• The Mathematical Education
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• v.47 no.2
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• pp.197-219
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• 2008

Unlike ordinary situations, deifinitions play a very important role in mathematics education in schools. Mathematical concepts have been mainly acquired by given definitions. However, according to didactical intentions, mathematics education in schools has employed mathematical concepts and definitions with less strict forms than those in pure mathematics. This research mainly discusses definitions used in geometry (promising) course in primary schools to cope with possibilities of creating misconception due to this didactical transformation. After analyzing problems with potential misconceptions, a survey was conducted $\underline{with}$ 80 primary school teachers in Jeju to investigate their recognitions in meaning of mathematical concepts in geometry and attitudes toward teaching. Most of the respondents answered they taught their students while they knew well about mathematical definitions in geometry but the respondents sometimes confused mathematical concepts of polygons and circles. Also, they were aware of problems in current mathematics textbooks which have explained figures in small topics (classes). Here, several suggestions are proposed as follows from analyzing teachers' recognitions and researches in mathematical viewpoints of definitions (promising) in geometric figures which have been adopted by current mathematics textbooks in primary schools from the seventh educational curriculum. First, when primary school students in their detailed operational stage studying figures, they tend to experience $\underline{a}$ collision between concept images acquired from activities to find out promising and concept images formed through promising. Therefore, a teaching method is required to lessen possibility of misconceptions. That is, there should be a communication method between defining conceptual definitions and Images. Second, we need to consider how geometric figures and their elements in primary school textbooks are connected with fundamental terminologies laying the foundation for geometrical definitions and more logical approaches should be adopted. Third, the consistency with studying geometric figures should be considered. Fourth, sorting activities about problems in coined words related to figures and way and time of their introductions should be emphasized. In primary schools mathematics curriculum, geometry has played a crucial role in increasing mathematical ways of thoughts. Hence, being introduced by parts from viewpoints of relational understanding should be emphasized more in textbooks and teachers should teach students after restructuring this. Mathematics teachers should help their students not only learn conceptual definitions of geometric figures in their courses well but also advance to rigid mathematical definitions. Therefore, that's why mathematics teachers should know meanings of concepts clearly and accurately.

• Journal of The Korean Association For Science Education
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• v.28 no.6
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• pp.546-564
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• 2008

The purpose of this study was to examine the types and characteristics of the knowledge constructed by pre-service secondary science teachers. Data included 26 student-teachers' narratives regarding their experiences in teaching high school students who were enrolled in extra-curricular science classes. It was revealed that the pre-service teachers awoke to the importance of subject matter knowledge, and learned it themselves in the situation of their own teaching. Especially their concern about science content knowledge was strongly associated with the matter of didactic transposition of the knowledge. The result also showed that the pre-service teachers constructed knowledge about the relationship with students as well as pedagogical knowledge to help students learn, and that they newly realized the nature of science in the context of teaching science. In addition, the teaching experiences allowed for the student-teachers to develop knowledge of oneself as a teacher and knowledge about science education in schools. It was believed that the knowledge constructed personally by the pre-service teachers from their teaching experiences could be a platform for the development of teacher expertise. Implications of the present study for science teacher education and relevant research were discussed.