In this paper, I would like to introduce some ideas and problems in mathematics teachers' education. The aims and content of teachers' professional education are discussed with an oriental perspective. What are mathematics teachers' needs in their professional development\ulcorner What contradictions do they meet in mathematics instruction\ulcorner The problems are described with the result of my survey.

It is undeniable that teachers play the principal roles in education. This is why education and professional development of teachers are so important. Some of recent works have made this fact clearer. In America, in particular, many reports and research papers have recently been published on these problems. In this paper, we first introduce briefly the current system of education, employment, and professional development of mathematics teachers in Korea. And then we mention a research project on education of mathematics teachers. The final report of the project contains some suggestions for curriculums of the department for education of mathematics teachers. We describe one example of extended syllabus which implements those suggestions. The example is on Modern Algebra I.

This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

The purpose of this paper is to diagnose the problems of the revision process of the curriculum, and identify the issues in relation to the 7th mathematics curriculum. From the review on the curriculum revision process in Korea, three issues were identified; timing and scale of curriculum revision, research and curriculum revision, and the relationship between the revision of the overall curriculum and that of a subject curriculum. Regarding the mathematics curriculum, the three issues were raised for further discussion; lack of philosophy behind the mathematics curriculum, optimization of mathematics educational content, and differentiated curricula for students of different abilities.

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.