• Communications of Mathematical Education
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• v.30 no.3
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• pp.375-392
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• 2016

The purpose of this study is to provide a philosophical reflection on mathematical process consistently emphasized in our curriculum and to stress the importance of sharing creativity and its applicability to the mathematical process with the value of sharing and participation. For this purpose, we describe five stages of changing process in a peer mentoring teaching method conducted by a teacher who taught this method for 17 years with the goal of sharing creativity and examine components of mathematical process and their impact on it in each stage based on learning environment, learning process, and assessment. Results suggest that six principles should be underlined and considered for students to be actively involved in mathematical process. After analyzing changes in the five stages of the peer mentoring teaching method, the five principles scrutinized in mathematical process are the principles of continuous interactivity, contextual dependence, bidirectional development, teacher capability, and student participation. On the basis of these five principles, the principle of cooperative creativity is extracted from effective changes of mathematical process as a guiding force.

• Proceedings of the Korean Society for the Gifted Conference
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• 2002.05a
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• pp.159-160
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• 2002

• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.117-126
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• 2004

Breidenbach et al(1992)는 APOS(Actions, Processes, Objects, Schemas)를 소개하였고 Sfard(1991)는 수학적 개념에서의 Process 와 Object의 상호관련성에 대해서 발표하였다. 본 연구자는 이 이론들을 기반으로 초등학생(4$^{\sim}$6학년)과 중등 영재학생(1학년)을 대상으로 하여 조한혁의 JavaMAL Logo를 이용한 실험을 실행하였다. 이 실험에서는 Process와 Object의 의미와 이 개념들 간의 상호관계를 분석하였고 이러한 관계가 학생들의 창의성에 어떠한 영향을 끼치는지 비교분석하였다.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.67-78
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• 2005

In this paper we deals with Leibniz's definition of infinite and infinitely small quantities, infinite quantities and theory of quantified indivisibles in comparison with Galileo's concept of indivisibles. Leibniz developed 'method of indivisible' in order to introduce the integrability of continuous functions. also we deals with this demonstration, with Leibniz's rules of arithmetic of infinitely small and infinite quantities.

• 한국정보교육학회:학술대회논문집
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• 2004.08a
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• pp.197-205
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• 2004

요즘 과학, 수학 교과 등은 기초 교육 강조는 물론 창의성 교육에까지 관심을 가지고 있다. 7차 교육과정의 등장과 사회의 변화 흐름을 통해 '창의성'이 강조되고 있고, 교육에서도 창의성 교육이 대두되고 있다. 그러나 우리나라의 컴퓨터 교육 현황을 살펴보면 창의성과는 거리가 멀 뿐만 아니라, 다른 교과를 배우는데 도움을 주는 교과로서의 역할만을 하고 있다. 또한 컴퓨터 활용 교육이 이루어짐에 따라 저학년에서 고학년까지 유사한 내용의 교육을 반복해서 받는 경우가 생기고, 특히 5, 6학년은 실과 시간과 재량 시간의 교육 내용이 서로 중복되어 교육 효율이 떨어지고 있다. 이에 본 연구에서는 교육의 기초를 다지는 시기인 초등학교에서부터 창의적인 컴퓨터 교육이 이루어질 수 있도록 하고자 하며 이를 위해 초등학교 수준에 맞는 프로그래밍 관련 교육을 살펴보고, 초등 컴퓨터 창의성 향상 교육을 뒷받침할 수 있는 프로그래밍 관련 교재 개발 방안을 제안한다.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.293-302
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• 2011

The objective of this study is to search the recognition of teacher on the pattern and characteristics of the questioning sentence of the newly appointed teachers for the mathematics class through the case study for the 2ndyear teachers. The study participants' class was recorded in video and individual interview was made for 4 times. The pattern of the questioning sentence in the observed class was analyzed using the classification frame with addition of creativity related items to the classification frame suggested by Mogan & Saxton(2006). The questioning sentence and recognition on the mathematics class for the newly appointed teachers were analyzed based on the individual meeting and class materials. In result, the questioning sentence for confirmation was most frequent (69%) and questioning sentence of understanding (25%) and the questioning sentence for introspection (6%) in its priority. It was known that the questioning sentence for extending the creativity didn't make it at all. It was revealed that the participant teachers in this study used the questioning sentence pattern for fact confirmation of the student most frequently and the use of the questioning sentence for accelerating the creative thinking of the student was lacked. In addition, the teachers recognized that they manage the class oriented to questioning sentence for obtaining the concept. It was known that the education for the questioning sentence which accelerates the creativity and other thinking as well as the fact confirmation pattern is necessary through the training for the new teachers in the future.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.389-407
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• 2017

Many researches related to STEAM education have been actively conducted for developing elementary and secondary school students' comprehensive and logical thinking ability in relation to creativity education in Korea. Each sub factor of STEAM education requires creative thinking with the ability to be merged together to solve problems as integrated or combined forms in the fields of Science, Technology, Engineering, Arts, and Mathematics. Also, these STEAM activities and experiences should be carried out at various places outside the classroom in school. Although various educational programs to enhance mathematical creativity have been emphasized for elementary and secondary school students, recent tendency to focus on classroom learning in the school makes it difficult to develop creative thinking ability of students. This research is mainly based on the result of the project "Development and Administration of STEAM Outreach Program in 2016" supported by KOFAC(Korea Foundation for the Achievement of Science & Creativity). The purpose of this research is to develop a STEAM outreach program including students' activity books, teachers' manuals and administration manual that can maximize STEAM-related interest of students, and to provide a chance for elementary and secondary school students to experience creative thinking based on sub factors of STEAM. The STEAM competency total score and the perception of convergence education were significantly increased for all students participating this program, but some sub factors showed different result by school levels. The STEAM outreach program developed by this study is designed to emphasize STEAM education especially 'based on' mathematics in order to provide students with the opportunity to experience more interest in the field of mathematics and will be able to provide an interesting creative STEAM outreach program that utilizes a variety of activities which, we expect, would help students to consider their career in the future.

• School Mathematics
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• v.6 no.4
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• pp.325-344
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• 2004

This study was carried out to investigate effects of the mindmap note-taking for the formation of the mathematical concepts structure and the matjematical creativity. Two classes were randomly chosen for this study from the third grade students of a middle school located in a medium size city. Thirty one lecture hours of the mindmap note-taking on the quadratic equation and functions were administered to the experimental class of 41 students, while same lecture hours of the ordinary instruction on the same contents were administered to the control class of 40 students. It was shown from this experiment that there ware significant evidences of improvement both in the formation of students' mathematical concepts structure and mathematical creativity through the mindmap note-taking lecture. Hence, the mindmap note-taking lecture is suggested for the improvement in the formation of student's mathematical concepts structure and mathematical creativity.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.171-186
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• 2009

$Poincar\acute{e}$ is mathematician and the episodes in his mathematical invention process give suggestions to scholars who have interest in how mathematical invention happens. He emphasizes the value of unconscious activity. Furthermore, $Poincar\acute{e}$ points the complementary relation between unconscious activity and conscious activity. Also, $Poincar\acute{e}$ emphasizes the value of intuition and logic. In general, intuition is tool of invention and gives the clue of mathematical problem solving. But logic gives the certainty. $Poincar\acute{e}$ points the complementary relation between intuition and logic at the same reasons. In spite of the importance of relation between intuition and logic, school mathematics emphasized the logic. So students don't reveal and use the intuitive thinking in mathematical problem solving. So, we have to search the methods to use the complementary relation between intuition and logic in mathematics education.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.