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The purpose of this study came to start to be helpful in that the teachers in field produced evaluation subject about the mathematics and applied by analyzing the performance capacity for the students about the subject developed through the application of subject about the teaching-learning model that can utilize the learners' learning experience and the development of items that can evaluate it by utilizing various and concrete operational materials as an object of the first year at the middle schools. The concrete purpose of realizing it is as follows. 1. This study is to develop the teaching-learning model centered on activities adequate to utilize various and concrete operational materials. 2. This study is to develop evaluation data for utilizing the concrete operational materials by making construction through the application of developed teaching-learning model as possible. 3. This study is to present standards initiative for reliable and fair marking about the evaluation data and to analyze the students' practice capacity by using it effectively. For accomplishing the purpose of this research, this study is the work-oriented teaching and learning model using learning data that can be easily found around the surroundings and 8 evaluation programs in order that the experience-oriented learning based on circumstances learning among the learning models of constructivism. Also, it is to examine the result after applying that on a basis of 25 students, consisted of only on class in a year, in the first year at the small size of agricultural middle schools. The result of this study from this research is as follows. First, as a result of frequency survey, of response about the developed evaluation data it showed positive response more than 80% of all the items. The atmosphere of self-directed learning was produced because the developed evaluation data could induce activity-based learning naturally by stimulating the students' curiosity and promoting interest. Second, this study executed t-test for the result of questionnaire about the mathematics propensity, and there were significant differences in 19 items among 25 items. It presented that the application of data about the teaching-learning and evaluation directly using concrete operational materials to the constructional learning by level might have desirable affect on the students' mathematical propensity. It came to be a motive that could increase value recognition and interest on the subject of mathematics by investigating a mathematical principle rule and confirming it through activity learning using the concrete operational materials.

The purpose of this study is to analyze thinking process in problem solving and to get some teaching materials to improve students' problem solving abilities. For this study, 14 girl and boy students in highschool were tested with 7 testing questions. The whole process of students' problem solving was observed by using 'Thinking aloud', recorded by Audio Tape and finally drawn up to Protocol. On the basis of that Protocol, coding system was set up and characteristics of thinking process in each stage were analyzed. -In the stage of planning, successful problem solvers tried to check the properties of words included in problems(Pr) and made it clear that they were seeking(O) -In the stage of planning, students used abstraction strategy(Ab, making equation(E) or using variable(V)) appropriately could solve more difficult problems. Successful problem solvers turned used unsystematical trial into systematical method and were good at using partial objects, assistant factors. - In the stage of carring out the plan, successful problem solvers to reduce the error, check the purpose, used formula, knowledge and calculation. -In the looking back stage, successful problem solvers generalized the answer and checked the total process.

The purpose of this study is to investigate the effects of a mathematics basis underachiever program on a mathematics achievement and mathematics attitudes. For this investigation, twenty eight-grade students as an experimental group were trained in a mathematics basis underachiever program by trained teachers in a middle school classroom for a period of 8 weeks. Twenty eight-grade students in another middle school, serving as a control group. Both groups were given a pretest and a posttest to check the mathematics achievement inspection tool(Likert-type Mathematics Attitude Survey; LTMAS) and a mathematics attitude inspection tool(KEDI, 2001). In the analysis of data Frequencies, percentiles, t-test were used. The results of the study are summarized as follows; First, the results showed that the experimental group demonstrated significantly higher differences than the control group in the mathematics achievement components of inequality equation, figure area and the whole in a mathematical achievement(p<.05). Second the results showed that the experimental group demonstrated significantly higher differences than the control group in the mathematics attitude components of positive mathematics attitude, negative mathematics attitude and the whole in a mathematical attitude(p<.05).

In case of Korea, while discrete mathematics is included in the traditional school curriculum the 7th Educational Reform adds a new topic of Graph Theory making it an optional subject of highschool mathematics. However, a systematic research on the curriculum of discrete mathematics is still unsatisfactory. This study is focused on comparing the curriculum of discrete mathematics in Korea with that of other countries including the United States, Britain, Japan, and Canada. Consequently, it looks into problems concerning the school curriculum of discrete mathematics in Korea to devise a proper measure to improve.

This study purported to develop the learning materials for the optional activities of mathematics, apply them to the students, and examine the effect on the learner's interest and attitude to mathematics. In order to conduct this study, the learning materials for the mathematics optional activities were developed according to the units of grade 8-Ga and the developed learning materials of the mathematics optional activities were inputted in two classes for 18 units after the second grade middle school students in Daejeon area received the questionnaire regarding the learning attitude and the interest in the mathematics. After that, the questionnaire regarding the learning attitude and the interest in the mathematics and the examination regarding the response to the application of the learning materials for mathematics optional activities were conducted and did t-test. The results of the study as follows : First The learning materials applied exciting games for mathematics optional activities aroused interest in mathematics and made the learners have confidence in mathematics learning. Second, There was affirmative change in the interest and attitude to the mathematics learning with the application of the mathematics optional learning materials. Third The leaning materials of the mathematics optional activities made the learners think mathematical questions connected with the real life and try various ways to solve the questions. Here are some suggestions to study the development of the learning materials such as story, game, quiz and craft. First it is necessary to develop the learning materials applied the games or the real life matters connected with mathematics for all grade middle school students and use them in the mathematics optional activities. Second, many students feel a great interest in animation. moving picture, sound graphic, etc. If the multimedia learning materials included the real life matters or the games are developed, the learners will feel more interest in mathematics. Third, the systematic and economical support is continuously needed in order that teachers are given much time to study and the opportunity to attend the training course for the understanding of the optional activities and the development of the various learning materials.

Among interactive dynamic geometry softwares, Cinderella has some merits on the accuracy of algorithms and compatibility with internet. In this paper we compare dynamic geometry softwares such as GSP, Cabri II, Cinderella briefly and we design a web based interactive learning materials using the exercise editor of Cinderella and some Java applets, and we propose a web based interactive teaching and learning model in which achievement test can be given by the clickings on the help icon.

This study concentrates on investigating teaching methods with which students of a commercial high school, located in a rural district, can improve their attitude toward mathematics. To begin with, this study examines the causes which make the students take negative views against it through a survey of their current attitude toward mathematics; offers a special class for them to develop a positive attitude toward it: and then, figure out how much they change their academic attitude within the class and how much they improve their academic achievement as well. The results can be summarized as follows: First, the experimental groups showed terribly negative attitudes toward mathematics, and their academic achievements were very low compared with students of academic high schools nearby, Second, thanks to the special class given to improve their attitude toward mathematics, the experimental groups ended up taking a meaningful positive attitude toward it and developing their academic achievements in the subject. On the other hand, the controlled groups without any chance to receive special lessons remained unchanged. Therefore, it is indicated that a special lesson, properly provided, would play an important role to improve students' positive attitude toward mathematics and develop their basic academic achievements.