• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.1-19
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• 2016

This study investigated the mathematical notation used today in terms of skip ping the parenthesis. At first we have studied the elementary and secondary curriculum content related to omitted rules. As a result, it is difficult to find explicit evidence to answer that question 'What is the calculation of the $48{\div}2(9+3)$?'. In order to inquire the notation fundamentally, we checked the characteristics on prefix, infix and postfix, and looked into the advantages and disadvantages on infix. At the same time we illuminated the development of mathematical notation from the point of view of skipping the parenthesis. From this investigation, we could check that this interpretation was smooth in the point of view that skipping the parentheses are the image of the function. Through this we proposed some teaching methods including 'teaching mathematical notation based on historic genetic principle', 'reproduction of efforts to overcome the disadvantages of infix and understand the context to choose infix', 'finding the omitted parentheses to identify the fundamental formula' and 'specifying the viewpoint that skipping the multiplication notation can be considered as an image of the function'.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.445-458
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• 2012

Current textbooks may provide students and teachers with three improper notions related to the quotient and the remainder in division for decimal numbers as in the following. First, only the calculated results in (natural numbers)${\div}$(natural numbers) is the quotient. Second, when the quotient and the remainder are obtained in division for decimal numbers, the quotient is natural number and the remainder is unique. Third, only when the quotient cannot be divided exactly, the quotient can be rounded off. These can affect students and teachers on their notions of division for decimal numbers, so improvements are needed for to break it. For these improvements, the following measures are required. First, in the curriculum guidebook, the meaning of the quotient and the remainder in division for decimal numbers should be presented clearly, for preventing the possibility of the construction of such improper notions. Second, examples, problems, and the like should be presented in the textbooks enough to break such improper notions. Third, the didactical intention should be presented clearly with respect to the quotient and the remainder in division for decimal numbers in teacher's manual.

• Journal of The Korean Association of Information Education
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• v.17 no.1
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• pp.43-52
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• 2013

As a tool of programming education, a robot is effective in creative problem solving abilities and logical thinking skills. It also provides practical, operational learning experience to learners, when using as a tool of learning, it can help learners' specific understanding for the contents of education and lead to an active participation in learning. This research focuses on the robot's instrumental use in the mathematics class. So the lesson activities with relation to the fourth grade math curriculum were developed after the functional analysis of the robot and the extraction of educational utilization with function. The result shows that there wasn't a significant difference in achievement test but there was a positive response in the most of the survey items. It shows that robots lead to an active participation in class, to be interested in math class and were helpful to understand math concepts. There was also a positive response in the result of learner interviews such as dynamic, collaborative communication, experiential, practical lessons that are rare sights in normal math class.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.357-366
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• 2005

This Study suggests some ideas how we develop a network of content structure based on informal context and method how we decide a sequence of mathematical syllabus from those Structures. 10th grade students in the process conceptual development was observed and interviewed in 2 hour teaching and learning experiment. Three related characteristics of student's thought in structuring math. Content and sequencing it were investigated as follows : (a) the reasoning that they do reflective abstraction well(or do not well) in acquisition of conceptual knowledge. (b) the method that teacher can use resuits in (a) to organize the content structure. (c) the ways that teacher find the process knowledge in informal content structure. That is, this study investigated the way we, curriculum designer, can create well defined content structure and instructional sequence strongly based on the learners' understanding.

• 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.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.513-541
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• 2008

The purposes of the study were to investigate whether the use of the Geometer's Sketchpad(GSP) is more effective than the use of traditional tools such as ruler and protractor to enhance eighth- grade students' understanding of quadrilaterals and geometric reasoning ability and to examine how the use of the software affects on the development of students' understanding and reasoning ability. According to the results of the posttest, there was a significant difference in student achievement between students using GSP and students using ruler and protractor. Students using GSP significantly outperformed students using ruler and protractor on the posttest. Student interview data showed that the use of the GSP was more effective in developing students' geometric reasoning ability. Students using GSP achieved higher degrees of acquisition for van Hiele level 2 and 3 than students using ruler and protractor. Dynamic visual representations and hands-on experiences provided in GSP learning environment helped students approach quadrilateral concepts more conceptually and realize their pre-existing conceptual errors and re-conceptualize their mathematical ideas.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.319-335
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• 2013

Chinese mathematical curriculum is divided 4 areas(number and algebra, space and figure, statistics and probability, practice and synthetic application). The purpose of this paper is to analyze the contents of the practice and synthetic application in yanbian elementary textbook. For this, 12-textbook which was published in yeonbeon a publishing company is analyze by topic, mathematical process, area of content and mathematical activity. mathematical process The following results have been drawn from this study. First, contextual backgrounds of practice are restricted in classroom. The contents of synthetic application are limited in connection of mathematical areas. Mathematical problem solving is a main in mathematical process, whereas reasoning activity is a few. Mathematical experience activity is a main in mathematical process, whereas synthetic activity is a few. We can use the suggestions of this paper for development of textbook and the contents of mathematical process.

• 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.