在教育改革浪潮下，台灣師資培育制度於1994年師資培育法公布之後，正式進入多元培育的體制。新制實施後，引發不少爭論。主要爭論焦點之一為新制培育的教師，其教師素質是否比舊制培育者為低。主張單一培育制度者認為師範院校具有獨特潛在課程，潛移默化學生專業精神，因而學生素質較佳；多元師資培育制度者則認為市場競爭、教師專業化取向有利提高教師素質。 本研究主要目的即透過「台灣教育長期追蹤資料庫」（TEPS）第二波國中教師及學生之資料，比較不同培育背景之數學教師於教師素質及學生數學成就上之差異，並釐清過去關於師資培育之爭論。 本研究數學教師樣本數為7,001，依據教師年資、是否就讀師範院校，以及是否修習教育學程等標準，將數學教師培育背景分成新制、舊制，及師範與非師範院校等共七類。教師素質則包含與教學效能及教師專業承諾等兩面向相關之指標。學生數學成就則以TEPS提供之數學能力IRT分數為指標。 本研究依不同研究假設，進行卡方檢定、單因子變異數分析、多元迴歸等統計分析。主要發現如下： 一、師範院校與非師範院校培育之教師相比，其教學效能及教師專業承 諾有顯著差異。在教學效能上，師範院校生較常使用傳統教學策略與教材，非師範院校生則較常使用新制教學策略與教材及常測驗考試；在教師專業承諾上，非師範院校生則表現較佳。但兩者在學生學習成就上則無顯著差異。 二、舊制與新制培育之教師相比，其教學效能及教師專業承諾有顯著差異。教學效能方面，舊制生於其他教材層面表現較佳，新制生則於維持秩序及常測驗考試層面表現較佳；而教師專業承諾上，舊制生於研究進修層面表現較佳，新制生則於教學不厭倦層面表現較佳。但舊制生於學生學習成就表現較佳。 雖然研究發現，不同培育背景之教師，其教學效能、教師專業承諾、及學生數學成就表現有顯著差異。但進一步分析，則發現整體而言，這些差異並不是很大。由此可見，多元師資培育政策並未影響教師素質，而一般大學師資培育機構之培育功效亦不亞於師範院校之師資培育機構。綜觀以上發現，可發現「教育系統標準化」的觀點更合乎台灣的現況。台灣之師資培育與學生的學習成就，在「國家機器」嚴格的控制把關之下，能夠維持一定水準。 / The pre-service teacher education in Taiwan has become multi-training since 1994. Considerable debates have been arisen since then, and one of which is “Teaching Quality.” Some argue that multi-training policy worsens teaching quality. For they think Normal Schools, providing more latent lessons to students’ spirit, are better than other pre-service teacher education programs. On the other hand, some argue that the new multi-training policy would advance teaching quality by the market competition and teacher’s professionalism. The main purpose of this study is to utilize the data of “Taiwan Education Panel Survey” (TEPS) to compare the effects of pre-service teacher education programs on the teaching quality and students’ math achievement in a bid to solve the controversy. In this study, the teachers’ sample, divided into 7 categories according to their teaching experience and training background, is 7001. Besides, “teaching quality” includes “teaching efficiency” and “teacher’s professional commitment.” “Students’ math achievement” is based on students’ math IRT score provided by TEPS. The study mainly utilizes statistical analyses based on Chi-square analysis, ANOVA, Regression analysis and so on, The study finds out, although teachers of different training backgrounds have significant differences on their teaching efficiency, teacher’s professional commitment and students’ math achievement, the differences are not magnificent. In other words, the effects of different pre-service teacher education programs on the teaching quality and students’ math achievement are not much diverse. The result suggests that under firm control of “the state apparatus”, teaching quality and students’ academic achievement in Taiwan could maintain at a level.

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

本研究主要目的是探討GSP電腦輔助教學對國三學生學習三角形外心、內心及重心之成效。研究採用準實驗研究法中之不等組前後測設計，以桃園縣一所國中三年級四班共127位學生為研究對象，分派兩班為實驗組共63位學生，進行GSP電腦輔助教學課程；另兩班為控制組共64位學生，進行一般傳統講述教學課程。學生學習風格採用Kolb學習風格量表區分成「主動實驗」及「省思觀察」兩種類型，為探究不同學習風格之學生接受不同教學方法之後，在數學學習態度、成就與保留上的差異，採用二因子共變數分析檢定研究假設。並於實驗教學後，以GSP電腦輔助教學意見調查表調查其看法及態度，整理檢定分析及調查結果後得到以下結論： 一、排除前測影響後，學生在數學學習態度上的表現： (一)教學方法因子效果及學習風格因子效果之間沒有交互作用。 (二)教學方法因子效果有顯著差異；GSP電腦輔助教學法優於傳統講述教學法。 (三)學習風格因子效果沒有顯著的差異。 二、排除前測影響後，學生在數學學習成就上的表現： (一)教學方法因子效果及學習風格因子效果之間有交互作用。 (二)對學習風格為省思觀察者而言，教學方法因子會造成顯著的差異；GSP電腦輔助教學法優於傳統講述教學法。 (三)以省思觀察者接受傳統講述教學法後表現最差。 三、排除前測影響後，學生在數學學習保留上的表現： (一)教學方法因子效果及學習風格因子效果之間沒有交互作用。 (二)教學方法因子效果有顯著差異；GSP電腦輔助教學法優於傳統講述教學法。 (三)學習風格因子效果沒有顯著的差異。 (四)以省思觀察者接受GSP電腦輔助教學法後表現最佳。 四、GSP電腦輔助教學的看法及態度方面： 主動實驗者表示GSP電腦輔助教學提供了實際操作的機會，而省思觀察者則表示GSP電腦輔助教學提供了詳盡的說明和動態演示。就實驗組學生使用GSP電腦輔助教學而言，大多抱持著正向及肯定的學習態度。 / The purpose of this study is to explore the effects on learning performance of circumcenter, incenter and centroid of a triangle by 9th graders based on computer -assisted instruction using GSP in mathematics teaching. This study was conducted as a quasi-experimental design. Four classes, which have a total of 127 students, were sampled from a junior high school in Taoyun County. Two classes were assigned as experimental group and the others as control group. The former took “computer -assisted instruction using GSP in mathematics teaching” method learning, while the latter two took “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 achievenments, mathematical learning retention. The study also investigated the views of points of the students in experimental group after the experiment. According to the analysis from the experiment, this study reached the following conclusions︰ 1.In mathematical learning attitudes: (1)Learning styles and teaching methods did’t interact significantly. (2)There was a significant difference between two teaching methods. The effect on experimental group was better than the control group. (3) There was no significant difference between two learning styles. 2.In mathematical learning achievements: (1)Learning styles and teaching methods interact significantly. (2)For the style RO, there was a significant difference between two learning styles. The effect on experimental group was better than the control group. (3)The effct on control group with the style RO was the worst. 3.In mathematical learning retention: (1)Learning styles and teaching methods did’t interact significantly. (2)There was a significant difference between two teaching methods. The effect on experimental group was better than the control group. (3) There was no significant difference between two learning styles. (4)The effct on experimental group with the style RO was the best. 4.After the experiment, most students in experimental group with the style AE said that “the experimental curriculums had provided the actual operation opportunity”; most students in experimental group with the style RO said that “the experimental curriculums had provided the exhaustive explanation and the dynamic demonstration”. They also agreed that the experimental curriculums were better.

為達成「精熟學習」的教與學過程中強調的個別化教學、學生學習的回饋、校正學生學習錯誤等高效能的教學理想。本研究自行發展一套數位化診斷系統，在不改變學校政策、班級作息、教室管理實施情況下，對準備參加科大入學測驗高工三年級的學生，在考前六週進行數學科總複習的「精熟學習配合數位化診斷」實驗教學。經由學生的作答反應，本診斷系統完成以下功能： (1)能快速的篩選出優良試題，並提供試題的難度、鑑別度、答對率與評鑑試題的品質。 (2)能診斷出個別學生與試題的差異性，並完成試題卷的信度、效度評鑑與S-P分析表。 (3)能提供完整的學習成就遷移記錄，並可歸類出學生學習潛能與整體學習表現。 (4)能彙整出學生學習成效與具體教學建議。 教師藉診斷系統所提供的資訊，對學生進行個別化校正或充實教學，期以達成精熟學習的教學理想。並在實驗教學後分析學生學習回饋單，大多數學生對實驗教學法持正面態度，且自認學習態度更積極，並建議若能提早實施精熟學習配合數位化診斷教學，應會有更好成績表現。 本研究並探討「實驗教學」的實驗A組學生，分別對「不同科別」的實驗B組學生與對「傳統教學」的控制C組學生的數學學習態度、學習成就、學習成就絕對均差的差異性，經單因子共變數分析，排除前測影響後，具體結論如下： (1)實驗A、B組與控制C組學生在數學學習態度後測得分並無明顯差異。 (2)實驗A組與控制C組在數學學習成就後測成績有明顯差異，且實驗A組分數明顯高於控制C組。 (3)不同科別實驗組的A組電機類與B組機械類學生，在數學學習成就後測成績有明顯差異，且電機類分數明顯高於機械類，但機械類排除未完成實驗的學生後，則不同科別的實驗A組、實驗B組，在數學學習成就後測成績無明顯差異。 (4)實驗A組與控制C組學生在數學學習成就後測成績的絕對均差有明顯差異，且實驗A組絕對均差小於控制C組。 最後為使實驗教學能更順利進行，建議教學前先營造愉快與舒適教學環境與良好的師生互動情誼再實施，這將會是實驗教學成功的關鍵 / Mastery Learning Strategy is a highly effective teaching method, emphasizing the importance of individualized tutoring, student feedback and learning error correction. In this study, a self-devised computerized diagnostic system was developed for the third-year vocational high school students who were preparing for the technological university entrance examination. An experimental teaching method using Mastery Learning Strategy with computerized diagnostic system was given to the aforementioned students as a math review lesson six weeks before the entrance examination, following the original school policy, class schedule or class management. From test responses, the diagnostic system achieved the following: (1)Quick selecting of good quality test items. It also evaluates the test items and provides the difficulty, discrimination, and correction rates of them. (2)Individualized diagnosis of each student vs. test items. It also completes the reliability, validity and S-P charts of the test. (3)Offering a comprehensive record of the learning process. It also analyzes the learning process of the students and sorts out their learning potential. (4)Analyzing students’ learning effects and coming up with teaching suggestions. In this experiment, the data gained from the diagnosis were used to provide each student with individualized instruction or error correction with the hope of attaining the goals of Mastery Learning. The analysis of the students’ feedback after the experimental teaching method showed that most students thought positively of the experiment, admitting that they developed a more aggressive learning attitude, and suggested that this computerized diagnostic system, had it been implemented earlier, would have helped them achieve even better grades. The students in this study consisted of three groups. Group A and B were both experimental groups except that group A were students from electrical engineering department while group B were students from mechanical engineering department. Group C was the control group receiving only conventional teaching method. Group A was compared with group B and group C respectively in terms of differences in math-learning attitude, math-learning achievement, and in the absolute mean deviation of learning achievement. By means of one-way analysis of covariance, with pre-test effects eliminated, the conclusions were as follows: (1)None of the groups exhibited significant grade differences on the math-learning attitude post-test. (2)Group A scored significantly higher on the math-learning achievement post-test than did Group C, the control group. (3)Group A of electrical engineering students scored significantly higher on the math-learning achievement post-test than did Group B of mechanical engineering students. However, if the grades of the Group B students who didn’t complete the experiment were unaccounted, no grade difference was noticeable on the math-learning achievement post-test between Group A and Group B. (4)Group A, the experimental group, had significantly lower absolute mean deviation on the math-learning achievement post-test than did Group C, the control group. Finally, it was suggested that creating a comfortable environment for teaching and learning as well as an advance establishment of a good teacher-student rapport are the key to a smooth-going and successful experimental teaching method.