This master's thesis is focused on knowledge discovery from databases, especially on methods of mining sequential patterns. Individual methods of mining sequential patterns are described in detail. Further, this work deals with extending the platform Microsoft SQL Server Analysis Services of new mining algorithms. In the practical part of this thesis, plugins for mining sequential patterns are implemented into MS SQL Server. In the last part, these algorithms are compared on different data sets.

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In this article, based on Dissection-Motion-Operations, DMO (decomposing a figure into several pieces and composing the resulting pieces into a new figure of equal area), a set of visual representations (models) of mathematical concepts will be introduced. The visual models are producible through manipulation and computer GSP/Cabri software. They are based on the van Hiele’s Levels (van Hiele, 1989) of Thought Development; in particular, Level 2 (Informal Deductive Reasoning) and level 3 (Deductive Reasoning). The basic theme for these models has been visual learning and understanding through manipulatives and computer representations of mathematical concepts vs. rote learning and memorization. The three geometric transformations or motions: Translation, Rotation, Reflection and their possible combinations were used; they are illustrated in several texts. As well, a set of three commonly used dissections or decompositions (Eves, 1972) of objects was utilized.

In this article, based on Dissection-Motion-Operations, DMO (decomposing a figure into several pieces and composing the resulting pieces into a new figure of equal area), a set of visual representations (models) of mathematical concepts will be introduced. The visual models are producible through manipulation and computer GSP/Cabri software. They are based on the van Hiele’s Levels (van Hiele, 1989) of Thought Development; in particular, Level 2 (Informal Deductive Reasoning) and level 3 (Deductive Reasoning). The basic theme for these models has been visual learning and understanding through manipulatives and computer representations of mathematical concepts vs. rote learning and memorization. The three geometric transformations or motions: Translation, Rotation, Reflection and their possible combinations were used; they are illustrated in several texts. As well, a set of three commonly used dissections or decompositions (Eves, 1972) of objects was utilized.

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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.

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics FCAT results were examined to determine if the GSP produced any effects. Students’ scores were compared based on assignment to the control or experimental group as well as gender and SES. SES measurements were based on whether students qualified for free lunch. The findings of the study revealed a significant difference in the FCAT mathematics scores of students who were taught geometry using GSP compared to those who used the traditional method. No significant differences existed between the FCAT mathematics scores of the students based on SES. Similarly, no significant differences existed between the FCAT scores based on gender. In conclusion, the use of technology (particularly GSP) is likely to boost students’ FCAT mathematics test scores. The findings also show that the use of GSP may be able to close known gender and SES related achievement gaps. The results of this study promote policy changes in the way geometry is taught to 10th grade students in Florida’s public schools.