본 논문의 목적은 두 가지이다: 첫째, 구성주의와 사회문화주의의 통합적인 이해를 통해 수학 교사 교육에서 사용할 수 있는 이론적인 잠재성을 토의한다. 둘째, 비고츠키의 사회문화주의에 대한 토의가 그리 많지 않은 상황에서 사회문화주의자들의 주장을 교사교육적 관점에서 설명한다. 학습을 개인적 타원에서 설명하는 구성주의와 학습을 사회적 차원에서 설명하는 사회문화주의는 그 발생 원리상 큰 차이점을 갖는다. 본 논문에서는 이러한 차이점에 대한 논란보다는 어떻게 이 두 가지 이론이 학생들의 수학 학습에서 교사의 역할에 대한 재조명과 이론적 지지 기반을 제공할 수 있는 가능성을 갖는지 다루고 있다.

수학학습장애는 독해장애와 더불어 학습장애의 주요영역으로 인식되고 있다. 그러나 독해 장애에 대한 연구와 비교하였을 때 상대적으로 주목받지 못한 분야로, 과연 수학학습장애는 무엇이며, 수학학습장애 아를 판별하는 기준을 어떻게 설정할 것인가의 문제가 여전히 논란이 되고 있다. 본고에서는 수학학습장애에 대한 최근의 세 가지 관점-신경학적 관점, 발달심리적 관점, 교육적 관점-의 고찰을 통해, 수학학습장애를 진단하기 위한 하나의 통합적 관점이 필요함을 제안하고 있다. 이것은 수학학습장애를 신경적 결함으로만 해석하려는 전통적 관점에 대한 발달심리학자들의 비판을 수용한 것이며, 오늘날 파행적인 교육체계에서 희생되고 소외되어온 학생계층을 포용하기 위한 한 가지 제안이 될 것이다.

There seems to be a public consensus that the content of Korean mathematics textbooks is extensive and of a high level of difficulty. However, such judgment is the result of a generalization based on individual experience or on the results from comparisons of the international levels of achievement. Therefore, a more objective and stricter approach to the determination of the quantity and level of difficulty of mathematics content is necessary. For this purpose, this study has compared the content of Koreas 6th and 7th junior high school curriculums, and the Korean mathematics curriculum to textbooks of the United States, which has a considerable influence on the making of Korean mathematics textbooks. First of all, a comparison of Koreas 6th and 7th junior high school mathematics curriculums showed a slight reduction in the total quantity of content, as more content was deleted than was added in the 7th curriculum. However, given the fact that the number of hours of mathematics classes has been reduced, the reduction in content cannot be regarded as anything more than a simple reflection of the reduction in hours, proving that the 7th curriculum has not met its revision objective of reducing the content by 30%. Meanwhile, the comparison of the United States junior high school mathematics textbooks to Korea's 7th curriculum showed that the 7th grade content in the United States was much broader, encompassing content which in Korea ranged from the 2nd grade of elementary school to the 2nd year of junior high school. Therefore, on the surface, it may appear that the overall level of content in the American mathematics textbook is lower than that of the Korean. However, there are several cafes, such as statistics and probability, where certain content was more difficult and introduced at an earlier grade in the United States than in Korea. In fact, it can be said that Korea students tend to find content of the mathematics textbooks to be harder than they actually are because they are delivered as a mere aggregate of algorithms, with little consideration to its application in their everyday lives. In this respect, there is much room for improvement on the mathematics textbooks of Korea.

In this paper, in order to explicate how mathematics education can contribute to humanity education, I enquired in which position mathematics occupy in Froebel's For this, I examined Froebel's theory of humanity education, his theory of mathematics education, and the applicational problem of his thoughts to nowaday education. Froebel's educational theory is based on the concept of the Divine Unity which is relevant to the notion of 'The Absolute' of Fichte, Schelling, Hegel. He claims that from inanimate objects to human being, all is subject to the eternal law, which is presided by God. So the world itself is the representation of this law of the Divine Unity and education consists in leading man to conscious and free representation of it. The revealing process of the inner law of the Divine Unity can be attained through the awareness of the divinity which resides in the self. And this process of self-consciousness is dialectical movement of the two opposites, i.e. 'inner' and 'outer' Froebel suggests that mathematics is the mediator between the inner and outer world, i.e. he suggests that since both human being and nature are the representations of the Divine Unity, mathematics is both the pure human spirits and the law of nature. Having such a role, mathematics becomes the main discipline in education. Though there are some criticism on Froebel's educational thoughts on mathematics discussed in this paper, it can provide a typical answer to the question about how mathematics education contributes to humanity education.

This study, after careful consideration on Piaget's structuralism, showed the relationship between Bourbaki's matrix structure of mathematics and Piaget's structure of mathematical thinking. This, studying the basic characters that structure of knowledge should have, pointed out that 'transformation' and to it, too. Also it revealed that group structure is a 'development' are essential typical one which has very important characters not only of mathematical structure but also general structure, and discussed the problem that learners construct the group structure as a mathematical concept.

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

A case study was conducted to investigate the understandings of the subject matter knowledge and pedagogical content knowledge held by 63 elementary preservice teachers in dealing with the division by a fraction. The study results showed that, in terms of the subject matter knowledge, the preservice teachers did not have a conceptual understanding of the division by a fraction and, in terms of the pedagogical content knowledge, they depended heavily on algorithms without a conceptual understanding of the meaning of the division by a fraction.

In this paper, we tried to analyze 7 textbooks for liberal mathematics in elementary teacher's colleges in Korea and 3 foreign textbooks (2 American textbooks and 1 Japan textbook) which are believed to be used for pre-service education. We tried also to analyze in 3 lesson plans in homepages of Japan teacher's colleges. Next we tried to grope for syllabus of Mathematics for Elementary Teachers, and we suggested one syllabus. But we think that syllabus as a tentative one. So, it must be criticized by other researchers to be better one.

The experimental software such as Cabri II, The Geometer's Sketchpad, etc. provides dynamic environment which construct and explore geometric objects interactively and inductively. It has the effects on mathematics itself differently from other technologies that are used in instruction. What is its characteristics\ulcorner What are the educational implication of it for the learning of geometry\ulcorner How is mental reasoning of geometric problems changed by transformation of the means of representation and the environment to manipulate them\ulcorner In this study, we answer these questions through the review of the related literatures and the analysis of textbooks, teaching materials using it and curricular materials. Also, we identify implications about how the criteria for choosing geometic content and the ways of constructing context, for orchestrating the students' exploration with the secondary geometry curriculum, can be changed.