• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.45-69
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• 2007

In the 21st century, knowledge-based and information-based society requires not just the capability of applying mathematics simply but mathematical power such as problem-solving ability which composes and solves problems using mathematical knowledge in real-life and fields of various subjects. However, to develop mathematical power, we need various teaching and learning methods which raise basic mathematical knowledge, the inference capability, problem- solving ability, the flexibility of thinking, the expressing and transforming ability of mathematical ideas, perseverance, interest, intellectual curiosity, and creativity. In this paper, we develop the teaching-learning plans based on real life using the various methods of learning and then we analyze the change of students's cognition of mathematics and the students's reaction of the class.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.483-497
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• 2008

This study investigated what kind of informal knowledge is emergent and what role informal knowledge play in process of solving 2-digit by 2-digit multiplication task. The data come from 4 times interviews with a 3th grade student who had not yet received regular school education regarding 2-digit by 2-digit multiplication. And the data involves the student's activity paper, the characteristics of action and the clue of thinking process. Findings from these interviews clarify the child's informal knowledge to modeling strategy, doubling strategy, distributive property, associative property. The child formed informal knowledge to justify and modify her conjecture of the algorithm.

• The Mathematical Education
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• v.60 no.3
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• pp.387-407
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• 2021

The present study was conducted on the assumptions that both progressivist and constructivist education emphasized the subjective knowledge of learners and confronted similar problems when the derived educational principles from the two perspectives were adopted and applied to mathematics research and practice. We argue that progressivism and constructivism should have clarified the meaning, purpose, and direction of 'emphasizing subjective knowledge' in application to the particular educational field. For the issue, we reflected Dewey's theory on the application of past progressivism, and aligned with it, we took a critical view of the educational applications of current constructivism. As a result, first, the meaning of emphasizing subjective knowledge is that each of the students constructs a unique mathematical reality based on his or her experience of situations and cognitive structures, and emphasizes our understanding of this subjective knowledge as researchers/observers. Second, the purpose of emphasizing subjective knowledge is not to emphasize subjective knowledge itself. Rather, it concerns the meaningful learning of objective knowledge: internalization of objective knowledge and objectification of subjective knowledge. Third, the application of the emphasis on subjective knowledge does not specify certain teaching/learning methods as appropriate, but orients us toward a genuine learner-centered reform from below. The introspections, we wish, will provide new momentum for discussion to establish constructivism as a coherent theory in mathematics classrooms.

• Communications of Mathematical Education
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• v.6
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• pp.411-428
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• 1997

• Communications of Mathematical Education
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• v.15
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• pp.153-159
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• 2003

수학 학습의 목표를 수학적 사고력의 신장이라는 측면에서 보았을 때 이를 위하여 문제에 대한 다양한 해법을 찾는 활동은 중요하다. 문제에 대한 다양한 접근은 문제해결의 전략을 학습시키고 사고의 유연성을 길러줄 수 있는 방법이 된다. 문제에 대한 다양한 해법을 찾는 과정에서 이미 알고 있는 지식이 어떻게 응용되는지를 알게 된다. 특히 기하 문제에 대한 다양한 접근은 문제해결의 전략을 학습시킬 수 있는 좋은 예가 된다. 본고에서는 문제해결을 통한 수학적 일반성을 발견하기 위한 방법으로서 문제에 대한 다양한 해법을 연역과 귀납에 의하여 일반화하는 과정을 탐색하고자 한다. 특히 수학 문제에 대한 다양한 해법을 찾는 것은 문제해결 전략으로서 뿐만 아니라 창의적 사고의 신장 측면에서 시사점을 던져준다.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.555-572
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• 2014

Teacher preparation programs are responsible for preparing teachers to be able to perform their work with professional knowledge and skills. What opportunities to learn such knowledge and skills the programs intentionally develop for prospective teachers can be discerned by looking at the curriculum of teacher education. The purpose of this study is to find implications for the curriculum in elementary teacher education in South Korea, especially as that pertains to opportunities to learn teaching mathematics. This paper compares the curricula of 21 teacher preparation programs for elementary teachers in South Korea and in the United States. It finds that the programs in both countries emphasize teacher preparation to teach subject matter and to help elementary students improve their academic knowledge. The overall structures of the curriculums outlined in the programs of both countries are relatively comparable. In terms of the opportunities to learn teaching mathematics, however, they are quite different in what authentic contents they offer. This paper discusses the need for more emphasis on mathematical knowledge for teaching.

• School Mathematics
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• v.12 no.1
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• pp.79-95
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• 2010

The purpose of this study is to examine into how the mathematically gifted cope with ambiguity when they are encountered to learn via resolving ambiguity. In this study 6 gifted students are asked to resolve the ambiguity. Participant in this study appeared to experience the need of mathematical justification and the flexible change of perspective. The gifted have constructed unified mathematical knowledge by making a relation between two incompatible perspective in the process of resolving the ambiguity. We suggest that dealing with ambiguity in mathematics class can be a good opportunity for enhancing the gifted student mathematics education.

• Communications of Mathematical Education
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• v.3
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• pp.141-167
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• 1997

• The Mathematical Education
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• v.62 no.4
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• pp.531-549
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• 2023

Despite the significance of mathematics teacher guidebooks as a support for teacher learning, there are few studies that address how elementary mathematics teacher guidebooks support teacher learning. The purpose of this study was to analyze the educative features of elementary mathematics teacher guidebooks for grades 3 and 4. For this, six units from each of ten kinds of teacher guidebooks were analyzed in terms of seven dimensions of Teacher Learning Opportunities in Korean Mathematics Curriculum Materials (TLO-KMath). The results of this study showed that mathematics content knowledge for teaching was richly provided and well organized. Teacher guidebooks provided teacher knowledge to anticipate and understand student errors and misconceptions, but were not enough. Sample dialogues between a teacher and students were offered in the teacher guidebooks, making it easier for teachers to identify the overall lesson flow and key points of classroom discourse. Formative assessment was emphasized in the teacher guidebooks, including lesson-specific student responses and their concomitant feedback examples per main activity. Supplementary activities and worksheets were provided, but it lacked rationales for differentiated instruction in mathematics. Teacher knowledge of manipulative materials and technology use in mathematics was provided only in specific units and was generally insufficient. Teacher knowledge in building a mathematical community was mainly provided in terms of mathematical competency, mathematical classroom culture, and motivation. This paper finally presented implications for improving teacher guidebooks to actively support teacher learning.