The 7th Curriculum emphasizes that in mathematics classes, mathematical concepts be understood and mathematical problems be solved through student's own exploratory activities including the use of data, manipulatives, andtechnological devices. Following the main idea of the Seventh Mathematics Curriculum, this paper dealt with instructional methods applied suitably and effectively in mathematics classes, and focused on the 'exploratory learning in groups' method in mathematics education. For this purpose, this paper reviewed and summarized theories related to general pedagogy and of mathematics education. Based on the results, it investigated appropriate instructional methods in mathematics education. In particular, this paper focused on studying the exploratory learning method while investigating its properties and understand- ing the relationship between the 'exploratory learning in groups' method and the discussion-centered method. Finally, in order to show the usefulness of the exploratory learning method, this paper developed an example of a teaching module using the exploratory learning method in addition to discussion and lecture-centered methods by the use of manipulatives. The main goal of the module was to make students understand the principle of multiplication of integers.

To solve the addition word problems provides young children the chance to learn about and exercise in problem solving. This paper focuses on two aspects to be considered in addition word problems: the homogeneity of objects and the variety of contexts. The homogeneity of objects involved in addition word problems has to be kept in the following reasons: concept of unit, effectiveness of information, prevention of inappropriate variety, inconsistency of mathematics with real world, continuity between elementary and secondary mathematics. And for the variety of contexts, the additive structure proposed by G. Vergnaud, can be considered: composition, transformation, relation of comparison, composition of two transformations, composition of two relations, transformation of a relation. According to this structure, some examples, which contain homogeneous objects, were extracted from the elementary school mathematics textbooks.

The purpose of this paper is to investigate the transfer in mathematics learning, especially focussing on arithmetic and algebra. There are many obstacles at the stage of transfer in learning. In the case of mathematics, each learning contents are definitely categorized by the learning level, therefore these obstacles are more happened than other subjects. First of all, this paper investigates the historical transfer from arithmetic to algebra by Sfard's perspectives. And we define prealgebra as the stage between arithmetic and algebra, which may be revised obstacles or misconceptions happened in the early algebra learning. Also, this paper discusses various obstacles and concrete examples happened in the transfer from arithmetic to algebra. To advance the understanding in the learning of algebra, we consider the core contents of the algebra learning which should be stressed at the prealgebra stage. Finally we present the teaching units of (pre)algebra which are sequenced from the variable concepts to equations.

There have recently been increasing exchanges between South and North Korea in many areas of society, involving politics, economics, culture, education. In response to these developments, research activities are more strongly demanded in each of these areas to help prepare for the final unification of the two parts of the nation. In the area of mathematics education, scholars have started to conduct comparative studies of mathematics education in South and North Korea. As a response to the growing demand of the time, in this thesis we compared the secondary mathematics education in South Korea with that in North Korea. To begin with, we examined the background of education, in North Korea, particularly predominant ideological, epistemological and teaching theoretical aspects of education in North Korea. Thereafter, we compared the mathematics curriculum of South Korea with that of North Korea. On the basis of these examinations, we compared the secondary school mathematics textbooks of South and North Korea, and we attempted to suggest a guideline for researches preparing for the unification of the mathematics curriculum of South and North Korea. As a communist society, North Korea awards the socialist ideology the supreme rank and treats all school subjects as instrumental tools that are subordinated to the dominant communist ideology. On the other hand, under the socialist ideology North Korea also emphasizes the achievement of the objective of socialist economic development by expanding the production of material wealth. As such, mathematics in North Korea is seen as a tool subject for training skilled technical hands and fostering science and technology, hence promoting the socialist material production and economic development. Hence, the mathematics education of North Korea adopts a so-called "awakening teaching method," and emphasizes the approaches that combine intuition with logical explanation using materials related with the ideology or actual life. These basic viewpoints of North Korea on mathematics education are different from those of South Korea, which emphasize the problem-solving ability and acquisition of academic mathematical knowledge, and which focus on organizing as well as discovering knowledge of learners' own accord. In comparison of the secondary school mathematics textbooks used in South and North Korea, we looked through external forms, contents, quantity of each area of school mathematics, viewpoints of teaching, and term. We have identified similarities in algebra area and differences in geometry area especially in teaching sequence and approaching method. Many differences are also found in mathematical terms. Especially, it is found that North Korea uses mathematical terms in Hangul more actively than South Korea. We examined the specific topics that are treated in both South and North Korea, "outer-center & inner-center of triangle" and "mathematical induction", and identified such differences more concretely. Through this comparison, it was found that the concrete heterogeneity in the textbooks largely derive from the differences in the basic ideological viewpoints between South and North Korea. On the basis of the above findings, we attempted to make some suggestions for the researches preparing for the unification in the area of secondary mathematics education.

Visualization have strong driving force that enables us to recognize abstract mathematics by direct and specific method in school mathematics. Specially, visual thinking helps in effective problem solution via intuition in mathematics education. So, this paper examines the meaning of visualization, the role of visualization in intuitive problem solving process and the methods for enhancement of intuition using visualization in mathematics education. Visualization is an useful tool for illuminating of intuition in mathematics problem solving. It means that visualization makes us understand easily mathematical concepts, principles and rules in students' cognitive structure. And it makes us experience revelation of anticipatory intuition which finds clues and strategy in problem solving. But, we must know that visualization can have side effect in mathematics learning. So, we have to search for the methods of teaching and learning which can increase students' comprehension about mathematics through visualization and minimize side aspect through visualization.

This study is on the introduction of the natural logarithm by the quadrature of the hyperbola. In School mathematics curriculum, Logarithm is introduced formally. But in that introduction, students could't know the meaning of the natural logarithm and e well. Historically, natural logarithm is related to the quadrature of the hyperbola. So in this study we consider the introduction of the natural logarithm by the means of quadrature of the hyperbola and the significance of the introduction.

In this article we drew out five definition-methods in school geometry. They are called synonymous method, denotative method, analytic method. And we analyzed them theoretically. On our analysis we tried to identify the level of common sense and the level of science in definition of those two levels on the definition-methods of circle. While the definition-method in elementary school could be regarded as the level of common sense, that in middle school could be considered as the level of science. Finally, we made the following didactical comments. Definitions in school mathematics might have the levels as regard to their roles. Thus, Mathematics teachers, curriculum developers, and text authors all need to recognize the subtle differences in the level of definition-methods.

This study investigated various effects of WBD(web-based discussion) on mathematical communication, interaction and problem solving in the classroom. We developed a web site including BBS and chat room in order to encourage students' mathematical curiosities and self-studies. The web site had been operated for 6 months. Five classes of 1st grade students were selected from an middle school in Daejon. Moreover, we analyzed several cases for interactional behavior and effect. WBD promote dialogue between a teacher and students. Analysis of feed-back from BBS revealed that student's negative attitudes could be changed to positive ones by step-by-step discussions. Moreover, collaborative learning is enhanced by on-line discussion. But the effects of WBD are affected by the character and ability of a student.

The concept of "set" in school mathematics has undergone many changes according to the revision of curriculum and the transition of the paradigm in mathematics education. In the discipline-centered curriculum, a set was a representative concept which reflected the spirit of New Math. After the Back to Basics period, the significance of a set concept in school mathematics has been diminished. First, this paper elaborated several controversial aspects of the terms related to set, such as a collection and a set, a subset, and an empty set. In addition, the changes of the significance imposed to a set concept in school mathematics were investigated. Finally, this paper provided two alternative approaches to introduce and explain a set concept which emphasized both mathematical rigor and learner's psychology.

In this study, on the basis of the seventh national mathematics curriculum, the achievement standards were developed to specify the objectives and contents of teaching-learning and the assessment standards were also developed to differentiate students' levels of achievement at school mathematics. The achievement standards were developed on the following guidelines; 1) to present the minimum standards based on the national curriculum, 2) to develop the standards based on the order of curriculum, 3) to suggest the minimum but ultimate achievement target, 4) to comprise not only of the intellectual but also of psychological spheres such as knowledge, function, attitude, aptitude, etc., and 5) to suggest the standards comprehensively and concretely. The standards were developed on the basis of the middle areas of contents of the curriculum in order not to be too comprehensive, nor to be too detailed. Learning activities, on the other hand, were provided for the assistance of instructions with emphasis on creativity rather than on the routine instruction. The assessment standards were established based on the following principles; 1) to establish the assessment methods, contents, and situations which are to be used for assessment, 2) to establish the criteria of classifying the assessed into the upper, intermediate and lower levels, 3) to develop the assessment standards in a proportionate balance to achievement standards, 4) to establish the intermediate level as a standard, and 5) to establish the minimum level in the contents, concepts, values and attitudes of basic learning. This study also suggested the exemplary test items including short-answer and open-ended questions while putting emphasis on students' real performance to increase their ability in solving problems rather than in calculating. In addition to the test items, it introduced the grading system developed to grade the items with concrete guidelines and to report students' achievement on doing mathematics.