• 전기의세계
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• v.39 no.12
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• pp.5-11
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• 1990

일상생활에서 우리가 정하는 대상중에 명확하게 그 소속을 정의 할 수 없는 경우가 많다. 이러한 대상들을 수학적으로 다루기 위하여 퍼지집합의 개념을 도입하였다. 이 퍼지집합 개념은 각 대상이 속한다, 안속한다라는 이원론적인 논리오부터, 각대상을 그 모임에 속하는 정도로 이해함으로써 일반화된 개념이다.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• School Mathematics
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• v.11 no.4
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• pp.643-664
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• 2009

This study was aimed to understand the problems that students experience during the self--directed study of a mathematics digital textbook and to find the implications for the design of digital textbook. For this study, we analyzed the process of self-directed learning on 'division of fractions with same denominator' using digital textbook by eight 6th graders. Students asked to use think aloud method while they study the unit. Their learning process was videotaped and analyzed by researchers after the experiment. After the self-directed learning, students filled out a test items and participated interview with a researcher. The result showed that students experienced several misconceptions and errors while using a digital textbook. The types of misconceptions and errors were cataegorized as "misconceptions and errors caused by a mathematics textbook" and "misconceptions and errors caused by a digital textbook". Especially, students showed several important misconceptions and errors because of the design factors. This implies we need to consider the causes of misconceptions for the design of a digital textbook.

• School Mathematics
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• v.12 no.2
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• pp.151-176
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• 2010

This research aims to conduct the teaching experiment based on the constructivism to elementary preservice teachers and report on how they construct and develop the mathematical knowledge on ratio concept. Furthermore, this research aims to examine the significances and difficulties of "constructivist teaching experiment" which are conceived by elementary preservice teachers. As the results of this research, I identified the possibilities and limits of mathematical knowledge construction by elementary preservice teachers in the "constructivist teaching experiment". And the elementary preservice teachers pointed out the significances of "constructivist teaching experiment" such as the experience of prior thinking on the concept to be learned, the deep understanding on the concept, the active participation to the lesson, and the experience of learning process of elementary students. Also they pointed out the difficulties of "constructivist teaching experiment" such as the consumption of much time to carry out the constructivist teaching, the absence of direct feedbacks by teacher, and the adaption on the constructivist lesson.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.469-483
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• 2018

The purpose of this study is to find out how pre-service mathematics teachers should prepare for the teaching of probability and statistics in school mathematics and to help improve teacher education. To do this, questionnaires and evaluation of probabilistic and statistical curriculum were conducted for pre-service teachers, and regression analysis and correlation between them were examined. Through the investigation, the items with low evaluation results due to level of difficulty were extracted and analyzed. As a result, first, it is necessary to teach pre-service mathematics teachers with link the contents curriculum of college and secondary school about probability and statistics. Second, accurate diagnosis of pre-service mathematics teachers' understanding of probability and statistics is needed. Third, the misconceptions and causes of pre-service mathematics teachers were analyzed in detail. And suggests that various follow-up studies related to this are needed.

• School Mathematics
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• v.7 no.4
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.443-459
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• 2009

Despite the many discussions of mathematics education, there are a lot of controversy of the Radian. Generally, Radian is taken to have two properties. One property is an angular property and other is a property of fore numbers. For this reason, both Students and teachers are hard to understand the radian. This study is to provide a base of the radian understand. In essence, radian has only angular property, and other property is a derived property. So radian is to be understood in an angle.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.709-730
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• 2010

The inverse function of a one-to-one correspondence is explained with a graph, a numerical formula or other useful expressions. The purpose of this paper is to know how low achieving students understand the learning contents needed reversible thinking about irrational functions. Low achieving students in this study took paper-pencil test and their written answers were collected. They made various mistakes in solving problems. Their error types were grouped into several classes and identified in this analysis. Most students did not connected concepts that they learned in the lower achieving students to think in reverse order in case of and to visualize concepts of functions. This paper implies that it is very important to take into account students' accommodation and reversible thinking activity.

• 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.21 no.2
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• pp.113-139
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• 2018

There is no doubt about the importance of teacher knowledge for good teaching. Many researches attempted to conceptualize elements and features of teacher knowledge for teaching in a quantitative way. Unlike existing researches, this article suggests an interpretation of preservice teacher knowledge in the field of geometry using the Shulman - Fischbein framework in a qualitative way. Seven female preservice teachers voluntarily participated in this research and they performed a series of written tasks that asked their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). Their responses were analyzed according to mathematical algorithmic -, formal -, and intuitive - SMK and PCK. The interpretation revealed that preservice teachers had overally strong SMK, their deeply rooted SMK did not change, their SMK affected their PCK, they had appropriate PCK with regard to knowledge of student, and they tended to less focus on mathematical intuitive - PCK when they considered instructional strategies. The understanding of preservice teachers' knowledge throughout the analysis using Shulman-Fischbein framework will be able to help design teacher preparation programs.