• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.137-154
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• 2012

The purposes of this study are to develop the formative assessment program in geometry area for a 1st-grade class of middle school and to test the effect of this program. This formative assessment program was based on mathematics curriculum for the 1st graders of middle school. In addition, we examined how the 1st graders of middle school understand the geometric concepts by analyzing their response in the pretest and the posttest. This formative assessment program and the results of its analysis would be the useful information for the effective teaching and learning in geometry area for the 1st grades of middle school.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.371-402
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• 2016

The aim of this study is to compare mathematics curriculum among the United States, Singapore, England, Japan, Australia and Korea and offer suggestions to improve mathematics curriculum of Korea in the future. In order to attain these purposes, the analysis was conducted in many aspects including mathematics education system, mathematics courses, mathematics contents, assessment syllabus for university entrance examination and the construction principles of mathematics curriculum. In the light of the results of this study, our suggestions for improving mathematics curriculum of Korea are as follows: revising the contents of analysis, geometry, probability and statistics strands; organizing curriculum based on spiral construction principle; providing various opportunities to select mathematics courses according to students'career; reflecting the contents of their courses in university entrance examination.

• School Mathematics
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• v.11 no.1
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• pp.147-164
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• 2009

This study investigated the development of geometrical thinking levels of the under achievers at mathematics through supplementary classes according to van Hiele's learning process by stages using mathematical journal writing. We selected five under achievers at mathematics among the fourth graders. We examined their geometrical thinking levels in advance and interviewed them to collect basic data related to their family backgrounds and their attitude toward mathematics and their characteristics. Supplementary classes for the under achievers were conducted a couple of times a week during 12 weeks. Each class was conducted through five learning stages of van Hiele and journal writing was applied to the last consolidating stage. After 12th class had been finished, posttest on geometrical thinking levels was conducted and the journals written by the pupils were analyzed to find out changes in their geometrical thinking levels. The result is that three out of five under achievers showed one or two level-up in their geometrical thinking levels, though the other two pupils remained at the same level as the results by the pretest. Moreover we found that mathematical journal writing could provide the pupils with opportunities to restructure the content which they study through their class.

• Proceedings of the Korea Multimedia Society Conference
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• 2004.05a
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• pp.737-740
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• 2004

오늘날과 같이 과학기술과 정보통신 기술의 급속한 발달로 인터넷이 다르게 성장하였으며 이로 인하여 다양한 학습용 사이트가 운영되고 있다. 따라서 웹상의 교육정보가 기하급수적으로 증가되었고, 이러한 교육용 웹 자료를 컴퓨터 보조 학습 매체로 활용하고 있다. 또한 CAI(Computer Assisted Instruction), ICAI(Intelligent CAI) 나 ITS(Intelligent Tutoring System) 등을 통해 컴퓨터를 수업매체로 활용하는 방법도 많이 연구되고 있다. 하지만 현재까지 개발된 대부분의 ITS들은 CAl나 ICAI의 이론적 특징을 살릴 수 있을 만큼 진보되어있지 못한 실정이다. 특히 현행 교육과정이 지향하고 있는 수준별 교육과정에 적합하지 않고 학생들의 능력, 적성, 필요, 흥미에 대한 개인차를 고려하지 않으며, 학생 개개인의 성장 잠재력과 교육의 효율성을 극대화하지 못하고 있다. 그리고 학습자가 원하는 요구를 정확하게 파악하여 학습효과를 향상 시킬 수 있는 방법을 제공하고 있지 않다. 따라서 본 논문에서는 학습자들의 개인차 변인을 파악하여 학습자의 요구나 능력에 맞게 학습자의 학업성취를 평가할 수 있고, 수준별 교육과정에서 학습 능력이 떨어지는 학생의 학습 결손을 예방할 수 있도록 인터페이스 모듈, 학습자 모듈, 교수전략 모듈, 전문가 모듈을 가진 자기 주도적 학습을 위한 웹 기반의 MITS(Multimedia ITS: MITS)를 설계하였으며, MITS의 각 모듈들이 효율적으로 상호작용 할 수 있는 알고리즘을 제안하였다.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.503-523
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• 2010

The current mathematics curriculum are consist of the following domains: 'Characteristics', 'Objectives', 'Contents', 'Teaching and learning method', and 'Assessment'. The mathematics standards which students have to learn in the school are presented in the domain of 'Contents'. 'Contents' are consist of the following sub-domains: 'Number and Operation', 'Geometric Figures', 'Measures', 'Probability and Statistics', and 'Pattern and Problem-Solving' (Elementary School); 'Number and Operation', 'Geometry', 'Letter and Formula', 'Function', and 'Probability and Statistics' (Junior and Senior High School). These sub-domains of 'Contents' are dealing with mathematical subjects, except 'Problem-Solving' at the elementary school level. In this study, the sub-domain of 'mathematical process' was suggested in an equal position to the typical sub-domains of 'Contents'.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.57-72
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• 2007

Recently, dissection puzzles such as pentominoes have been used in mathematics education. But they are not actively applicable as a tool of problem solving or introducing mathematical concepts since researches about the historical background and developments of mathematical applications of such puzzles have not been effectively accomplished. In this article, in order to use pentominoes in mathematical teaming effectively, we first investigate geometric problems related to dissection puzzles and the historic background of development of pentominoes. And then we collect and classify data related to pentomino activities which can be applicable to mathematics classes based on the 7th elementary school national curriculum. Finally, we suggest several basic materials and directions to develop more systematic learning materials about pentominoes.

• East Asian mathematical journal
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• v.26 no.4
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.479-491
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• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• KDI Journal of Economic Policy
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• v.10 no.1
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• pp.133-173
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• 1988

최근 과학기술(科學技術)의 영향을 받아 급변하는 국내외의 환경을 감안할 때, 과학교육(科學敎育)의 중요성은 심각히 인식되고 있으며 특히 수학교육(數學敎育)은 그 비중이 크다고 할 수 있다. 따라서 수학교과과정(數學敎科課程)의 편성(編成)은 매우 중요한 위치에 있으며 현재 문교부(文敎部)에서도 중(中) 고등학교(高等學校)의 수학교과서(數學敎科書)를 새로이 개편하는 작업을 진행하고 있다. 이러한 국가적으로 중요한 작업이 체계적(體系的)인 연구(硏究)와 제도적(制度的)인 개선(改善)을 바탕으로 이루어져야 한다는 생각 아래에서, 각급학교(各級學校)의 교과과정(敎科課程), 행정(行政) 및 제도(制度), 교과서(敎科書) 집필(執筆) 및 지도평가방법(指導評價方法)에서 나타나는 문제점(問題點)을 파악하고 개선방향(改善方向)을 모색하는 데에 본고(本稿)의 목적이 있다. 수학교육(數學敎育)의 목적을 이해하는 데에는 수학(數學)의 특성(特性)을 파악함이 가장 중요하다고 생각된다. 이 특성(特性)의 근원을 산수(算數)와 기하(幾何)의 발단(發端)에서 찾아보았으며 각급학교(各級學校)의 학과내용(學科內容)을 수학(數學)의 역사적(的) 발전단계(發展段階)와 현대수학(現代數學)의 특징(特徵)에 비추어 분석하여 보았다. 그 결과 각급학교(各級學校) 교과과정(敎科課程)이 일관성있게 배열되지 않은 면이 있고 하위(下位)의 능력평가(能力評價)에 치우친 감이 많아, 다음 단계의 교육에 지장을 초래하면서도 오히려 학생들이 수학(數學)을 어렵게 생각하게끔 만드는 원인들을 찾을 수 있었다. 이러한 문제를 개선하기 위해서는 장기적(長期的) 연구(硏究)를 할 수 있는 전문연구집단(專問硏究集團)과 활성화된 교사(敎師)의 재훈련제도(再訓練制度)의 필요성과 아울러 인시제도(人試制度), 지도방법(指導方法), 평가방법(評價方法)의 개선(改善)이 이루어져야 하겠다.