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.

本研究主要目的在瞭解透過動態評量回饋系統輔助教學對提升國中數學學習成效及數學學習態度的影響。本研究針對新北市某國中八年級兩班學生共38人，每週進行五節，總計為六週之數學教學實驗。本研究採準實驗研究設計，自變項為教學模式，在實驗組以動態評量回饋系統融入學習之數學教學課程而在對照組使用一般傳統教學方法進行數學評量及回饋課程。依變項為「數學學習成效測驗」、「數學學習態度量表」，共變項為八上三次段考平均。以單因子共變數分析與二因子重複量數混合設計變異數分析進行統計分析，研究結果如下: 一、在數學科學習成效方面：以動態評量回饋系統輔助數學教學，能提升數學科學習成效。 二、在數學學習態度方面：在數學學習態度分向度之「外在動機」向度上，實驗組與對照組有顯著差異，證實以動態評量回饋系統輔助數學教學，能提升數學學習態度之外在動機。在數學學習態度整體面向並未有顯著差異，證實以動態評量回饋系統輔助教學並未能提升數學整體學習態度。 三、學生對動態評量回饋系統輔助教學的回饋： 1、學生普遍具有正向、積極的反應。 2、學生願意多花時間來加強數學的學習。 綜上所述，本研究針對結果提出具體建議，以提供教學設計、數學教學及未來相關研究之參考。 / The purpose of this study was to investigate junior high school students’ mathematics learning achievement by using a Dynamic Assessment and Feedback (DAF) system. The overall investigation process is designed as a quasi-experiment, where two classes of eighth-grade junior high school students in New Taipei County were randomly assigned to either the experimental(n=18) or the control groups(n=20). It took totally six weeks, and there were five classes per week to perform the instructional experiments. In the experiments, the independent variables were instructional strategies and the dependent variables were Mathematics Achievement Test and Mathematics Learning Attitude. The measurement instruments include Questionnaire for Mathematics Learning Attitude, Mathematics Achievement Test, and Questionnaire for Students’ Perception of Mathematics Instruction with DAF system. According to the students’ Mathematics Achievement Test, the statistical analysis was performed by one-way ANCOVA. By conducting t-test for the scores of the math learning attitude measurement, the analysis of math learning attitude was carried out by the two-way Mixed ANOVA. After analyzing the data, the findings of this study are summarized below: 1.Mathematics Achievement: The experimental group scored higher in the Mathematics achievement test than the control group did. 2.Mathematics Learning Attitude: No significant interaction between the teaching methods was found in attitude for learning Mathematics. A significant difference was found between the experimental group and the control group in their extrinsic motivation for Mathematics Learning Attitude. 3.The students’ feedback after the (DAF) system mode: I.Most students in the experimental group did enjoy the DAF system. II.Most students were willing to spend more time using the DAF system to practice Mathematics. Finally, based on these findings, this study proposes several suggestions for school administrators, teachers in junior high school math curriculum and future research are also discussed.

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.