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.

本研究旨在探討分段式評量教學法對高二學生於學習數學時學習成就的影響。研究對象為台北縣某國立高中二年級理組學生，分為實驗組42位及控制組44位共86位學生，以20週的時間進行實驗，觀察分析其學習成就的改變。 本研究結果發現，在相同教學時間下： 1. 分段式評量教學法在整體學習成就方面有正面影響且結果達顯著差異。 2. 對不同學習風格學習成就之正面影響雖未達顯著水準，但學習成就相對改善值似乎有增加的趨勢。 3. 對不同學習程度分組而言，中分組與低分組學生之學習成就方面有正面影響且達顯著差異。 4. 實施分段式評量教學法的學生比使用傳統教學法的學生在學習態度方面似乎較不會有放棄數學的現象。 綜而論之，分段式評量教學法可提供教學者，在面對數學學習成就低落的學生一個有效的引導方法，讓這些學生不僅不會放棄數學，還能漸漸的建立良好的學習習慣。 / This research mainly aims at evaluating how divided assessment teaching method would effect junior students’ mathematics-learning performance in high school. A case study was conducted on science-team junior students in a Taipei-county high school, composed of 42 students in experimental group and 44 ones in control group respectively, amounting to 86. This experiment spanned as long as 20 weeks for analysis on how students’ learning performance would be benefited. It is thus concluded in this research after evaluating both 2 group’s learning performance in term of equal length of time as below: 1. Divided assessment teaching method would have positive effect on learning performance at significance level. 2. Although divided assessment teaching method has positive effects on learning performance for various learning style subgroups, these positive effects are not significant. Their relative improvements of learning performance seemed to be increased, too. 3. When evaluated in term of original-performance level, students’ learning performance in average-level and in inferior-level subgroups both would be benefited positively at significance level. 4. Students taking divided assessment teaching method would have more persistent learning attitude than those taking traditional teaching method. In summary, divided assessment teaching method could help teachers to offer more effective teaching-guidance to students who had inferior learning performance. As a result, students would not only persist in mathematics learning but also cultivate enthusiastic learning attitude gradually.

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.