• 대한수학교육학회지:학교수학
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• 제1권1호
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• pp.123-133
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• 1999

For an appropriate assessment in mathematics, students should play an active role in their learning by becoming aware of what they have learned in mathematics and by being able to assess their attainment of mathematical knowledge. The process of actively examining and monitoring students' own progress in learning and understanding of their mathematical knowledge, process, and attitude is called self-assessment, Researchers in mathematics education have found some important facts about the meta-cognitive process which is related to self-assessment : i. e. meta-cognition progress is composed of being aware of ones' own personal thinking of content knowledge and cognitive process(self-awareness) and engagement in self-evaluation. Tipical method for self-assessment in mathematics developed upon above finding about meta-cognitive progress is describing about students' knowledge and their problem solving strategies. In the beginning of the description in mathematics about themselves, students are required to answer which part they know and which part they don't know. Self-assessment of students' attitudes and dispositions can be just as important as assessment of their specific mathematical abilities. To make the self-assessment method a success, teachers should let students' have confidence and earn their cooperation by let them overcoming fear to be known the their ability to other students. In conclusion, self-assessment encourages students to assume an active role in development of mathematical power. For teachers, student self-assessment activities can provide a prism through which the development of students' mathematical power can be viewed.

• 대한수학교육학회지:수학교육학연구
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• 제14권3호
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• pp.283-304
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• 2004

본 논문은 1년 동안 학생중심 수학교실문화를 구현하려고 노력하는 3명의 초등학교 교사들을 대상으로 6개의 수학교실문화를 분석함으로써 교사중심에서 학생중심의 문화로 바꿔나가는 과정을 상세하게 탐색한다. 연구대상 교실 모두에서 일반적인 사회적 규범과 관련하여 학생중심 교수법의 전형적인 양상이 구현된 반면에, 사회수학적 규범과 수학적 관행 측면에서는 학생들의 아이디어가 수학적 담화와 활동의 중심이 되는 정도에 따라서 유사성보다는 차이점이 부각되었다. 이러한 연구 결과를 바탕으로 수학교실문화 개선의 난제, 사회수학적 규범과 수학적 관행의 중요성, 교사의 역할 등에 관해 논의한다.

• 한국과학교육학회지
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• 제30권7호
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• pp.920-932
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• 2010

Many topics in science, especially, abstract concepts, relationships, properties, entities in invisible ranges, are described in mathematical representations such as formula, numbers, symbols, and graphs. Although the mathematical representation is an essential tool to better understand scientific phenomena, the mathematical element is pointed out as a reason for learning difficulty and losing interests in science. In order to further investigate the relationship between mathematics knowledge and science understanding, the current study examined 793 high school students' understanding of the pH value. As a measure of the molar concentration of hydrogen ions in the solution, the pH value is an appropriate example to explore what a student mathematical structure of logarithm is and how they interpret the proportional relationship of numbers for scientific explanation. To the end, students were asked to write their responses on a questionnaire that is composed of nine content domain questions and four affective domain questions. Data analysis of this study provides information for the relationship between student understanding of the pH value and related mathematics knowledge.

• 한국수학교육학회지시리즈A:수학교육
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• 제62권3호
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• pp.363-380
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• 2023

본 연구의 목적은 초등학교 교사가 수학 교과서 과제를 수학적 모델링 과제로 변형하는 과정에서 경험하는 어려움과 수학적 모델링 과제 개발을 위한 지식 변화의 사례를 분석하는 것이다. 이를 위해 10년 경력의 초등교사가 교사연구공동체의 반복적인 논의에 참여하면서 초등학교 5학년 수학의 자료와 규칙성 영역 중 평균 지도를 위한 과제를 수학적 모델링 과제로 변형하였다. 연구결과, 첫째, 교사는 과제 변형 과정에서 현실성의 반영, 수학적 모델링 과제의 적절한 인지적 수준 설정, 수학적 모델링 과정에 따른 세부 과제의 제시에 어려움을 겪었다. 둘째, 반복된 과제 변형을 통해, 교사는 학습 내용과 학생의 인지적 수준을 고려한 현실성 있는 과제의 개발, 과제의 복잡성 및 개방성 조정을 통한 과제의 인지적 수준 조정, 학생의 과제 해결 과정에 대한 사고실험을 통한 수학적 모델링 과정에 따른 세부 과제의 제시를 수행할 수 있었으며, 이는 수학적 모델링의 개념과 과제의 특징 등 수학적 모델링 과제 개발을 위해 요구되는 교사 지식이 향상되었음 보여준다. 본 연구결과는 향후 수학적 모델링 교사교육과 관련하여, 교과서 과제 변형을 통한 수학적 모델링 과제 개발 역량 향상의 기회를 제공하는 교사교육, 수학적 모델링의 이론 및 실제를 결합한 교사교육, 교사연구공동체에의 참여를 통한 교사교육이 필요함을 보여준다.

• 대한수학교육학회지:수학교육학연구
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• 제9권2호
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• pp.459-471
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• 1999

This study is to develop a mathematics assessment framework based on the mathematics assessment framework and content strands suggested by KEDI, NCTM, NAEP, TIMSS, Oregon State, New Zealand. According to the literature review, there has been more emphasis that students themselves 'communicate' what they 'understood' and how they 'thought' during the situation of 'solving problems'. As a result, communication ability is considered one of the most important factors in assessment situation, which always accompany the abilities of understanding, thinking, problem-solving, etc. In conclusion, the framework related to mathematical knowledge consists of content and behavior domains. The content domain is categorized into 6 content areas of the 7th mathematics curriculum, and the behavior domain is divided into computation, understanding, inference, problem-solving, and communication.

• 한국생활과학회지
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• 제17권1호
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• pp.35-43
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• 2008

The purpose of this study is to develop evaluation tools for young children's mathematical ability based on the content standards of NCTM and to verify the suitability of the tools. The tools consist of 5 sub-tests with 90 items, including number and operation, algebra, geometry, measurement, data analysis and probability. The tool analysis was examined with 300 three-to five-years-old children and 31 math education professionals. The results of this research are as follows : First, in order of age the passing rate increased. The gap between high and low score group reveals a statistically meaningful difference. Second, the internal consistency reliability coefficient, Cronbach ${\alpha}$, is .96. Test-retest reliability is around .90. The concurrent validity correlation between this tools and Choi Hye-Jin's test(2003) is .85. The analysis of the content validity was proved appropriately by math education professionals.

• 대한수학회보
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• 제51권1호
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• pp.29-41
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• 2014

In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+${\cdots}$+f(nx) = 0, with $n{\geq}2$, which are related to the partial sums of the Riemann zeta function. These curves ${\alpha}$-densify a large class of compact sets of the plane for arbitrary small ${\alpha}$, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the $n^{th}$ power of the density approaches the Jordan content of the compact set which the curve densifies.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권1호
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• pp.27-40
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• 2011

The purpose of this paper is to analyze and discuss the viewpoint dealing with the fundamental figures-point, line segment, and angle-of elementary school teachers. In fact, our main subjects in this article are as follows; how do elementary school teachers deal with the fundamental figures?, what is the general notion about the fundamental figures of elementary school teachers? Our such subjects come from the survey results about the 'fundamental figures in J. A. Ko(2009); the elementary school students have a tendency to regard the fundamental figures as not mathematical figures. In this article, we discuss mainly the meta-cognitive shift in the transform of notion, for example, from 'congruent' concept to 'equal' concept, about the fundamental figures.

• East Asian mathematical journal
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• 제23권3호
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• pp.313-326
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• 2007

The purpose of education of propositional logic is to understand the basic structure of the mathematics and to improve the logical thinking in normal life. But in the seventh curriculum, some basic terms, for examples $\wedge$ and $\vee$, are not introduced, the proposition $p{\\rightarrow}q$ is not defined properly, and use the wrong term $\Rightarrow$ so that it is difficult to understand the propositional logic. In this paper, we present a suitable content for the propositional logic in high-school mathematical class. We also present a proper definition of the proposition $p{x}{\Rightarrow}q{x}$ without using the notation $\rightarrow$. We finally give proper definitions of necessary conditions, sufficient conditions, and necessary and sufficient conditions.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.177-189
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• 2006

This study focuses on the analysis of prospective elementary teachers' representation of trapezoid area and teacher educator's reflecting in the context of a mathematics course. In this study, I use my own teaching and classroom of prospective elementary teachers as the site for investigation. 1 examine the ways in which my own pedagogical content knowledge as a teacher educator influence and influenced by my work with students. Data for the study is provided by audiotape of class proceeding. Episode describes the ways in which the mathematics was presented with respect to the development and use of representation, and centers around trapezoid area. The episode deals with my gaining a deeper understanding of different types of representations-symbolic, visual, and language. In conclusion, I present two major finding of this study. First, Each representation influences mutually. Prospective elementary teachers reasoned visual representation from symbolic and language. And converse is true. Second, Teacher educator should be prepared proper mathematical language through teaching and learning with his students.