The purpose of this study is to examine the The correlation between information processing types and mathematical communication abilities / word problem solving abilities. The results obtained are as follows: 1 Simultaneous/continuous information process types showed statistically high correlation with mathematical communication abilities. However, the correlation between simultaneous information process and mathematical communication abilities is a little higher than the correlation between continuous information process and mathematical communication abilities. 2. There is a high correlation between mathematical communication abilities and word problem solving abilities. Especially, speaking ability is much more correlated with four factors of word problem solving than reading, writing and listening, Through this study, we can conclude that information process types should be consider ed in order to improve mathematical communication abilities and mathematical communication abilities is essential in word problem solving.

This paper investigated the teaching and teaming of contents-related graphing in Korean secondary textbooks and suggested the improved methods of graph instruction through this analysis. reification-the case of function, In Harel, G., Dubinsky(Eds.), The Concept of Function : Aspects of Epistemology and Pedagogy Textbooks are analyzed from the viewpoint of the proportion of graphing contents, their sequencing, the proportion of each domain in graphing activities (interpretation vs. construction, quantitative vs. qualitative aspect, local vs. global aspect) and tasks (prediction, translation, scaling), and the difference in the graphing contents between the sixth and the seventh curriculum. This analysis demonstrates that graphing contents are increasing in textbooks, therefore the high school textbooks appear in almost every content area. The graphing activities concentrate on the construction, the quantitative aspects, and the local aspects, and are gradually focusing on the interpretation and global aspects of high school textbooks. Furthermore, most of graphing tasks favor translation. In contrast, the current seventh curriculum includes a balance of interpretation and construction activities and has more global aspects than the sixth curriculum based textbooks; however, the qualitative approach still rarely appears. For the graphing tasks, translation is still prevalent, but the importances of prediction tasks based on graph have increased in comparison with the sixth curriculum textbooks. Further, the seventh curriculum based textbooks are designed to stimulate more dynamic graphing instruction by introducing new tools such as graphing calculators and computer software. We suggest that the qualitative and global aspects should be emphasized in early graph instruction, a variety of graph activities in realistic contexts should be performed, and educational technology such as graphing calculator and computer can be efficient to implement these ideas.

Performance assessment has been introduced to school education as an alternative measure of the former educational assessment which put much emphasis on the result rather than the process of learning, memorization than pursuit of knowledge, and passive than active study. As for the subject of mathematics, the change of the assessment came to replace multiple choice tests with descriptive- and statement-type tests. This means animprovement on the testing system, focusing on the process of finding out the answer. The main focus, however, is still on the intellectual domain without paying due attention to the emotional domain of mathematics education. The previous studies on the assessment of emotional domain In mathematics have shown that there are stumbling blocks in the application of the assessment, such as the disputes on the reliability, objectivity, and fairness as well as the complicated procedure of applying the results to school records. The lack of the development and supply of the appropriate assessment tools have also been pointed out. Therefore, this study has been carried out with the intention of establishing an applicable standard of assessment on the emotional domain of high school matematics. As a result, detailed standards of performance assessment, which adopt oral examination, discussion, observation, and report have been developed. The problems which are likely to emerge In the course of the application of the newly developed assessment are under study as a continuing research project.

In school mathematics, the negative numbers have been instructed using the intuitive models such as the number line model, the counting model, and inductive-extrapolation on the additionand multiplication and using inverse operation on the subtraction and division. Theseinstructions on the negative numbers did not present their formal nature and caused the difficulty for students to understand their operations because of the incomplete function of the intuitive models. In this study, we tried to improve such problems of the instructions of the negative numbers on the basis of the didactical phenomenological analysis. First of all, we analysed the nature of the negative numbers and the cognitive obstructions through the examination about the historic process of them. Second, we examined hew the nature of the negative numbers were analysed and described in mathematics. Third, we explored the improving directions for them on the ground of the didactical phenomenological analysis. In school mathematics, the rules of operations using the intuitive models of the negative numbers have been Instructed rather than approaching toward the nature of them. The negative numbers have been developed from the necessity to find the general solution of equations. The study tries to approach the operations instructions of the negative numbers formative]y to overcome the problems of those that are using the intuitive models and to reflect the formative Furthermore of the negative numbers. Furthermore, we examine the way of the instruction of the negative numbers in real context so that the algebraic feature and the real context should be Interactive.

Researchers have started to conduct comparative studies of mathematics education in South and North Korea. Most of these studies have a tendency to compare with the curriculum of South and North Korea in the macroscopic standpoint. But microscopic comparative studies on each topic of school mathematics have not been attempted yet. Microscopic studies as well as macroscopic studies are required to prepare for unification the curriculum of South and North Korea. This paper attempts to compare the contents related pythagorean theorem which is dealt with in secondary school mathematics textbook of South and North Korea. Through this study, meaningful differences between textbooks are founded and some implications are obtained. Specially, 'cutting off and rearranging' method needs to be taken into consideration for active learning. Also the construction of the figure using the pythagorean theorem needs to be dealt with in order to develop the logical thinking.

The purpose of this paper is to investigatethe relationship between Korean elementary teachers' teaching practice and students' perceptions of classroom learning environment. It is important to examine whether teachers conceive of mathematics and their teaching practice are consistent with their actual teaching mathematics in classroom. To do so, two reform-oriented and two traditionally-oriented elementary teachers in Seoul and a total of 130 students from these four selected teachers' classes participated in the present study Using classroom environment survey scale [CES] the differences in students' perceptions on classroom learning environment were examined. The results show that students taught by reform-oriented teachers have significantly higher score in the area of participation, relevance, and commitment to learning than traditionally-oriented group of students. Thus, we may conclude that the reform-oriented group of students have more benefits in learning mathematics than do the traditionally-oriented group of students.

In recent elementary school mathematics a word 'stipulation' newly appears. The word is used instead of definition. However, there seems to be some differences between definition and stipulation. So, in this paper we investigate those differences through the concept 'function of definition'. In school mathematics textbooks there are definitions which carry out special functions In mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. Functions of definition are classified as, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in recent elementary school mathematics textbooks. As a result of analysing functions of definition we found that generally speaking, stipulation-function is excessively emphasized and the other functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding and the mathematics teachers should be aware of the functions of definitions. Finally, we comment that textbook author, teacher, and researcher should be careful in using the word 'stipulation' instead of definition, because, although there are various functions of definitions, students might ream only stipulation-function.

This study intended to search for the way of NIE use as follows: 1) Setting up theoretical base about the way of NIE use to math loaming in primary school. 2) Analyzing the course mathematising through NIE use in math learning in practice. 3) Searching for the way of NIE use to aim at mathematising. As the result, this presented NIE model for mathematising according to the character of each step of the mathematising course. This paper says two things : The first, the way for using learning materials as reonstructing articles of newspapers to teach math learning 1) is searched for each information, scrapped to materialize. 2)is to extract the contents of NIE teaming available to the field and the unit of math curriculum. 3) searches for and applies the model for math NIE teaming. 4) makes up learning materials for each level using articles and presents the matters of deepening and supplement suitable for students. The second, the way for teaching math NIE with a view to helping students' mathematising during the course of teachers' math teaming. 1) reconstructs materials chosen by students' reality. 2) should offer students' communication and abundant context materials which mathematical model is possible. 3)needs to guide students to have motivation teaming so that they can mathematise their real matters by rediscovery 4) progresses mathematical activity using newspapers so that they can apply to new reality by applying informed Idea.

In this study we tried to find the method of using the tangrams and the mosaic puzzles together for learning the elementary geometry in the Korean primary schools. The tangram and the mosaic puzzle activity-panels were developed and the activity-cards for them also were designed. The criteria to be used for the analyses of contents of the activity-cards were developed. We surveyed and analyzed the students' responses, A previous research had insisted that solely using the tangrams were not useful in learning about an obtuse-angled triangle in the elementary geometry (Welchman, 1999), but the combinative uses of the tangrams and the mosaic puzzles were found to extend the limits of the previous study in investigating the figures of the plain diagrams. Actually, the tangrams and the mosaic puzzles helped the students to learn the concepts of several elements of the plain diagrams such as 'angles', 'sides', and 'angular points', with students'operational comparison of the diagrams developed with them. They also provided useful clues in learning the relationship between the 'length' and the 'area' of the Plain diagrams. The students participated in the class with much activities, using the operational learning materials. They also comprehended the concepts and the principles of the elementary geometry more thoroughly, expressing their ideas in spoken or written languages through interactive communication. In conclusion, the tangram and mosaic puzzles can be used for learning the elementary geometry of the primary school level as motivative learning materials, helping students enhance diverse mathematical thinking and discover mathematical principles.

In this paper, a teaching unit on series of number sentences with patterns is designed according to Wittmann's perspectives. In this paper, series of number sentences wish patterns means number sentences in which some patterns are contained. especially, seven kinds of number sentences wish patterns are offered as basic materials, and fifteen tasks based on these basic materials are offered. These tasks are for ninth grade students and higher grade students. These tasks heap students to recognize patterns, and to understand mechanism underlying in those patterns by looking for patterns and proving whether these patterns are generally hold. As working on these tasks, students can reinforce meaning of algebraic expression, its manipulation, and concept of number series. Students also can reinforce mathematical thinking such as analogical thinking, deductive thinking, etc. In this point, this teaching unit reveal important objectives, contents, and Principles of mathematics education. This teaching unit can also be rich sources for student's activities. Especially, for each task's level is different, each student's personal ability is considered fully. Since teachers can know mathematical facet, psychological facet, and didactical facet holistically, this teaching unit can offer broad possibilities for experimental studies. SD, this leaching unit can be said to be substantial. In this paper, this leaching unit is not applied in classroom directly. Actually such applying in classroom is suggested as follow-up studies. By appling this teaching unit in various classroom, some effective informations for teaching this teaching unit and some particular phenomenons in those teaching processes can be identified, and this teaching unit can be revised to be better one.

The purpose of this study is to compare the eighth-grade mathematics textbooks of Korea, Japan on the one hand, and those of the United States and England on the other, and to explore the implications for mathematics education in the East and the West. As a result, the dichotomy between the East and the West were set up with the sacrifice of the details. First, the textbook development and publication policies of the East are characterized as uniformity, and those of the West are diversity. Second, for the choice of content, the East and West can be represented by essential and discretionary respectively. Third, the physical appearance of Eastern textbooks is rather plain while that of the Western textbooks is colorful, Fourth, in terms of the characteristics of the content, the dichotomies between the East and the West are linear vs. spiral, content vs. context, formal abidance vs. metacognitive shift, and simple vs. realistic. Each of the Eastern and Western approaches has its own weak points as well as its strong points. For instance, textbooks In the West may help students realize how useful mathematics can be in their lives, but if the link between a mathematical concept and the corresponding real life situation is not made clear, sometimes students may not be able to completely grasp the mathematical concept. In turn, the Eastern textbooks may succeed In conveying ideas in an economical way, but they often fail to motivate students to follow the course. Therefore it is important to take a critical view of each approach. It is through a critical understanding of the differences between different cultures that we are able to learn from each other and to put the results of such comparative studies to better use in the future.