• 한국수학교육학회지시리즈A:수학교육
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• 제39권2호
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• pp.151-166
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• 2000

The purpose of this study is to understand what two models of SOLO taxonomy and van Hiele theory suggest and find out what relation there is between the category system of the SOLO taxonomy and the thinking level of the van Hiele theory. The van Hiele theory describes in line of ranking level so that it may increase the teaching effects by putting together a class, which takes into consideration the students thoughts. The SOLO taxonomy focused on the response mode of the students rather than the thinking level or the developmental stage of them to pursuit the method that can describe the students understanding in depth quality-wise. Although the SOLO taxonomy and the van Hiele model seem to have different form and character from outside in terms of their goals, a closer examination reveals that the two stances have much in common and that the models are complementary. Although the van Hiele placed more focus on the thoughts, because the conclusion was based on the students responses, the van Hiele theory can be interpreted within the structure identified in the SOLO model. In this study, we have tried to understand how the response structure form the SOLO taxonomy and the thinking level of the van Hiele theory are related, based on the studies of Pegg and Davery1998). If you briefly look at them, there are following corresponding relation between the SOLO taxonomy and the van Hiele theory. a) The relational level(R) in iconic moe is van Hiele level 1. b) The multisturctural level(M$_2$) in the second cycle of concrete-symbolic mode is van Hiel level 2. c) The relation level(R$_2$) in the second cycle of concrete-symbolic mode is van Hiele level 3. d) The unistructural level(U$_2$) in the second cycle of formal mode is van Hiele level 4. e) The postformal mode is van Hiele levle 5. Though it would be difficult to conclude that these correspondences were perfectly done, if you look at their relation, you can see that the learning process of the students were not carried out uniformly. Therefore, by studying the students response structure, using the SOLO taxonomy, and identifying the learning cycle and understand the geometrical concept more in depth.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권1호
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• pp.85-109
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• 2010

The purpose of the study is to devise syllabus in which traditional textbooks were rearranged by van Hiele Level theory and van Hiele instruction step 5 was applied to syllabus which used computer software, GSP especially in step 2 for students who studied properties and relations of the figure. Another purpose is to analyze the van Hiele Level distribution and find out how significant improvement syllabus based instruction could make compared with the traditional classes using textbooks. The results of the study revealed that more than half of the students were less than Level 1 in the comparative group but more than half of the students have reached Level 3 in the experimental group. And improvement of van Hiele Level was significant in syllabus based classes compared with traditional classes using textbooks by the Welch-Aspin tests and Chi-squared tests.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권2호
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• pp.103-128
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• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권4호
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• pp.349-377
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• 2009

In this work we present a study undertaken with in-service mathematics teachers of primary and secondary school where we describe and analyze the didactical competences needed to implement an innovative design in geometry applying Van Hiele's models. The relationship between such competences and an ideal teacher profile is also studied. Teachers' epistemology is established in terms of didactical competences and we can see that this epistemology is an element that helps us understand the difficulties that teachers face in practice when implementing an innovative curriculum, in this case, geometry based on the Van Hiele theory.

• 한국초등수학교육학회지
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• 제11권1호
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• pp.81-98
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• 2007

현재 초등학교 학생들은 도형 영역을 어려워하고 있으며, 학교 수학에서 배운 도형 관련 지식을 실제 생활에 잘 적용시키지 못하고 있다. 도형의 성질을 제대로 알지 못하거나 도형 사이의 포함관계를 이해하지 못하며, 전형적인 예에서 조금만 벗어나면 무슨 도형인지 알아채지 못하는 학생들이 많이 있다. 이에 본 연구에서는 학생들이 수학의 기하적 개념들을 쉽고 재미있게 학습할 수 있도록 하기 위하여 van Hiele의 이론을 바탕으로 하여 GSP를 활용할 수 있도록 교과서를 재구성하였다. 또한 재구성한 교과서가 실제 학생들의 van Hiele 수준 상승에 어떤 효과가 있는지 살펴보고, 초등학교 도형 학습에 GSP가 활발히 활용될 수 있는 계기를 마련하는데 목적이 있다.

• 한국학교수학회논문집
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• 제1권1호
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• pp.175-184
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• 1998

The purpose of this study is that the Van Hiele theory can be applied to even vocational high school students. Through the comparison of Van Hiele level distribution of middle school students and high school students, it is that the aims of this study is to study the geomatric level of vocational high school students and to analize them, even so it can be to find for them the effective method of Geomatric education The subject of study is three kinds of vocational high school - commercial high school, industrial high school, fisheries high school - boys (240), girls (120) in Boryeong city, Chungchong Nam Do. We referred to Kim Mi-cheong′ thesis(1994) and Cheong Yean-sok′s thesis(1992) and compared my result with them. The method and the process of the study were based on the th method of CDASSG project. And we used Van Hiele Level Test as an instrument of measurement. We got the following conclusion as the result of the study 1. The 86％ of the subject of the study was applied to the theory of Van Hiele - "Any students can reach level n just through level n-1." Even so the propriety of the theory proved to be from this study again. 2. The 88% of the subject of the study is applicable to below level 2. So if the proof is introduced to them in the class, it was very difficult for them to understand it. 3. The geometric level of vocational high school students is the same as the second grade of middle school. But we think to be desirable that a basic concept puts first in importance through recomposed teaching materials, because 68% of the students is seldom changed at level 1.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제13권2호
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• pp.85-97
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• 2010

학생들은 학교수학에서 중요한 위상을 차지하는 도형과 관련하여 다양한 사고를 하게 되며 학생들의 사고 수준의 파악은 교수-학습 효과로 직결되기 때문에 도형 지도와 관련하여 van Hiele의 기하 사고수준 이론은 중요하게 다루어진다. 기하 사고 수준의 도약적 특성 때문에 서로의 의사소통 불가능성까지 감안해야 한다는 시사점을 고려하면 지도하고자 하는 학생의 기하 사고 수준을 파악하는 것은 필수적이며, 뿐만 아니라 그들의 사고 수준 향상을 위해서 어떠한 지도 내용 및 방법을 구현해야 하는가도 핵심적인 기하 영역의 교육문제이다. 본 연구에서는 경남 통영의 한 초등학교 4학년 학생 10명을 대상으로 그들의 기하 사고 수준을 고려한 도형 단원의 교수-학습 지도안을 작성하여 적용함으로써 사고 수준의 변화를 관찰하고 수업을 분석한 결과, 학생들의 사고 특성 및 교수학적 시사점을 도출할 수 있었다.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.291-298
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• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권3호
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• pp.263-279
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• 2010

Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

• 한국학교수학회논문집
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• 제11권1호
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• pp.69-96
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• 2008

본 논문은 현행 중등수학에서 기하교육의 문제점을 인식하고 Freudenthal의 학습이론에 토대를 둔 수학화 활동에 적합한 학습자료의 개발 및 교수-학습활동에 따른 수학화 과정을 분석하는데 그 목적이 있다. 이를 위해 중학교 수학 8-나 단계 기하영역을 중심으로 Freudenthal의 학습 이론과 관련된 활동 중심의 학습자료와 van Hiele의 학습 단계 이론을 토대로 교수-학습 모형을 개발하여 수업에 적용한 후 수학화 활동의 효과를 분석한다.