• Communications of Mathematical Education
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• v.30 no.1
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• pp.1-22
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• 2016

We had a full scale of literature survey and case survey of mathematics Flipped Learning class models. The purpose of this study is to design and adopt a Flipped Learning 'Linear Algebra' class model that fis our need. We applied our new model to 30 students at S University. Then we analyzed the activities and performance of students in this course. Our Flipped Learning 'Linear Algebra' teaching model is followed in 3 stages : The first stage involved the students viewing an online lecture as homework and participating free question-answer by themselves on Q&A before class, the second stage involved in-class learning which researcher solved the students' Q&A and highlighted the main ideas through the Point-Lecture, the third stage involved the students participating more advanced topic by themselves on Q&A and researcher (or peers) finalizing students' Q&A. According to the survey, the teaching model made a certain contribution not only to increase students' participation and interest, but also to improve their communication skill and self-directed learning skill in all classes and online. We used the Purposive Sampling from the obtained data. For the research's validity and reliability, we used the Content Validity and the Alternate-Form Method. We found several meaningful output from this analysis.

• Journal of the Korean School Mathematics Society
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• v.18 no.1
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• pp.61-82
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• 2015

This study investigated the learning process of Chines international student within a technology environment, who was studying in Korea to be well equipped as a math teacher in future. Her activities were observed and guided in a class for pre-service teachers in one university, Kyunggido, in the second semester of 2014. She experienced obstacles such as the lacks of comprehending Korean sentences, Korean math terminologies, mathematical concepts, and fidelities of technology in her learning. She was recovered by bilingual effect, visualization activities, repetition activities, and group activities. There was a learning helper who made her learning possible in a bilingual way. Thus, the bilingual education is crucial for students with multi-cultural background.

• Journal of Science Education
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• v.43 no.1
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• pp.17-42
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• 2019

This study, as an attempt to integrate mathematics and information for convergence education, was conducted to develop teaching-learning materials on mathematics education combined with coding education, which has recently been emphasized. We chose the subject of digital signature for coding education, and used SageMath as a coding program. In this study, we overview mathematics used in the elliptic curve digital signature algorithm, one of the many methods for digital signature, and developed the teaching-learning materials on the algorithm for mathematics education integrated with information education based on coding. The elliptic curve digital signature algorithm utilized in transactions of Bitcoin, which many people recently are interested in, is a good example, showing students that mathematics is applied to problem-solving in the real world and provides an optimal environment for implementation by coding. Accordingly, we expect that a class on algorithm will provide a specific teaching-learning program to achieve the goal of integrated mathematics education. By comprehensively considering the opinions of mathematicians, mathematics teachers and mathematics education experts, we expect that the teaching-learning program will be realized as a meaningful class in science high schools, high school's math clubs, and 'number theory' class in colleges.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.573-588
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• 2015

In this paper, we introduce development process and application of a simple and effective model of a statistics laboratory using open source software R, one of leading language and environment for statistical computing and graphics. This model consists of HTML files, including Sage cells, video lectures and enough internet resources. Users do not have to install statistical softwares to run their code. Clicking 'evaluate' button in the web page displays the result that is calculated through cloud-computing environment. Hence, with any type of mobile equipment and internet, learners can freely practice statistical concepts and theorems via various examples with sample R (or Sage) codes which were given, while instructors can easily design and modify it for his/her lectures, only gathering many existing resources and editing HTML file. This will be a resonable model of laboratory for studying statistics. This model with bunch of provided materials will reduce the time and effort needed for R-beginners to be acquainted with and understand R language and also stimulate beginners' interest in statistics. We introduce this interactive statistical laboratory as an useful model for beginners to learn basic statistical concepts and R.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.102-106
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• 2003

In this paper, we propose a novel model and authoring method of digital contents which improves the educational effects in the area of cyber educations through Web. Especially we offer a new model of contents authoring for engineering departs using JAVA technology and concept-based branch strategy, making unit-contents separated in accordance with their characteristics and then accessing them at arbitrary instant in the replaying time. In proportion to the proposed model and strategy, the resultant contents might show advanced adaptabilities and interactions for users and the educational effects are really improved. Combining and realizing the proposed conceptual branch method and JAVA applet library with the conventional page-branch or subject-blanch we expect to get a novel basic scenario of engineering cyber contents and the scenario might improve the authoring and educational effects of the contents by applying its good interactive properties and realistic operations.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.259-282
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• 2010

In this paper, we introduce a modified Moore Method designed for the multivariable calculus course, and discuss about the effective teaching and learning method by observing the changes in the understanding of students' learning and the effects on students' learning in the class implemented by this modified Moore Method. This teaching experiment research was conducted with the 15 students who took the multivariable calculus course offered as a 3 week summer session in 2008 at H University. To guide the students' active preparation, stepwise course materials structured in the form of questions on the important mathematical notions were provided to the students in advance. We observed the process of the students' small-group collaborative learning activities and their presentations in the class, and analysed the students' class journals collected at the end of every lecture and the survey carried out at the end of the course. The analysis of these results show that the students have come to recognize that a deeper understanding of the subjects are possible through their active process of search and discovery, and the discussion among the peers and teaching each other allowed a variety of learning experiences and reflective thinking.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.717-754
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• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, which is very similar to the pattern of 'Conjectures and Refutations'(Lakatos, 1976). Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as humility and courage (Lampert, 1990), which is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.

• Education of Primary School Mathematics
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• v.19 no.4
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• pp.349-360
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• 2016

This cross-national study examines the similarities and differences between Korean and U.S. pre-service teachers' views on equitable mathematics teaching. Pre-service teachers enrolled in mathematics education courses at the two sites (Korea, n=51; U.S., n=33) were administered a survey consisting of the following: (a) items about pre-service teachers' views on equity relative to mathematical ability, classroom policies and practices, and access to learning opportunities, (b) items about pre-service teachers' agreement in their views on recommended practices, and (c) items about participants' past learning experiences in an equitable learning environment as students. Similarities were found between the sites regarding the following: (a) advocating for equitable mathematics teaching, and (b) conceptualizing equitable teaching as a way to support the learning of less capable students. Differences were found with regard to nurturing growth mindsets in mathematics; positioning toward equal opportunities and outcomes in learning; and relating to grouping as collaborative learning strategies.

• Communications of Mathematical Education
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• v.34 no.1
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• pp.1-15
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• 2020

Today's healthcare, intelligent robots, smart home systems, and car sharing are already innovating with cutting-edge information and communication technologies such as Artificial Intelligence (AI), the Internet of Things, the Internet of Intelligent Things, and Big data. It is deeply affecting our lives. In the factory, robots have been working for humans more than several decades (FA, OA), AI doctors are also working in hospitals (Dr. Watson), AI speakers (Giga Genie) and AI assistants (Siri, Bixby, Google Assistant) are working to improve Natural Language Process. Now, in order to understand AI, knowledge of mathematics becomes essential, not a choice. Thus, mathematicians have been given a role in explaining such mathematics that make these things possible behind AI. Therefore, the authors wrote a textbook 'Basic Mathematics for Artificial Intelligence' by arranging the mathematics concepts and tools needed to understand AI and machine learning in one or two semesters, and organized lectures for undergraduate and graduate students of various majors to explore careers in artificial intelligence. In this paper, we share our experience of conducting this class with the full contents in http://matrix.skku.ac.kr/math4ai/.

• Journal of the KSME
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• v.26 no.5
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• pp.389-393
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• 1986

고유치는 여러 공학문제에서 중요하다. 예를들어 비행기의 안전성은 어떤 행렬(matrix)의 고유 치에 의해서 결정된다. 보의 고유진동수는 실제로 행렬의 고유치이다. 좌굴(buckling) 해석도 행렬의 고유치를 구하는 문제이다. 고유치는 여러 수학적인 문제의 해석에서도 자연히 발생한다. 상수계수 일계연립상미분방정식의 해는 그 계수행렬의 고유치로 구할 수 있다. 또한 행렬의 제곱의 수렬 $A,{\;}A^{2},{\;}A^{3},{\;}{\cdots}$의 거동은 A의 고유치로서 가장 쉽게 해석할 수 있다. 이러한 수렬은 연립일차방정식(비선형)의 반복해에서 발생한다. 따라서 이 강좌에서는 행렬의 고유치를 수치적으로 구하는 문제에 대하여 고찰 하고자 한다. 실 또는 보소수 .lambda.가 행렬 B의 고유치라 함은 영이 아닌 벡터 y가 존재하여 $By={\lambda}y$ 가 성립할 때이다. 여기서 벡터 y를 고유치 ${\lambda}$에 속하는 B의 고유벡터라 한다. 윗식은 또 $(B-{\lambda}I)y=0$의 형으로도 써 줄 수 있다. 행렬의 고유치를 수치적으로 구하는 방법에는 여러 가지 방법이 있으나 그 중에서 효과있는 Danilevskii 방법을 소개 하고자 한다. 이 Danilevskii 방법에 의하여 특 성다항식(Characteristic polynomial)을 얻을 수 있고 이 다항식의 근을 얻는 방법 중에 Bairstow 방법 (또는 Hitchcock 방법)이 있는데 이에 대하여 아울러 고찰하고자 한다.