• The Mathematical Education
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• v.41 no.2
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• pp.173-187
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• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• Research in Mathematical Education
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• v.15 no.3
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• pp.209-228
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• 2011

Many studies such as Pepin (1999a; 1999b), Kaiser (2002), and Park & Leung (2006) revealed that there is a strong dependence of mathematics teaching on cultural traditions in different countries. This study was set up as a detailed comparison between the intended curricula in Berlin and Hong Kong to explore how cultural tradition influenced the intended curriculum. In this study, the intended curriculum is what the (local, state or national) curriculum developers stipulate in the official documents. The German educational system is influenced by the curriculum tradition called Didaktik. Didaktik is a tradition about teaching and learning. Since 16th century, Didaktik has been the most important tool for planning, enacting, and thinking about teaching in most of northern and central Europe (Westbury, 1998). On the other hand, the education system in Hong Kong is influenced by both the Anglo-Saxon curriculum tradition and the Confucian heritage culture (CHC). It was found in this study that, although many studies revealed that there is a strong dependence on cultural traditions of mathematics teaching in different countries, other factors such as social factors or the education system also played an important part in shaping the intended mathematics curriculum. So a simplistic view of dependence of the curriculum on cultural traditions is not warranted. The formation of the curriculum is a much more complicated process encompassing various factors including needs of society, advancement of technology, and government policies at different levels.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.205-230
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• 2014

New teaching and learning theory on various aspects about class is needed to implement education which reflects constructivism, ideally. For an ideal learner-centered mathematics class, tangible and intangible elements related to education(view of knowledge, view of leaner, teacher's role, evaluation, the form of class, learning, teaching material, etc.) should be integrated from a constructive perspective and especially, teaching material has to be premised on that learners have intellectual abilities to construct knowledge themselves, and reflect integrity of knowledge, diversity and others, and contain open attributes. In addition to this, teaching material should have characteristics different from those when objective epistemology applies, so there is a need to analyze whether teaching material has those characteristics. For this, this study compared and analyzed <1. Three-Digit Numbers> which belongs to the domain of numbers and operations out of the units of mathematics(3) textbook of the 2009 revised curriculum for the first and second grade that first introduced story-telling, and <3. Understanding of Place Values> for the second grade of constructive math class used in the U.S.

• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.409-424
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• 2002

The historico-genetic principle has been advocated continuously, as an alternative one to the traditional deductive method of teaching and learning mathematics, by Clairaut, Cajori, Smith, Klein, Poincar$\'{e}$, La Cour, Branford, Toeplitz, etc. since 18C. And recently we could find various studies in relation to the historico-genetic principle. Lakatos', Freudenthal's, and Brousseau's are representative in them. But they are different from the previous historico- genetic principle in many aspects. In this study, the previous historico- genetic principle is called as classical historico- genetic principle and the other one as modern historico-genetic principle. This study shows that the differences between them arise from the historical views of mathematics and the development of the theories of mathematics education. Dewey thinks that education is a constant reconstruction of experience. This study shows the historico-genetic principle could us embody the Dewey's psycological method. Bruner's discipline-centered curriculum based on Piaget's genetic epistemology insists on teaching mathematics in the reverse order of historical genesis. This study shows the real understaning the structure of knowledge could not neglect the connection with histogenesis of them. This study shows the historico-genetic principle could help us realize Bruner's point of view on the teaching of the structure of mathematical knowledge. In this study, on the basis of the examination of the development of the historico-genetic principle, we try to stipulate the principle more clearly, and we also try to present teaching unit for the logarithm according to the historico- genetic principle.

• Smart Structures and Systems
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• v.24 no.2
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• pp.233-242
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• 2019

In this paper, an inverse approach based on uniform load surface (ULS) is presented for structural damage localization and quantification. The ULS is excellent approximation for deformed configuration of a structure under distributed unit force applied on all degrees of freedom. The ULS make use of natural frequencies and mode shapes of structure and in mathematical point of view is a weighted average of mode shapes. An objective function presented to damage detection is discrepancy between the ULS of monitored structure and numerical model of structure. Solving this objective function to find minimum value yields damage's parameters detection. The teaching-learning based optimization algorithm has been employed to solve inverse problem. The efficiency of present damage detection method is demonstrated through three numerical examples. By comparison between proposed objective function and another objective function which make use of natural frequencies and mode shapes, it is revealed present objective function have faster convergence and is more sensitive to damage. The method has good robustness against measurement noise and could detect damage by using the first few mode shapes. The results indicate that the proposed method is reliable technique to damage detection in structures.

• The Mathematical Education
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• v.59 no.2
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• pp.185-199
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• 2020

The purpose of this study is to discuss what the incorporation of humanistic imagination into mathematics means to mathematics education and to suggest implications for mathematics education in school mathematics. Traditionally, mathematics has been perceived to be far from our life problems because it targets logical and pure abstract thinking. According to international mathematics and science studies such as TIMSS and PISA, Korean students have relatively high mathematics achievement in the international research, but their attitude toward mathematics is very negative and their awareness of why they are learning mathematics and their satisfaction with life is low. In mathematics education, linking mathematics with humanities imagination allows students to view problems of human life from a humanities perspective, and to have an understanding of others and reflect on themselves from a new perspective. The researcher introduces several examples of whether mathematics and humanistic imagination can be combined for mathematics education. In this study, the ultimate reason for learning mathematics is to achieve learners to realize the principles of life or Dharma, and to live a happier life. However, in order to expand its rich meaning by making these new attempts in mathematics education, the researcher argued that tolerance and patience are needed for many challenges and difficulties in improving the quality of mathematics content itself including applying humanistic imagination to mathematics properly.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.101-119
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• 2017

This paper is a follow up study of [2]. In this paper we analyse the contents of middle school mathematics textbooks published in the 1st National Curriculum Period centered on the concept 'straight line' and discuss how they are different from contemporary mathematics textbooks in view of connectedness of contents, mathematical terms, textbook as a learning material vs. teaching material, relationship between contents of national curriculum and textbooks, and some topics related to direct proportion, function, method of equivalence as a method for solving simultaneous linear equations and so on. The results of our analysis and discussion suggest implications for reforming mathematics curriculum and developing mathematics textbooks.

• The Mathematical Education
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• v.50 no.3
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• pp.285-308
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• 2011

The objective of this study is to review how researches on mathematics education are being conducted currently in Korea and overseas and to examine the current state of domestic researches on mathematics education from a broader view. Although many efforts have been made to understand trends in researches on mathematics education, there have been few in depth studies on research trends in overseas or for comparison between domestic and overseas trends. Thus, this study classified and analyzed 181 domestic articles between 2005 and 2009 in the journals and and 201 overseas articles in the journals and according to year, research area, research contents, school level, research method, and key words using the PME classification system with some modification. Through these analysis, we examined research trends on secondary mathematics education in Korea and overseas. The research findings are as follows. First, 'teaching learning process' was a spotlight area both at home and overseas, and 'realistic mathematics' and 'social cultural subjects' were not covered much either at home or overseas. 'Mathematical communication' occupied a very small portion in Korea but was a highly interesting area in overseas research. Second, research contents of interest were different between Korea and overseas. Research on general area was the mainstream. But geometry and statistics were mainly studied in Korea and algebra and analysis in overseas. Third, research related to middle school was twice more than that related to high school in Korea, But, research related to middle school was the same as high school in overseas. Fourth, qualitative research was the absolute majority both at home and overseas, and philosophical didactical analysis was used only in Korea. Fifth, the order of key words were problem solving - teacher - curriculum - creativity - textbook in Korea, but teacher - teaching - semiotic - affective factor - proo f- problem solving - technology in overseas.

• Journal of the Korea Convergence Society
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• v.13 no.4
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• pp.63-70
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• 2022

Due to the recent changes in the education market and Corona, Consumers have moved to the tutoring and online learning markets, and the large-scale education service franchise business is reorganized into a small-scale franchise, a business model that maximizes the profit structure from a position where sales are important. Recently, a new learning balance model that can provide individualized services from teacher-centered to student-centered, motivate students is required. In this paper, we propose a new mathematical franchise model (K-MODEL) that can improve a company's profit structure while satisfying the recent education trends and consumer needs from the point of view of the franchise. K-MODEL expects franchisor and franchisees to have a stable profit structure by developing differentiated content and services, learning and operating processes, and various programs to improve learning achievement.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.309-325
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• 2009

The purpose of the study was to investigate the differences between Korean mathematics textbooks and CPMP textbooks in the view of conceptual network, structure of mathematical contents, instructional design, and teaching and learning environment to explore the implications for mathematics education in Korea. According to the results, Korean textbooks emphasized the mathematical structures and conceptual network, on the other hand, CPMP textbooks focused on making connections between mathematical concepts and corresponding real life situations as well as mathematical structures. And generalizing mathematical concepts at the symbolic level was very important objective in Korean textbooks, but in the CPMP textbooks, investigating mathematical ideas and solving problems in diverse contexts including real- life situations were considered very important. Teachers using Korean textbooks preferred an explanatory teaching method with the use of concrete manipulatives and student worksheet, however, teachers using CPMP textbooks emphasized collaborative group activities to communicate mathematical ideas and encouraged students to use graphing calculators when they explore mathematical concepts and solve problems.