• Education of Primary School Mathematics
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• v.20 no.1
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• pp.117-130
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• 2017

Euclid's elements have been recognized as a significant textbook in mathematics and mathematics education because of importance of its contents and methodology. This study discussed how the elements is connected with understanding of math textbooks in elementary school, trying to reveal the value for teacher training. First, when details in elementary textbooks were considered in aspect of elements, the importance of elements was illustrated with the purpose of understanding contents of elementary school by examining educational implications. In addition, the study discussed the value of the elements as the place for teachers and would-be teachers to experience math system.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1079-1092
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• 2009

The purpose of this study is to investigate Newton's binomial theorem that was on epistemological basis of the emergent background and developmental course of infinite series and power series. Through this investigation, it will be examined how finding the approximate of square root of given numbers, the method of the inverse method of fluxions by Newton, and Gregory and Mercator series were developed in the course of history of mathematics. As the result of this study pedagogical analysis and discussion of the history of mathematics on Newton's binomial theorem will be presented.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.297-312
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• 2006

As research on the instruction method of the concept of irrational numbers, this thesis is theoretically based on the Freudenthal's Mathematising Instruction Theory and a conducted case study in order to find an introduction method of irrational numbers. The purpose of this research is to provide practical information about the instruction method ?f irrational numbers. For this, research questions have been chosen as follows: 1. What is the introducing method of irrational numbers based on the Freudenthal's Mathematising Instruction Theory? 2 What are the Characteristics of the teaming process shown in class using introducing instruction of irrational numbers based on the Freudenthal's Mathematising Instruction? For questions 1 and 2, we conducted literature review and case study respectively For the case study, we, as participant observers, videotaped and transcribed the course of classes, collected data such as reports of students' learning activities, information gathered through interviews, and field notes. The result was analyzed from three viewpoints such as the characteristics of problems, the application of mathematical means, and the development levels of irrational numbers concept.

• Journal of the Korea Society of Computer and Information
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• v.16 no.2
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• pp.235-242
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• 2011

The industry of computer has been changed quickly by developing and growing info-communications industry and by supplying new technologies. The importance of software field which is based on this change is gradually emphasized. Nowadays more people tend to have realization of mathematics and statistics that are basic theory of software study, moreover, discrete mathematics is especially getting more important in whole mathematics field. It's essential to understand discrete mathematics in order to understand existing knowledge about software field in computer engineering and develop new technologies in different areas in the future. The way people get education about discrete mathematics, however, is improper as a result of massive materials and uncertain standard. This study subdivides discrete mathematics according to different tracks in the computer software study. In addition, the research which is suitable to individuality in different fields is able to be efficiently carried out by selecting related parts and the method of mathematics education is provided to deal with rapidly changed applications in related fields.

• School Mathematics
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• v.14 no.3
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• pp.395-408
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• 2012

This study aims to examine the trends in research design and methods used in research on K-12 mathematics curriculum. By analyzing 124 peer-reviewed research articles published between 2000 and 2010, we concluded that more rigorous and various research design and methods should be conducted to improve educational research on curriculum. Although increasing scholarly attention has recently been given to systematic empirical studies about this topic, a large proportion of the studies examined in this study appeared to lack either a coherent conceptual framework or a systematic analytic tool or method. More effort needs to be made on improving the rigor of research in terms of research design and methods.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.261-275
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• 2016

Many students have dualistic beliefs about mathematics and its learning- for example, there is always just one right answer in mathematics and their role in the classroom is receiving and absorbing knowledge from teacher and textbook. This article investigated some epistemic implications and limitations of common mathematics teaching practices, which often present mathematical facts(or procedures) and treat students' errors in a certain and absolute way. Langer and Piper's (1987) experiment and Oliveira et al.'s (2012) study suggested that presenting knowledge in conditional language which allows uncertainty can foster students' productive epistemological beliefs. Changing the focus and patterns of classroom communication about students' errors could help students to overcome their dualistic beliefs. This discussion will contribute to analyze the implicit epistemic messages conveyed by mathematics instructions and to investigate teaching strategies for stimulating students' epistemic development in mathematics.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.15-24
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• 2005

오늘날 제 7차 교육과정은 학습자의 사고과정과 능력을 다양한 평가방식으로 실시하도록 권유하고 있다. 이러한 목적을 구현하기 위하여 수학과 평가는 교수-학습에 유용한 평가, 과정 중심의 평가, 다양한 방법을 활용하는 평가가 되어야 할 것이다. 이는 학습자로 하여금 스스로 학습하도록 가정하는 인식론적 변화에 바탕을 둔 최근의 평가 동향과 맥을 같이 하고 있다. 평가에서 학생의 수학활동 역시 특히 인지적 영역의 다양성을 지닌 개인에 의하여 이루어지기 때문에 수학 평가는 단편적인 정형화된 지식이 아닌 문제 해결의 전략이나 발견술과 같은 요소에서 강조되고 있는 비정형의 문제들을 통한 메타인지적인 발달과정을 고려해야 한다. 본 연구에서는 학생이 준개방형 평가문제를 해결하는 과정을 통해 자신이 얼마나 알고 있는가를 인식하며 자신의 문제 해결 전략을 점검하고 평가하는 인지적 능력에서 일어나는 변화를 알아보는 데 그 목적이 있다. 지금 현재 연구가 진행 중이며 본 연구의 결과는 다음 논문집에 발표할 예정이다.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.311-331
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• 2014

For preservice teachers' instrumental-to-relational pedagogical content knowledge transformations, this research designed several didactical tasks based on Kinach's cognitive strategies. The researcher identified preservice teachers' understanding about what is a definition and how to teach it. By challenging their fixed ideas about definitions, the researcher could motivate them to embrace the new teaching approach which guides reinvention of definitions. The PCK development was not the simple process of filling their tabular rasa PCK with theories of mathematics education, but the dialectical process of identifying, challenging, changing and extending preservice teachers' existent PCK. This research will contribute to explore new directions of mathematics teachers' PCK development and the method of teacher education.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.91-106
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• 2005

History of mathematics must be analysed to discuss mathematical reality and thinking. Analysis of history of mathematics is the method of understanding mathematical activity, by these analysis can we know how historically mathematician' activity progress and mathematical concepts develop. In this respects, we investigate teaching algebra through historico-genetic analysis and propose historico-genetic analysis as alternative method to improve of teaching school algebra. First the necessity of historico-genetic analysis is discussed, and we think of epistemological obstacles through these analysis. Next we focus two concepts i.e. letters(unknowns) and negative numbers which is dealt with school algebra. To apply historico-genetic analysis to school algebra, some historical texts relating to letters and negative numbers is analysed, and mathematics educational discussions is followed with experimental researches.

• The Mathematical Education
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• v.59 no.4
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• pp.331-355
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• 2020

The purpose of this study is to systematically analyze the results of the existing research on mathematical beliefs, compare and synthesize the valuable results and to suggest implications for mathematical beliefs and research. As a result of checking the methodological quality of 59 articles in total using the MQA(Methodological Quality Assessment) checklist, most of them surveyed mathematical beliefs using questionnaires, and most of the studies were conducted on prospective teachers. As a result of systematic review, the conceptual characteristics of mathematical beliefs, object-specific characteristics, and the educational influence of mathematical beliefs were able to synthesize the meaning. Mathematical beliefs had important educational influences in the practice of teachers, students, and math classes. As the results of the study, we emphasize the importance of changing the beliefs of students and teachers in order to solve the problem of mathematical education, where students rely on private education rather than activity thinking, and teachers do not pay attention to students thinking. It has been shown that concrete support is needed for practicing participatory instruction focused on mathematical thinking.