• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.389-407
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• 2005

수학은 위계적이고 구조적인 특성을 가지고 있어서 학생들이 적절하게 학습하면 내적 동기유발이 가능하고 흥미 있게 학습해 나갈 수 있는 반면 단편적인 지식들로 학습하려 한다면 그 양이 방대해지고 제대로 이해하기가 어렵다. 그러므로 교사는 수학적 지식의 구조를 깨달아 지식의 본체가 내적으로 어떻게 조직되고 상호 관련되어 있는지 알아야 하고 학생들이 수학적인 아이디어와 절차를 획득하고 탐구하게 하는 적절한 문제를 제시하여 문제해결을 통해 가르쳐 가는 방법을 생각해야 할 것이다. 이 때에 학생들은 문제해결 과정에서 능동적인 역할을 하면서 자신이 학습하고 있는 것의 핵심을 인식하고 호기심을 갖고 유의미한 기능들을 이끌어내는 학습을 해야 하는데, 이는 오랜 전통의 탐구 학습과 그 맥락을 같이 하는 것이다. 수학교과 고유의 특성을 살려 지식의 구조를 가르침에 있어서 교수 방법으로의 문제해결을 통한 지도와 학습 방법으로의 탐구학습 과정은 잘 조화될 수 있다. 이러한 조화된 모습을 드러나게 하고자 초등학교 5학년 가 단계에서 '평면도형의 넓이와 둘레 사이의 관계'를 탐구하게 하는 문제해결을 통한 탐구학습 과제를 제시해 보았다. 30-40년을 거슬러 올라가는 역사를 갖는 지식의 구조나 탐구학습, 문제해결에 대한 관심은 오늘날에도 여전히 시사하는 바가 크다고 하겠다. 수학교육에 관한 연구들은 완전히 새로운 것이기보다는 이전의 것들이 주는 의미를 되새기고 오늘의 상황에 비추어 해석할 때 수학교육은 한 단계 올라서게 된다.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.569-594
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• 2010

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out several research as follows : 1) establishment of observation elements for selecting examples of good mathematics instruction between 2001 and 2002, 2) development of the standards on teaching evaluation between 2004 and 2006, and 3) investigation on the elements of Pedagogical Content Knowledge including understanding of learners between 2007 and 2008. The purposes of development of mathematics teaching evaluation standards through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those three studies (namely, evaluation standards) focused on the teacher knowledge of learners' understanding. For this purpose, the meaning of learners' understanding was also investigated in-depth. Finally, the concrete elements on teaching evaluation focused on the teacher knowledge of learners' understanding in math class were new developed, based on the literature reviews on learners' understanding. Then, those evaluation elements were developed according to the five domains of learners' understanding such as evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies.

• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• Journal of the Korean School Mathematics Society
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• v.24 no.4
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• pp.327-348
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• 2021

This study examines the effects of mathematics learning mentoring activities on mathematical knowledge for teaching (MKT) of pre-service mathematics teachers. We choose six pre-service mathematics teachers in the department of mathematics education at M University. The pre-service mathematics teachers conducted 1:1 mathematics learning mentoring for two hours at a times and twice a week for 15 weeks. The pre-service mathematics teachers submitted the mentor log, which recorded weekly learning and emotional observations. We collected the mentor log and the reflection log of pre-service mathematics teachers and the interviews with pre-service mathematics teachers. Based on the collected data, we analyzed the effects of MKT, the understanding of students, and pre-service mathematics teachers' introspection by mathematics learning mentoring. We obtained conclusions as follows. First, mathematics learning mentoring provides an opportunity for pre-service mathematics teachers to apply the theory of mathematical education to schools. Thus pre-service mathematics teachers express theoretical knowledge as practical knowledge. Second, mathematics learning mentoring helps pre-service mathematics teachers have the ability to understand students and provide opportunities to reflect on their attitudes as learners. Third, mathematics learning mentoring helps advance teaching activities by providing pre-service mathematics teachers with opportunities to reflect on their teaching activities. Finally, mathematics learning mentoring has positively influenced the change in pre-service mathematics teachers' beliefs and teaching intuition.

• School Mathematics
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• v.18 no.3
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• pp.503-526
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• 2016

The study aimed at determining the identity of mathematics essay test in the university entrance examination. For this purpose, a document research was conducted for higher order thinking and mathematics essay ability and it analyzed the goal of assessment and the tendency of problem settings and looked into mathematics essay problems of twenty-five universities. As a result, the study found out that evaluation factors of mathematics essay test requires higher order thinking ability including mathematical knowledge and essay ability such as mathematical knowledge, understanding, problem solving, logical and critical thinking, creative ability, power of expression, argument skills. Also, problems from previous mathematics essay tests were set mainly to assess mathematical knowledge, understanding and problem solving. Based on the findings, the past mathematics essay tests in university entrance examination in Korea that require logical and critical thinking, creative ability, power of expression, argument skills were a rather small percentage of questions.

• 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 of Educational Research in Mathematics
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• v.17 no.2
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• pp.147-162
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• 2007

This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.129-142
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• 2004

These days, constructivism has become a central theory in mathematics education. A essential concept in constructivism is 'construction' and the meaning of construction of mathematical knowledge is a core issue in mathematics educational field. In the basis of Dewey's epistemology, this article is trying to explicate the meaning of construction of mathematical knowledge. Dewey, Kant and Piaget coincide in construction of knowledge from the viewpoint of the interaction between mind and environment. However, unlike Dewey's concept, Kant and Piaget are still in the line of traditional realistic epistemology. Dewey's concept of construction logically implies teaching-learn learning principles. This can be named as a principle of genetic construction and a principle of progressive consciousness.

• Communications of Mathematical Education
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• v.14
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• pp.61-70
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• 2001

수학은 추상적인 학문이다. '추상'은 몇 개 또는 무한히 많은 사물의 공통성이나 본질을 추출하여 파악하는 사고작용이다. 이렇게 추상된 것들을 모아 분류를 하고 그 다음에 이름을 붙이는 것이 바로 개념이 형성되는 과정이고 수학자가 수학을 하는 과정이다. 이 개념들은 여러 가지 모양으로 결합하여 스키마라고 부르는 개념 구조를 형성하게 되는데, 이 스키마는 수학적 사고를 하는데 매우 중요한 역할을 하여 수학을 개념적으로 이해하는데 도움을 주며, 새로운 지식을 얻는데 필요한 필수적인 도구가 된다. 본 논문에서는 연속적인 수열의 합의 공식에 대하여 학생들이 Skemp가 말한 '관계적 이해'를 할 수 있도록 스키마를 이용하여 문제를 해결할 수 있는 모델과 원주의 스키마를 이용한 생활 속의 문제를 제시하여 학생들이 공식을 암기하기보다는 수학의 구조를 파악하고 연계성을 이해함으로서 능동적인 구성활동을 유발하여 수학에 대한 흥미를 느낄 수 있도록 도움을 주고자 한다.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.