• Communications of Mathematical Education
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• v.12
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• pp.67-82
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• 2001

발생적 원리는 수학을 공리적으로 전개된 완성된 것으로 가르치는 형식주의의 결함을 극복하기 위하여 제기되어온 교수학적 원리로, 수학을 발생된 것으로 파악하고 그 발생을 학습과정에서 재성취하게 하려는 것이다. 특히, 수학을 지도함에 있어서 역사적으로 발생, 발달한 순서를 지켜 지도해야 한다는 것이 역사-발생적 원리로, 수학이 역사적으로 발생, 발달 되어온 역동적인 과정을 학생들이 재경험해 보게 하기 위해서는 이러한 일련의 과정을 효과적으로 설명할 수 있는 교수-학습 방법이 필요하다. 변증법적인 방법론은 헤겔에 의해서 꽃을 피운 철학으로, 정일반일합(正一反一合)의 원리에 따라 사물의 발생과 진화 과정을 역동적으로 설명할 수 있는 방법론이다. 따라서, 본 연구는 초등학교에서 역사-발생적 원리에 따라 수학을 지도할 수 있는 방법으로 변증법적인 방법을 고찰하여, 역사-발생적 원리의 수학 교수-학습 방법에 대한 시사점을 얻고자 한다.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.237-252
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• 2013

The philosophy of science of Bachelard is introduced mainly with epistemological obstacles in the discussions within mathematics education. In his philosophy, epistemological obstacles are connected with the dialectical developments of science. Science progresses through generalization of concepts and theories by negating things which were recognized as obvious. These processes start with ruptures against the existing knowledge. Epistemological obstacles are failure in keeping distance with the existing knowledge when reorganization is needed. This concept means that there are the inherent difficulties in the processes of concept formation. Finally I compare the view of Bachelard on the developments of science and the 'interiorization-condensation-objectification' scheme of reflexive abstraction in mathematics education and discuss the inherent difficulties in the learning mathematics.

• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

• Journal of The Korean Association For Science Education
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• v.41 no.3
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• pp.267-281
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• 2021

The shift in the perspective on learning as participation draws attention to learners' identity work. This manuscript foregrounds the ongoing and fluid processes of identity, and focuses on the structure surrounding learners where identity work occurs and the expression of individual agency. From the perspective of learning as participation, we introduce Holland et al. (1998) identity-in-practice theory, as the theoretical lens that dialectically describes structure, agency and identity. The concepts representing this theory are 'figured world', 'positionality' and 'authoring self'. The figured world is a web of meaning encompassing the continuous construct/reconstruct through human actions and also exerts as the social force that shapes human actions. 'Positionality' on the other hand, means an understanding of one's social position in the world. The notion of 'authoring self', is a dimension that synthesizes the above two concepts, which describes the improvisation of one's self through the orchestration and collaboration of various social voices. Next, we analyzed and described various cases of this theory that we found within the scope of science education. However, due to the nature of this theory, which takes a sociocultural approach, international research studies cannot be simply applied to the Korean context. Therefore, we sought to expand the applicability of this theory as a methodological tool, by discussing the directions in which this theory can be used in a domestic context. It is intended that the introduction of this theory, which emphasizes multi-layered, continuous and cumulative identity work, will be used as a resource to further expand the horizon of science education reform that is required for the times.

• Journal of The Korean Association For Science Education
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• v.44 no.1
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• pp.87-103
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• 2024

The content system table of the subject-matter curriculum is considered important in the Korean national curriculum, textbook writing, and teaching and learning in the classroom. However, studies that comprehensively organize the issues concerning the format of the subject-matter curriculum content system have been scarce. This study scrutinized the evolution of the content system from its inception in The 6th Curriculum to the most recent 2022 Revised National Curriculum, focusing on science curricular. The following issues and suggestions were derived for the format of the subject content system. First, caution should be exercised in using terms such as "domain," "field," and "category," and it should be clarified whether these terms are intended simply for logical differentiation or to serve as a content organizer with a specific emphasis. Second, the nature of components such as "core ideas," which can serve as innovative content organizers, should be strictly defined. Third, while the introduction of three-dimensional content elements such as "knowledge and understanding," "process and skill," and "value and attitude" is viewed positively, it is suggested that a further delineation be made, elaborating how each can be utilized to form core competencies. Fourth, the construction of the subject-specific content system in national curriculum needs caution because whether it will resolve or exacerbate the 'disparity between general curriculum and subject-matter curriculums' is uncertain. Finally, as an apparent pendulum motion of the subject-matter content system is observed in national curriculum documents, efforts should be made to ensure that it does not result in meaningless repetition, but instead achieves meaningful dialectical progress.

• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• Journal of the Korean association of regional geographers
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• v.6 no.3
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• pp.117-138
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• 2000

This study is, from the view point of constructive social studies which is the foundation of the 7th curriculum, to explore whether there is any viable program and to investigate it by which students, using photo resources in social studies, can organize their knowledge in the way of self-directed thinking. The main results are as follows: If it is a principle of knowledge construction process of constructive social studies that individual construction (cognitive construction) develops into communal construction(social construction) and yet communal construction develops itself, interacting with individual construction, it will be meet the objectives of social studies. In social studies, photos are a powerful communication tool. communicating with photos enables to invoke not only the visual aspects but also invisible aspects of social phenomena from photos. It, therefore, can help develop thinking power through inquiry learning, which is one of the emphasis of the 7th curriculum. Having analyzed photo resources appeared on the regional textbooks in elementary social studies, they have been appeared that even though the importance and amount of space photo resources occupy per page is big with regard to total resources, most of the photos failed to lad to self-directed thinking but just assistant material in stead. Besides, there appeared some problems with the title, variety, size, position, tone of color, visibility of the photos, and further with the combination of the photos. Developing of photo resources for constructive social studies is to overcome some problems inherent in current text books and to reflect the theoretical background of the 7th curriculum. To develop the sort of photo that can realize the point just mentioned, it would be highly preferable to provide photo database to facilitate study with homepage through web-based interaction. To take advantage of constructive photo resources, the instruction is strategized in four stages, intuition, conflict, accommodation, and equilibration stage. With the advancement of the era of image culture, curriculum developers are required to develop dynamic, multidimensional digital photos rather than static photos when develop text books.