• Communications of Mathematical Education
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• v.32 no.1
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• pp.97-111
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• 2018

This study is to establish the domains and the standards of instructional evaluation on the teacher knowledge dealing with the knowledge of 'teaching and learning methods and assessment'. Especially, in this study, the instruction assessment standards are developed focused on the six types of mathematics competencies such as problem solving, communication, reasoning, creativity and collaboration, information and handling, attitude and practice which were emphasized in the mathematical curriculum revised in 2015. By the result, seventh evaluation domains such as an instruction involving problem-solving activity, an instruction involving reasoning activity, instruction involving communication activity, instruction on information and handling activity, instruction involving learners' achievement level and attitude, instruction involving the development of assessment method and tool, instruction applying on assessment result were new established. According to those domains, the 19 instructional evaluation standards were developed totally. This study is limited to consider the domain of 'teaching and learning methods and assessment' among the domains of teacher knowledge, while dealing with the elements of mathematics competencies in the standards. However, instructional evaluation standards reflecting these competencies should be developed in the other diverse domains of teacher knowledge.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.517-534
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• 2012

As observing the learning of middle school mathematics students for three years, I examined the relationship between students' procedural knowledge and their conceptual knowledge as they develop those knowledges in the rational number domain. In particular, I explored the implications of an unbalanced development in a student's conceptual knowledge and procedural knowledge by considering two conditions: (a) the case of a student who has relatively strong conceptual knowledge and weak procedural knowledge, and (b) the case of a student who has relatively weak conceptual knowledge and strong procedural knowledge. Results suggest that conceptual knowledge and procedural knowledge are most productive when they develop in a balanced fashion (i.e., closely iterative or simultaneously), which calls into question the assumption that one has primacy over the other.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.355-369
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• 2009

Though there is no agreement on the definition of analogical reasoning, there is no doubt that analogical reasoning is the means of mathematical knowledge construction. Mathematicians generally have a tendency or desire to find similarities between new and existing Ideas, and new and existing representations. They construct appropriate links to new ideas or new representations by focusing on common relational structures of mathematical situations rather than on superficial details. This focus is analogical reasoning at work in the construction of mathematical knowledge. Since analogical reasoning is the means by which mathematicians do mathematics and is close]y linked to measures of intelligence, it should be considered important in mathematics education. This study investigates how mathematicians used analogical reasoning, what role did it flay when they construct new concept or problem solving strategy.

• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.331-352
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• 2012

The purpose of the study is to verify what cognitive variables have significant effect on proportional problem solving. For this aim, the study classified proportional problem into well-structured, moderately-structured, ill-structured problem by the level of structuredness, then classified the cognitive variables as well into factual algorithm knowledge, conceptual knowledge, knowledge of problem type, quantity change recognition and meta-cognition(meta-regulation and meta-knowledge). Then, it verified what cognitive variables have significant effects on 6th graders' proportional problem solving abilities through multiple regression analysis technique. As a result of the analysis, different cognitive variables effect on solving proportional problem classified by the level of structuredness. Through the results, the study suggest how to teach and assess proportional reasoning and problem solving in elementary mathematics class.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.447-462
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• 2003

The purpose of this study was to Investigate the preservice elementary teachers' pedagogical content knowledge of addition and subtraction. The subjects for data collection were 29 preservice elementary teachers and data were collected through open ended problems. The findings imply that the preservice elementary teachers show low level of understanding of addition and subtraction such as the word problem posing and the contexts of part-part-whole and compare. The research results indicate that the preservice elementary teachers possess primarily a procedural knowledge of pedagogical content knowledge and don't understand relationship with real-world situation. This study provide the information available on developing program for preservice elementary teachers.

• School Mathematics
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• v.11 no.4
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• pp.607-623
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• 2009

This study aims to investigate a child's informal knowledge of carrying and borrowing in additive calculations. The additive word problems including three types of calculations are posed a child that is the first grader and has no lessons about carrying and borrowing. By analysing his answers, his informal knowledge, that is his methods and strategies for calculating the additive problems are revealed. As a result, conceptual aspects and procedural aspects of his informal knowledge are recognized, and the didactical implications are induced for connecting his informal knowledge and the formal knowledge about carrying and borrowing.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.1
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• pp.97-101
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• 2003

최근 수학구조 및 교수-학습과 관련된 연구에 지식공간 이론을 응용하고자하는 논문들이 많이 나오고 있다. 실제로 유의미 학습과 관련된 수행평가와 수학문제를 푸는 능력에 관한 평가를 연구하는데 지식구조가 응용되고 있지만 이를 활용하는데는 많은 애로사항이 있으며 이를 보완하기 위한 여러 가지 방법이 연구되어오고 있다. 특히, Schrepp교수는 스피드문제의 경우로 제한하여 지식공간론을 응용한 일반화된 수학구조의 연구방법을 제시하였다. 본 논문에서는 주관적 지식의 평가를 하게되는 수학구조 및 공간에 관한 연구를 하는데 효과적으로 응용될 수 있는 퍼지지식공간론에 관한 전반적인 기초 이론을 정의하고 그 성질들을 연구하고자한다.

• The Mathematical Education
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• v.43 no.3
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• pp.257-273
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• 2004

In this paper, we analyze what the components of mathematics teacher` knowledge are, and find that mathematics teacher need knowledge of three areas: subject matter knowledge, pedagogical knowledge, and pedagogical content knowledge. Studies of practicing teachers suggest that When teachers lack understanding in their respective disciplines, it inhibits them from providing students the best learning opportunities, but that a teacher possessing pedagogical content knowledge provides learners with multiple approaches into learning. Some teachers having sound knowledge of mathematics and students were able to respond appropriately to students' questions, design appropriate learning activities involving a variety of mathematical representations, and orchestrate mathematical discourse in the classroom. Thus, it appears that mathematics teachers' knowledge positively affect teaching and student learning..

• Communications of Mathematical Education
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• v.15
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• pp.71-76
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• 2003

학생들의 분수 나눗셈에 대한 이해는 개념적 이해를 바탕으로 수행되어야 함에도 불구하고 분수 나눗셈은 많은 학생들이 기계적인 절차적 지식으로 획득할 가능성이 높은 내용이다. 이것은 학생들이 학교에서 분수 나눗셈을 학습할 때에 일상생활에서의 경험과 선행 학습과의 연결이 잘 이루어지지 못하고 있는 것에 큰 원인이 있다고 본다. 본 연구에서는 학생들의 분수 나눗셈의 개념적 이해를 돕기 위하여 경험적 지식과의 연결 관계를 활용한 교수 방안을 실험 교수를 통해 조사하였다. 결과로서 번분수를 활용한 수업은 분수 나눗셈의 표준 알고리즘이 수행되는 이유를 알 수 있게 하는데 도움이 되나 여러 가지 절차적 지식이 뒷받침되어야 하며 분수 막대를 직접 잘라 보는 활동을 통한 수업은 분수 나눗셈에서의 나머지를 이해하는데 효과가 있다는 것을 알았다. 결론적으로, 학생들의 경험과 학교에서 이미 학습한 분수 나눗셈들의 관련 지식들을 적절히 연결하도록 한다면 수학적 연결을 통해 분수 나눗셈의 개념적 이해를 이끌 수 있다.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.17-28
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• 2008

이 논문은 중학교 기하 영역의 수업에 대한 학생들의 성취도가 낮은 것을 관찰하고, 그에 대한 고민으로 교육과정을 분석하고, 수학교육의 질적 접근을 위한 교수 실험을 통해 실제 중학교 과정에서 운용되는 논증기하 교육의 문제점과 그 대안을 탐색하고자 하였다. 본 연구에서는 교사가 반드시 갖춰야 할 지식으로 Shulman(1986)이 제시한 교과 내용 지식과 교수학적 내용 지식, 그리고 교육과정 관련 지식을 받아들였으며, 중학교 기하 영역에서 이런 지식을 갖추기 위해 교사가 폭넓은 고민을 하여 수업의 개선점을 찾는 과정을 보여주고 있다. 연구를 통해서 학생들에게 명제를 지도할 때 주의할 점과 학습자에게 증명을 하도록 제시하는 방법상의 문제점, 그리고 이등변삼각형의 지도에서의 그 증명이 갖는 의미를 잘 이해하여 학생들에 증명 학습에 진정한 도움이 될 수 있는 방향을 탐색하였다. 그리고 절차만을 학습시키는 현행 작도 수업을 개선하기 위한 여러 시도와 등변사다리꼴의 학습에서와 같이 학생들이 수학 용어를 되돌아보는 수업이 필요성을 탐색하여, 많은 교수 실험을 통한 교육과정의 바람직한 개정을 제안하였다.