• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.27-45
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• 2009

Recently there has been a high request for support for teachers' professional development and quality control to meet the demand of educational policy to introduce teacher evaluation, master teacher status, incentives for teacher competency, etc. It has been suggested that reeducation and support for professional development would be more effective to beginning teachers with a high developmental potential than to experienced teachers with routinized instruction. Since 2005 KICE-TLC has conducted research on the development of teacher supporting programs such as teaching consultation and pedagogical content knowledge(PCK) in school subjects. In line with the current education policy and previous research by KICE, this research has been conducted to meet the need for novice teacher induction by developing consulting program focused on PCK The goal of this research was to (1) explore the in light meaning of PCK in light of teaching consultation, (2) conduct a preliminary study on how to develop teaching consulting programs for secondary beginning teachers, (3) develop teaching consulting programs focused on pedagogical content knowledge(PCK), and (4) suggest implications for educational policy regarding pre-service and in-service teachers' continuing professional development and support.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.197-230
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• 2009

The purpose of the study was to reveal the current situations and suggest some ideas to improve the mathematics education of magnet high schools in Korea. Magnet high schools were founded to offer special professional education for students who are interested in a specialized area. Students were selected based on their abilities and potentials in those fields. In Magnet high schools, the curriculums were constructed based on these objectives. Also close connections were established with universities through professional education. However, many magnet high schools are facing difficulties to chase two rabbits at the same time. Those are university admissions and specialized education for near future employment. Furthermore, increasing number of students who want to study at the university level cause more difficulties. The results of the study indicated several suggestions to improve current situation of the magnet high schools.

• Journal of the Korean School Mathematics Society
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• v.25 no.3
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• pp.279-306
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• 2022

The purpose of this case study is to get an implication on elementary pre-service teacher education programs by exploring how a pre-service teacher's noticing changes within a learning community. The pre-service teacher participated in a learning community with researchers. Data includes recordings and transcription of actual class and pre- and post discussion in the learning community, the pre-service teacher's reflection essays, field notes, and students' worksheets. Results are as follows. First, the pre-service teacher's attending moved from the result of tasks to students' mathematical thinking. Second, the pre-service teacher's interpretation changed from a lack of diversity and specificity of evidence to diversity and specificity. Third, the pre-service teacher's decision-makings changed from unproductive deciding to productive deciding.

• The Mathematical Education
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• v.62 no.2
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• pp.257-268
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• 2023

The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

• School Mathematics
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• v.17 no.3
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• pp.493-513
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• 2015

This study is based on the perspective that tasks in local and global contexts are important to raise students' ability to mathematically analyze and solve diverse phenomena and social issues as members of future civil society. Therefore, this study analyzes 880 real world tasks from 13 types of 7th grade textbook based on 2009 revised Curriculum. As a result of analyzing tasks by using 3 types of context category and 9 types of ways as analysis framework and allowing repetitive coding, personal context was most frequent in the context of Younbokhap. In level of Integrated ways of Yungbokhap, sequential model in which other subjects' topics were not directly related to mathematics problem or presented in simple description is most frequent. The result shows that the textbooks are too limited to develop learner's competencies. Through such analysis result, we discuss about the necessity and methods of developing tasks which allow learners to study further in future society and global context and which connect other subjects' knowledge and social issue with mathematics in deeper level.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.415-441
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• 2017

The purpose of this study is to develop elementary school math classes for the gifted and talented with a focus on social issues to investigate the possibility of character education through specialized subject classes. As suggested in the goals of the math education for social justice, which provide the fundamental theoretical basis, through mathematics activities with a theme of social issues, mathematically gifted and talented young students can critically perceive social issues, express a sense of mathematical and critical agency throughout the course and develop a willingness and mindset to contribute to social progress. In particular, the concept of Figured Worlds and agency is applied to this study to explain the concept of elementary math classes for the gifted and talented with a focus on social issues. The concept is also used as the theoretical framework for the design and analysis of the curriculum. Figured Worlds is defined as the actual world composed of social and cultural elements (Holland et al., 1998) and can be described as the framework used by the individual or the social structure to perceive and interpret their surroundings. Agency refers to the power of practice that allows one to perceive the potential for change within the Figured Worlds that he is a part of and to change the existing Figured Worlds. This study sees as its purpose the fostering of young talent that has the agency to critically perceive the social structure or Figured Worlds through math classes with a theme of social issues, and thus become a social capital that can contribute to social progress.

• Journal of The Korean Association For Science Education
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• v.26 no.2
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• pp.246-257
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• 2006

TIMSS (Trends in International Mathematics and Science Study) aims to produce reliable and internationally comparable indicators of student achievement. The TIMSS science achievement scale summarizes student performance on test items designed to measure a wide range of student knowledge and proficiency. This study analyzed Korean middle school students' science achievement at the advanced and high international benchmarks of the four benchmark levels of the benchmarks classified in TIMSS 2003 in light of science content areas (physics, chemistry, biology, earth science, and environmental science) and item characteristics. The average percent correct on items at the advanced benchmark by Korean students was highest in physics followed by earth science, biology, chemistry, and environmental science, whereas internationally the order was earth science, chemistry, biology, physics and lastly environmental science. Korean students performed relatively better in physics yet somewhat worse in chemistry than other top-performing countries. According to item analysis, Korean students reaching the advanced international benchmark understood some fundamentals of scientific investigation, but demonstrated weakness in written explanations of scientific principles, abstract science concept comprehension, and application of scientific concepts to solve quantitative problems. In addition, Korean students reaching the high international benchmark demonstrated relative weak conceptual understanding of ecology compared with other countries.

• East Asian mathematical journal
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• v.31 no.2
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• pp.211-244
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• 2015

The arithmetic operation have double-sided character. One is calculation as a process, the other is understanding in results as an outcome of the operation. We harbored suspicion on students' misunderstanding in an outcome of the operation, because the curriculum has focused on the calculation, as a process of arithmetic operation. This study starts with the presentation of this problem, we tried to find the recognition ability and character in the arithmetic operation. We researched the recognition ability for 7th grade 27 students who have enough experience in arithmetic operation when studying in elementary school. And we had an interview with 3students individually, that has an error in understanding in results of arithmetic operation but has no error in calculation. We focused on 3students' detailed appearance of the ability to understand in results of arithmetic operation and analysed the changing appearance after recommending unit record using operation expression. As a result, we could find the abily to underatanding in results of arithmetic operation and applicability to recommend unit record using operation expression. Through these results, we suggested educational implications in understanding in results of arithmetic operation.