This study is for finding out if using the method "Mind Map" in the section "function" during the math class affects on the disposition and solving problems of the students or not The study has found the following results: 1. The chains of concepts has formed by using both right brain and left brain in the students′ notebooks. 2. The power of math in the ability of solving problems has been strengthened.

The idea to be changed first among the general ideas of mathematics is that, from the standpoint of teachers, one-sided teaching is efficient due to the progress of classwork of excessive quantity, and, from the standpoint of students, they say they gave up mathematics publicly feeling uneasiness in every class because of the deficiency of previous learning and interest, and they think all problems are due to the educational system, neglecting their studies, not participating actively in lessons. Therefore this study is, after giving learning points and problem papers of which the degree of difficulty differs to the groups of students divided into the advanced, intermediate, and elementary by personal abilities of learning and concerns, tried out to remove uniformity and integrity of lessons through solving the problems students can, to convert lessons to the learner-oriented that learners take part in voluntarily through discussing, solving the problems, and correcting the errors of them by group-cooperative actions, for the students to realize that they can solve everything only by their own endeavors.

The purpose of this study is to investigate the degree of anxiety factors for learning mathematics and look into the reason of anxiety of mathematics and show the method of eliminating negative and anxious factors in elementary school, secondary school and high school. To have learner take an interest in learning mathematics, develop the positive attitude about learning mathematics and maximize the effect of learning of mathematics, three kinds of hypotheses are established as follows: 1. There would be difference in anxiety factor of learning mathematics according to elementary school, secondary school and high school. 2. There would be difference in anxiety factor of learning mathematics according to sex. 3. There be difference in anxiety factor of learning mathematics according to the level of achievement. The results of this study are as follows: 1. Hypotheses I was testified. The anxiety factor between mathematics learning and mathematics teacher was significant difference according to elementary school, secondary school and high school. 2. Hypotheses II was testified. The result of hypotheses II was significant difference only in high school. The anxiety factor of mathematics teacher was significant difference according to boy student and girl student. 3. Hypotheses III was testified. The anxiety factor of mathematics, teacher and test was significant difference only in elementary school and high school.

This study has been done to help teach mathematics on the spot of education by providing the history of mathematics and illustrations concerning mathematics, which were rearranged for the level of the second grade students in highschool and intented to interest students in mathematics classes. The contents of teaching, according to each unit (Matrix, Sequence, Limit, Differentiation, Integration, Probability, Statistics) include the life of the representative mathematician, the historical background centered on episodes, questions linked with reality, questions making sensations in history and something for maxim in mathematics. If such contents are properly used, they are expected to be able to stimulate students' curiosity, and to be effective in improving students' learning ability in mathematics by causing them to show their active attitudes toward learning mathematics.

Development of new and highly efficient computer technologies are providing schools and homes with faster and multi-functioning computers, and text-oriented education softwares are now being rapidly replaced by multimedia CAI. There are also increasing needs for computer-literate teachers and more effective CAI materials. The goal of this study is to present effective ways to use computers as teaching aids in mathematics classrooms and how computers affect the students' achievement, interest and attitude in mathematics. Theoretical reviews on learning theories of CAI and multimedia were made before designing teaching plans for mathematics classrooms and the plans were applied to classrooms. The result of this study shows that there is a significant difference in achievement between control group and experimental group, and also indicates that CAI increases the students' interest and attitude in mathematics to a certain extent. Although using computers in classrooms are considered to be more effective in teaching than text-oriented lectures, the number of computers in schools is limited and all the students can not take advantage of individualized drill and practice programs or tutorial programs. One way of various solutions to this problem is developing teaching materials for middle or large sized classes and providing teachers with easy-to-carry notebook computers. And also mathematics teachers should be given more chances to train themselves in developing and using CAI materials.

The purpose of this research consists in understanding how the effects of Teaching Method by Questions on the achievement ability of math study and learning attitude are in the aspect of teaching and learning procedure, compared with those of the traditional teaching way. To attain the purpose, the research questions have been set up as follows: ［Research Question 1］ How to make a teaching plan of effective Learning by Questions\ulcorner ［Research Question 2］ Can Learning by Questions bring about a meaningful difference between two groups (experimental group and comparative group) in the aspect of the achievement ability of math study\ulcorner ［Research Question 3］ Can Learning by Questions change the Learning attitude of the students positively\ulcorner The outcome is as follows: First, it shows that the experimental group with Learning by Questions have marked more significant difference than the comparative group in the aspect of the achievement ability of math study. That is, Learning by Questions has a positive effect on the achievement ability of math study. Second, the experimental group with Learning by Questions have brought about more positive learning attitude than the comparative group without Learning by Questions.

Above all, the ability to solve problems must be emphasized as a basic skill of mathematics, but it is neglected when we teach. In this study, learning task means ［same meaning］ ［same form］ ［same technique］, so I tried to extend mathematical scholastic ability of the students as an extensional problem solving that is a basic element of mathematics. The purpose of this study is the investigation of level type learning, using the basic learning elements to extend thinking ability. From the constructed hypothesis as follows and then implement it. I selected basic learning elements from an analyzed textbook and then task learning material was created for each level type learning. The problem solving ability will be extended through the level type learning of the small group, using the level type learning task material. The conclusions this study are as follows. The level type learning in small group learning, using and making level type learning material, having basic learning elements in analysed text are. Basic learning content is understood clearly and deeply, so, fundamentally, it is effective in achieving the problem solving in mathematics. It is an effective method to achieve the meta-cognitive faculty because achieved the expected method of solving problems and resulted in the true learning of content.

The Ministry of Education have had us practice the performance test as a substitute proposal, however, all the more for the idealistic purport, our education front does not have such a sufficient condition as to practice the performance test for many classes and miscellaneous duties and over-populated class, and that practice has been enforced so abruptly without any drastic preparation and has caused much confusion from the beginning of that enforcement. Thus, these problematic concerns are remained as the tasks of the teachers to be solved by themselves in the front of education, and herein I came to do this research. The followings are the conclusions that I got as the results of the research (1) Performance test style should be applied in consideration of the students' achievement level and the gap of the teachers' recognition; descriptive test, portfolio assignment and formative test styles were proper for the students lacking basic study ability. (2) Descriptive test should have its beginning with the question items to which students can write the problem solving procedure logically rather than those to evaluate the creation ability and thinking ability: and putting down specifically the assessment standard could prevent students' confusion and scheme the impartiality of the assessment. (3) Portfolio assignment evaluation should be given with as interesting and suitable amounts as possible so that the students can do by themselves. (4) Utilizing the performance test table enabled easy management of documentary evidence. And it is needless to say that the success of the performance test should have preceding conditions like the teachers' understanding and their positive participation. Therefore, I'd like to give suggestions herein like the followings; (1) The performance test should not always be made into grades, and there is a need to develop the test gradually in the condition that the education surroundings permit by checking time, frequency, ratio and contents of the test while practicing the multiple choice writing test. (2) As long as the performance test has the aims of improving the studying and learning activities, any performance test only for the sake of making numerals with the thought that assessment is the disposal of the grades should be avoided, and the change of the lecturing styles and development of various assessing types and studying materials should be endeavored to confirm with the aims.

The situation of unification has been changing in the rapid speed. In this condion it is most important that we understand North Korea's current situation correctly, by overcoming the differences between South and North Korea and trying to pursuit the national homogeneity. One of the most effective ways to understand North Korea is to understand their education. So, I wrote this thesis as a way of getting ready for the united Korea by konwing mathematics texts and their system, composition, contents of junior high school in North Korea Anyway, I hope that this study will be helpful to the integration of mathematics education after unification of North and South

Mathematics is extreme the differences of the scholarly attainments in comparison with other subjects at a middle school. Specially, the students at islands and places leave much to be desired the scholarly attainments standards of mathematics. Therefore, every school takes movement class according to level these days. And the small schools put in effect the cooperation of group work through the small groups. These classes are effective at the scholarly attainments extension to some degree, but each student is extreme the differences of scholarly attainments. On this, the small school was the subject of study at the present research and put in effect the cooperation of group work through the small groups. The students were divided in three groups; the top class, average, the low class, And they were offered the fitting textbooks matching the cooperation of group work and the opportunities of discovery learning fitting an individual ability and standard. Consequently, some educational materials were made, for example, question papers, commonness learning materials, choice learning materials. These materials were put in effect to the students to be able to succeed discovery learning. With this, the students were investigated an interest of mathematics and the influence giving at the studies attainment. And the students were put in effect the cooperation of group work through the small groups to improve uniformity and sturdiness of the mathematical education. The conclusion at the present research is as follows. 1) When the students put in effect the cooperation of group work through the small groups, the scholarly attainments of mathematics totally didn't display useful changes as improvement. However, the students of average and the low class gradually seemed to improve the scholarly attainments of mathematics as the help of the top class positively. 2) An individual and cooperation learning in the method of the cooperation of group work through the small groups displayed many changes at the learning attitude of the students by means of discovery learning thanks to the learning heads. 3) When the investigator put in effect the cooperation of group work through rather the small groups than the large groups, the numbers of the students experiencing interest about mathematics increased in 26% and this learning method should continue to progress.

The purpose of this thesis is that the students understand the sentence stated math problems closely related to the real life and adapted the right solving strategies try to find the solution to a problem. The following research problem were proposed. 1. How repeated thinking lessons develop the understanding of problems and influence the usage of correct problem solving strategies and extensions of problem solving. 2. There are how much differences of achievement for each type of sentence stated problems by using comparative analysis of upper class, intermediate class, and lower class for each level between the experimental and comparative classes. In order to conduct this research the classes were divided into three different level - upper class, intermediate class and lower class. Each level include an experimental class and a comparative class. The two classes (experimental class and comparative class) of the same level were tested on the basis of class division record with the experimental class repeated learning papers for two weeks were used to guide the fixed thinking algorism for each sentence stated math problems. Eight common problems were chosen from a variety of textbooks : number calculation problems, velocity-distance-time problems, the density of a mixture, benefit problems, distribution problems, problems about working, ratio problems, the length of a figure problems. After conducting this research experiment The differences in achievement level between the experimental class and comparative class, were compared and analyzed through achievement tests made from the achievement test papers with seven problems, which were worth seventy points (total score). The conclusions of this thesis are as follows: Firstly, leaning activities through the usage of repeated learning papers for each level class produce an even development of achievement level especially in the case of the upper class learners, they have particular differences (between experimental class and comparative class) compared to the intermediate level and lower classes. Secondly, according to the analysis about achievement development each problems, learners easily accept the strategies of solution through the formula setting up to the problem of velocity -distance-time, and to the density of the mixture they adapted the picture drawing strategies interestingly, However each situation requires a variety of appropriate solution strategies. Teachers will have to employ other interesting solution strategies which relate to real life.

본 논문의 목적은 G. Cantor 에 의하여 출발된 집합론을 보통집합 이론이라고 구별하여 부를 때, 보통 집합 이론이 그 바탕에 깔고 있는 논리적 제한 점들 곧, 배중률이라든지 모순의 법칙 등을 어떻게 보완할 수 있을 것인가\ulcorner 하는 점과 그러한 점을 보완하여야 할 필요성에 대하여도 생각하고자 한다. 그런 관점에서 보통집합 이론과 퍼지집합 이론의 기본개념을 상호 비교함으로써 앞서 제기한 문제의 보완 요소를 찾아보려고 한다. 실제에 있어 인간의 사고 가운데에서는 중간을 배제하는 일이 없음에도 불구하고 이를 수학적으로 접근하고 표현하는 수단이 부족함으로 인하여 부자연스러운 논리의 법칙을 받아들일 수밖에 없었던 것도 사실이다. 특히, 논리적 응용력이 부족한 중등과정의 학생들에게 있어서 수학이 전적으로 2가 논리에 의하여 지배되고 있다는 방식으로만 지도하는 것은 여러 가지 측면에서 그 내용의 보완이 요구된다. 보다 다양한 수학적 표현의 여지를 열어주는 지도법은 쉼없이 연구되어야 할 것이다. 무엇보다도 배우는 학생들이 보다 폭 넓은 사고의 영역을 소유하고, 그를 바탕으로 창의적이고 자유로운 발상이 이어 질 수 있도록 하기 위하여는 교사의 수학적 시야가 보다 넓고 유연해져야 한다함은 재론할 필요가 없을 것이다. 그런 의미에서 본 논문이 작은 역할을 할 수 있기를 바란다.