一元二次方程式來的更好。 四、在國中七、八年級的數學課程內容，學生的答題表現最差的在於以下兩點： (一)將等差數列、等差級數的公式活用，解決生活上相關的問題。 (二)利用特殊三角形的性質，找出三角形全等的條件，證明出題目所要求的邊或角。 五、同樣都是幾何的題目，學生們對勾股定理的答題表現，會比利用特殊三角形的性質求角度，以及利用三角形全等求邊或角這兩種題目，表現得更好。 / The purpose of this study is to discuss what different ways the 9th graders use on solving the seventh and eighth's math questions in New Taipei City. According to Competence Indicators or Benchmarks of math in "Grade 1-9 Curriculum", the researcher designed 15 questions and random sampled 9th graders from five schools in New Taipei City. By analyzing these data through statistic software, TESTER for Windows 2.0 and SPSS 15.0, the researcher drew conclusions from evidence as follows: 1. About the ability to solve problems, boys just did a little better than the girls but the statistic result didn’t achieve significant difference. However, the result showed that boys actually did better than girls on three parts of the math problems – discount ratio concept, complex multiplication formula, and spatial concept. 2. Students couldn’t do very well on those problems along with complicated calculation, especially when they need to use the multiplication formula. 3. Questions about equation, students could have better performance. Besides, they could do better on linear equation in two variables than first degree polynomial in one variables and quadratic equation. 4. In math curriculums of the 7th and 8th grade, students did the worst on the following two points: (1) Solve the associated problems in their life by making good use of the formula of arithmetic progression and arithmetic series. (2) Find out conditions of congruent triangles by using the character of special triangle and prove the triangle side or angle what the question asks for. 5. When it comes to geometric questions, compared with these two kinds of questions - getting the angle by using the character of special triangles and getting a triangle side or the angle by congruent triangles, students can do better on answering Pythagorean theorem.

本研究主要目的是探討複式評量融入數學教學對不同學習風格的高二學生在圓與球面課程的學習成效。研究採用不等組前後測準實驗研究設計，以桃園縣一所完全中學高中部二年級社會組兩班共80名學生為研究對象，教師為研究者，非隨機分派一班為實驗組，進行「複式評量融入數學教學」之實驗教學，另一班為控制組，實施「傳統數學科教學」。學生學習風格採用Kolb學習風格量表區分為「主動驗證」及「被動觀察」兩類型。為探究不同學習風格的學生接受不同教學方法後，在數學學習態度、成就及保留三方面的差異性，採用二因子共變數分析之統計方法檢定研究假設，並於實驗教學後以實驗教學回饋單調查其對複式評量之看法及態度，檢定分析及調查結果整理後得如下結論。 一、排除前測影響後，學生在數學學習態度上的表現： （一）學習風格因子與教學方法因子之間沒有交互作用。 （二）學習風格因子不會造成顯著差異。 （三）教學方法因子會造成顯著差異；複式評量教學優於傳統教學。 二、排除前測影響後，學生在數學學習成就上的表現： （一）學習風格因子與教學方法因子之間有交互作用。 （二）以傳統教學法而言，學習風格因子會造成顯著差異；主動驗證風格優於被動觀察風格。 （三）以被動觀察風格而言，教學方法因子會造成顯著差異；複式評量教學法優於傳統教學法。 （四）以被動觀察風格接受傳統教學法後為最差。 三、排除前測影響後，學生在數學學習保留上的表現： （一）學習風格因子與教學方法因子之間有交互作用。 （二）以複式評量教學法而言，學習風格因子會造成顯著差異；主動驗證風格優於被動觀察風格。 （三）以主動驗證風格而言，教學方法因子會造成顯著差異；複式評量教學法優於傳統教學法。 （四）以主動驗證風格接受複式評量教學法後為最佳。 四、實驗組學生在圓與球面課程實施「複試評量融入數學教學」後，絕大多數的學生喜歡此教學方法，而對未來數學課程實施「複試評量融入數學教學」則絕大多數抱持贊成的看法。 最後針對研究結果提出數點建議，以供教師教學及後續研究之參考。 / The purpose of this study is to explore the effects on learning performance of 11th graders based on two factors – teaching methods and learning styles. This study was conducted as a quasi-experimental design. Two classes,which have a total of 80 students, were sampled from a high school in Taoyuan County. One was assigned as an experimental group and the other one as a control group. The first one took a “composite assessment embedded in mathematics teaching” method learning, while the second one took a “traditional mathematics teaching” method learning respectively. This study used the learning styles inventory (LSI) of Kolb to classify learners into two groups – “active experimentation (AE)” and “Reflective Observation (RO)”. Two-way ANCOVA was conducted to test all hypotheses in order to find variations of mathematical learning attitudes, mathematical learning achievements, and mathematical learning retention. The study also investigated the views of points of the students in control group after the experiment. According to the analysis, we reach the following conclusions︰ 1. In mathematical learning attitudes: (1) Teaching methods and learning styles don’t interact significantly. (2) There is no significant difference between two learning styles. (3) There is a significant difference between two teaching methods. The effect on experimental group is better than that on control group significantly. 2. In mathematical learning achievements: (1) Teaching methods and learning styles interact significantly. (2) For the control group, there is a significant difference between two learning styles. The effect on style AE is better than that on style RO significantly. (3) For the style RO, there is a significant difference between two teaching methods. The effect on experimental group is better than that on control group significantly. (4) The effect on control group with the style RO is the worst. 3. In mathematical learning retention: (1) Teaching methods and learning styles interact significantly. (2) For the experimental group, there is a significant difference between two learning styles. The effect on style AE is better than that on style RO significantly. (3) For the style AE, there is a significant difference between two teaching methods. The effect on experimental group was better than that on control group significantly. (4) The effect on experimental group with the style AE is the best. 4. After the experiment, most of the students in the experimental group like “composite assessment embedded in mathematics teaching” method. They also agree that “composite assessment embedded in mathematics teaching” should be conducted in the future. Finally, suggestions for the teachers and future researches are also discussed.

本研究主要依據建構主義理論基礎，在一般教學和學習理論基礎上建構所謂的「建構主義取向的教學方法」。為探討建構取向教學法在數學學習成效的效果，乃選取國中一年級兩個班為研究對象，進行為期兩個月的教學實驗，以進行實地的建構取向教學與傳統教學之比較，並對學生在教學前後與其間所填答的問卷或資料進行分析，本研究所採的研究工具計有：(一)數學段考考卷；(二)數學學習成就測驗；(三)國中新生數學能力測驗；(四)數學學習經驗量表；(五)學習日記表格；(六)數學學習回饋問卷。使用的資料分析方法有：(一)獨立樣本單因子共變數分析；(二)質的分析。精分析結果如下： 一、建議教學組的學生與傳統教學組的學生在數學段考成績無顯著差異存在。 二、建構教學組的學生與傳統教學組的學生在數學學習成就測驗後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 三、建構教學組的學生與傳統教學組的學生在數學焦慮量表後測得分無顯著差異存在。 四、建構教學組的學生與傳統教學組的學生在數學動機信念量表後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 五、建構教學組的學生與傳統教學組的學生在班級氣氛量表後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 六、建構教學組的學生與傳統教學組的學生在民主溝通態度量表後測得分無顯著差異存在。 七、由接受建議教學法的學生的數學學習回饋問卷與學習日記上可發現多數學生對建議教學持正面肯定的態度。 本研究針對上述發現加以討論，並對數學教學、行政措施與未來研究提出若干建議以供參考。 / The experiment on math achievement of the seventh grade students - the constructvist approach

本研究的主要目的在於比較「GSP融入數學教學」與「傳統講述教學」對學生學習幾何課程之成效，並探討實驗組學生經由「GSP融入數學教學」後的態度與看法，以便可以作為將來在國中階段發展GSP輔助教學之參考。 本研究採不等組前後測準實驗研究設計，以桃園縣某國中三年級兩班共67名學生為研究對象，非隨機分派一班為實驗組，進行GSP融入數學教學；另一班為控制組，進行傳統講述教學，經由Kolb學習風格量表受測，區分為「具體經驗」及「抽象概念」兩類的學生，教學實驗為期六週共十二節課，教學內容為國三第五冊幾何單元「圓」，探究不同性別與不同學習風格之學生分別接受不同教學方法之後，在數學學習態度、學習成就與學習保留上的差異，採用二因子共變數分析統計方法驗證假設，並於實驗教學後針對實驗組做「GSP使用態度調查表」以了解學生的態度與反應。檢定分析與調查結果，得到以下結論： 一、排除前測影響後，學生在數學學習態度上的表現： (一)不同教學方法分別與不同性別、不同學習風格之間沒有交互作用。 (二)不同性別、不同學習風格均無顯著差異。 (三)不同教學方法會造成顯著差異；GSP融入數學教學優於傳統講述教學。 二、排除前測影響後，學生在數學學習成就上的表現： (一)不同教學方法分別與不同性別、不同學習風格之間沒有交互作用。 (二)不同性別、不同學習風格均無顯著差異。 (三)不同教學方法會造成顯著差異；GSP融入數學教學優於傳統講述教學。 三、排除前測影響後，學生在數學學習保留上的表現： (一)不同教學方法與不同性別之間沒有交互作用，且均無顯著差異。 (二)不同教學方法與不同學習風格之間有交互作用。 (三)以GSP融入數學教學而言，不同學習風格會造成顯著差異；抽象概念的學生優於具體經驗的學生。 (四)以抽象概念風格而言，不同教學方法會造成顯著差異；GSP融入數學教學優於傳統講述教學。 四、實驗組學生使用GSP態度分析 實驗組學生在幾何單元「圓」實施「GSP融入數學教學」後，絕大多數的學生喜歡此種教學方法，並抱持著正向及肯定的學習態度。 最後根據研究結果提出具體建議，以供學校、教師及未來研究者參考。 / The main purpose of this study is to compare the effectiveness of learning geometry using new teaching method (i.e. GSP in mathematics teaching) and traditional teaching method. For the possibilities of applying GSP to junior high school math teaching in the future, this study also analyze how students learn and react toward ‘GSP in mathematics teaching’. There are two grade 9 classes with totaled 67 students in the study. One class is assigned as the experimental group (i.e. GSP in mathematics teaching). Another class, the control group, is taught by traditional narrative teaching. All student are categorized, based on Kolb Learning Style Inventory(LSI), into two types: Concrete Experience and Abstract Conceptualization. The experiment consists of 12 classes in 6 weeks. The geometry content is ‘circle’, in book V for 9th graders. The study analyzes how students with different learning styles and genders react to these two math teaching methods. The attitudes , achievements and retentions of students learning are the main interests. The hypotheses are tested using two-way ANCOVA. Students in the experimental group are further evaluated with GSP questionnaire at the end of the experiment. The conclusions are as follow: I. For the attitude of students in learning math: 1. There is no interaction between teaching method and gender and between teaching method and style. 2. There is no significant difference between different genders and between different learning styles. 3. Different teaching methods have significant difference: GSP in math teaching is much better than traditional narrative teaching. II. For the achievement of students in learning math: 1. There is no interaction between teaching method and gender and between teaching method and style. 2. There is no significant difference between different genders and between different learning styles. 3. Different teaching methods have significant difference:GSP in math teaching is much better than traditional narrative teaching. III. For the retention of students in learning math. 1. There is no interaction between teaching method and gender. In addition , there are no significant differences between teaching method and between different gender. 2. There is interaction between teaching method and learning style. 3. Learning styles have significant difference when GSP is used in math teaching. Students categorized in Abstract Conceptualization perform better than those in Concrete Experience. 4. Among those Abstract Conceptualization students from GSP in math teaching class is significantly better than those from traditional narrative teaching. IV. For the attitude of students with GSP: Most students in experimental group are fond of GSP in math teaching, and hold a positive attitude toward learning . Finally, suggestions based on this study will be provided for school authority, teachers and other researchers. Keyword: GSP, computer-assisted instruction, learning style, mathematics learning attitude, mathematics learning achievement, mathematics learning retention, ANCOVA

本研究主要目的是以文獻分析、問卷調查、潛在成長模式等方法探討數學焦慮、數學學習動機與數學學業成就等三個變項的縱貫模式及因果結構模式。根據五百二十九位國三學生所填的五波調查問卷資料，進行兩部分研究。 研究一乃在估算數學焦慮、數學學習動機、數學學業成就的潛在改變量模式及 數學焦慮、數學學習動機、數學學業成就兩兩之間的因果結構模式。結果發現1.數學焦慮縱貫模式上，符合「焦慮遞增理論」；2.數學學習動機縱貫模式上，符合「動機先升後降理論」；3.數學學業成就縱貫模式上，符合「成就先升後降理論」； 4.數學焦慮與數學學習動機因果結構模式上，符合「動機焦慮交互激發效果理論」；5.數學焦慮與數學學業成就因果結構模式上，符合「焦慮成就交互抑制效果理論」；6.數學學習動機與數學學業成就因果結構模式上，符合「動機成就交互激發效果理論」。 研究二則依據研究一二變項因果結構統計驗證成立的三套理論，建構出三變項因果結構六模式，並驗證有無中介效果。結果顯示，1.前焦慮、中動機、後學業成就因果模式上，符合「動機未完全中介前焦慮、後學業成就理論」；2. 前動機、中焦慮、後學業成就因果模式上，符合「焦慮未完全中介前動機、後學業成就理論」；3.前焦慮、中學業成就、後動機因果模式上，符合「學業成就未完全中介前焦慮、後動機理論」；4.前學業成就、中焦慮、後動機因果模式上，符合「焦慮未完全中介前學業成就、後動機理論」；5. 前動機、中學業成就、後焦慮因果模式上，符合「學業成就未完全中介前動機、後焦慮理論」；6.前學業成就、中動機、後焦慮因果模式上，符合「動機未完全中介前學業成就、後焦慮理論」。 除了上述結果外，研究也對數學焦慮、數學學習動機與數學學業成就縱貫模式的趨勢與時間效果量，國三學生轉折點界定，數學焦慮、數學學習動機與數學學業成就適當模式產出及個別中介角色剖析有深入探討。 / This study, using literature review, questionnaire survey, and latent growth model, investigated the longitudinal model and causal model among math anxiety, learning motivation, and academic achievement. After collecting 529 students with 5 waves, I conducted two studies. The purpose of study 1 was to estimate the latent change model and the causal model of math anxiety, learning motivation, and academic achievement. Results showed that 1. The anxiety increasing theory was supported by the math anxiety longitudinal model. 2. The first increasing then decreasing theory was supported by the math learning motivation longitudinal model. 3. The first increasing then decreasing theory was supported by the math academic achievement longitudinal model. 4. The reciprocal activated effect theory was supported by the math anxiety and learning motivation causal models. 5. The reciprocal inhibitive effect theory was supported by the math anxiety and academic achievement causal models. 6. The reciprocal activated effect theory was supported by the math learning motivation and academic achievement causal models. According to the final three theories stated above and proved by study 1, I constructed the six causal models in order to verify the mediated effects of math anxiety, math learning motivation, and math academic achievement. I found that 1. Math learning motivation did not mediate fully the effects on early math anxiety and late math academic achievement. 2. Math anxiety did not mediate fully the effects on early math learning motivation and late math academic achievement. 3. Math academic achievement did not mediate fully the effects on early math anxiety and late math learning motivation. 4. Math anxiety did not mediate fully the effects on early math academic achievement and late math learning motivation. 5. Math academic achievement did not mediate fully the effects on early math learning motivation math and late math anxiety. 6. Math learning motivation did not mediate fully the effects on early math academic achievement and late math anxiety. In addition, the research also explored the longitudinal model trend and effect, the key period for 3rd year junior high school students, the proper models, and the mediated roles among math anxiety, learning motivation, and academic achievement.