• Journal of the Korean School Mathematics Society
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• v.22 no.3
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• pp.257-275
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• 2019

Technology-based convergence education is being emphasized for students in the era of the fourth industrial revolution. In math education, students need to increase their capabilities in the future by having them experience mathematical problems using robots and sensors, a key technology in the era of the fourth industrial revolution. To this end, it is necessary to present educational uses for educational robots in relation to math and curriculum from a 'mathematics education perspective' and analyze its educational use in relation to the mathematics and curriculum, considering the role of mathematics at the base of the process of exploring real-world phenomena and solving problems. Based on the analysis of Van Hiele levels of development in geometry and the LOGO activity level of Olson et al.(1987), this study analyzed and presented the level of LEGO Mindstorm activity, a representative educational Robot capable of collecting and analyzing data and programming in the form of block language, in the first to fourth level.

• Education of Primary School Mathematics
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• v.13 no.2
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• pp.85-97
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• 2010

The purpose of this study is to develop a teaching program in consideration of the geometrical thinking levels of students to make a contribution to teaching figures effectively. To do this, we checked the geometrical thinking levels of fourth-graders, developed a teaching program based on van Hiele's theory, and investigated its effect on their geometrical thinking levels. The teaching program based on van Hiele's theory put emphasis on group member interaction and specific activities through offering various geometrical experiences. It contributed to actualizing activity-centered, student-oriented, inquiry-oriented and inductive instruction instead of sticking to expository, teacher-led and deductive instruction. And it consequently served to improving their geometrical thinking levels, even though some students didn't show any improvement and one student was rather degraded in that regard - but in the former case they made partial progress though there was little marked improvement, and in the latter case she needs to be considered in relation to her affective aspects above all. The findings of the study suggest that individual variances in thinking level should be recognized by teachers. Students who are at a lower level should be given easier tasks, and more challenging tasks should be assigned to those who are at an intermediate level in order for them to have a positive self-concept about mathematics learning and ultimately to foster their thinking levels.

• The Mathematical Education
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• v.49 no.1
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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.

• The Mathematical Education
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• v.34 no.2
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• pp.141-202
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• 1995

van Hiele의 사고수준 이론에는 기초수존, 제1수준, 제2수준, 제3수준, 제4수준 등 5가지가 있고, 이 중에서 국민학교에 해당되는 것은 기초수준 (1학년), 제1수준(2, 3학년), 제2주순 (4, 5, 6학년) 등 세 가지 뿐이다. 그리고 기하학적의 구조 인식론에는 관제, 구성, 정의, 공리, 정리, 증명, 척도, 자호, 응용 등 9가지 단계가 있고, 이 9가지 단계를 기초수준, 제 1수준, 제 2수준의 각 수준에 대응시켜서 거기에 해당되는 기하도형 학습을 연구·분석하였다. 기하도형에 관한 학습은 주로 경험성과 창의성을 바탕으로 하는 보기문제를 제시하여 그 흐름을 해결함으로써 각 수준의 각 단계들을 스스로 인식하도록 하였다. 특히 여기에서 처음으로 등장하는 기하학의 구조 인식론이라는 것은 위에서 언급한 9가지 단계를 차례로 거쳐 가야만 아동들은 도형을 올바르게 빠짐없이 인식할 수 있다는 이론이다. 이 이론의 특징을 예를 하나 들어서 설명해 보면, 흔히들 정의를 단순히 무정의어와 정의어로 구분하고 있는데 반하여, 이 이론에서는 서로 역동적인 관계를 갖고 있는 기초정의, 상황정의, 포괄정의, 기본정의, 부수정의, 특수정의 등으로 나누었다는 점이다.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.81-98
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• 2007

In order to help students learn geometric concepts in mathematics in an easy and interesting way, the present study restructured the textbook so that it utilizes GSP based on van Hiele's theory. In addition, we purposed to examine how effective the restructured textbook is in enhancing students' van Hiele level and to lay a base for the active use of GSP in learning figures in elementary school. In conclusion, the results of this study is expected to solve problems in the structure of the current textbook such as the violation of continuity in van Hiele's theory and inconsistency between the level of textbook contents and students' level through the restructuring of the textbook using GSP and provide helps for effective figure learning. In addition, this research is expected to be an opportunity for the active use of GSP in teaching figures in elementary school.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.435-452
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• 2016

This study was designed to explore students' instrumentalization in relation to the van Hiele's teaching method within a technology environment using GeoGebra. To carry out the study, a total of 4 lesson units was developed based on van Hiele teaching method for two slow learners in Gyeonggi province, Korea. The results of study were as follows. Instrumentalization of students was actualized from preparation, to adaptation, and to application stages. In preparation, and adaptation stages, depending on visualization, students used a trial-and-error method a lot, however in application stage the role of GeoGebra was just to check the solution of what they conjectured. Therefore, a teacher should prepare geometric tasks according to the processes of instrumentalization based on geometric teaching method. During instrumentalization and instrumentation of users, usage scheme(US) and instrumented action scheme(IAS) should be concrete.

• School Mathematics
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• v.11 no.1
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• pp.147-164
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• 2009

This study investigated the development of geometrical thinking levels of the under achievers at mathematics through supplementary classes according to van Hiele's learning process by stages using mathematical journal writing. We selected five under achievers at mathematics among the fourth graders. We examined their geometrical thinking levels in advance and interviewed them to collect basic data related to their family backgrounds and their attitude toward mathematics and their characteristics. Supplementary classes for the under achievers were conducted a couple of times a week during 12 weeks. Each class was conducted through five learning stages of van Hiele and journal writing was applied to the last consolidating stage. After 12th class had been finished, posttest on geometrical thinking levels was conducted and the journals written by the pupils were analyzed to find out changes in their geometrical thinking levels. The result is that three out of five under achievers showed one or two level-up in their geometrical thinking levels, though the other two pupils remained at the same level as the results by the pretest. Moreover we found that mathematical journal writing could provide the pupils with opportunities to restructure the content which they study through their class.

• The Mathematical Education
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• v.39 no.2
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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.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.513-541
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• 2008

The purposes of the study were to investigate whether the use of the Geometer's Sketchpad(GSP) is more effective than the use of traditional tools such as ruler and protractor to enhance eighth- grade students' understanding of quadrilaterals and geometric reasoning ability and to examine how the use of the software affects on the development of students' understanding and reasoning ability. According to the results of the posttest, there was a significant difference in student achievement between students using GSP and students using ruler and protractor. Students using GSP significantly outperformed students using ruler and protractor on the posttest. Student interview data showed that the use of the GSP was more effective in developing students' geometric reasoning ability. Students using GSP achieved higher degrees of acquisition for van Hiele level 2 and 3 than students using ruler and protractor. Dynamic visual representations and hands-on experiences provided in GSP learning environment helped students approach quadrilateral concepts more conceptually and realize their pre-existing conceptual errors and re-conceptualize their mathematical ideas.

• Education of Primary School Mathematics
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• v.1 no.1
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• pp.59-71
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• 1997

기하학적 사고력 개발이라는 우리의 목표는 궁극적으로 보다 낮은 수준의 학생들에게 보다 높은 수준으로 나아가게 하는 경험을 주는 것이다. 학생들이 보다 높은 수준에서 추론할 수 있도록 하기 위하여 그들이 보다 낮은 수준에서 충분하고 효율적인 학습 경험을 가져야 한다는 것이다. 예를 들면 분수에서 이루어지는 것처럼 기계적인 암기식으로 사물을 학습함으로써 수준(단계)을 뛰어 넘으려고 노력하면은 그들이 학습한 것에 관한 많은 것을 기억할 수 없을 것이다. 조작에 관한 보다 풍부한 경험과 시각적으로 입체감을 주는 설명을 들은 어린이들이 보다 훌륭한 공간 추론을 할 수 있을 것이라 믿는다. 본 고에서는 기하학적인 사고의 개발에 관한 van Hiele 모델이 초등학교에서 기하 수업의 토론을 위한 기초로서 사용되어졌다. 그 모델의 수준들이 묘사되었고 일반적으로 초등학교 아동들의 사고는 0수준과 1수준이라 는 것이 밝혀졌다. 단지 극소수의 아동들이 2수준의 사고에 도달해 있을 것이다. 그러나 만약 초등학교에서의 수업이 기하학적인 개념을 구성하는데 주안점을 둔다면 보다 많은 어린이들이 2 수준의 사고를 보여줄 수 있을 것으로 생각된다. 0 수준의 어린이들은 도형의 형태에 초점이 맞추어져있고 1 수준의 어린이들은 도형의 성질을 이해하는데 에 있다. 2 수준의 사고자는 도형의 포함관계를 이해하고 비공식적으로 추론 할 수 있다. 처음 세 수준에서의 활동들에 대한 지침이 주어져 있으며 0 수준과 1수준에 연관되는 다수의 활동들을 묘사했다. 0수준의 어린이들을 위해 묘사된 활동들은 그들이 2차원 및 3차원의 도형 둘 다를 시각화하는데 도움을 주는 것이다. 1 수준에서 사고하는 학습자들을 위해 묘사된 활동들은 2차원 및 3차원 도형의 성질들을 강조했다. 아울러 본 고에서 언급한 활동들은 상호교수에의 접근을 반영했다. 그러한 접근방식은 학습자들로 하여금 그들의 활동과 의견으로부터 개념을 구성하게 해주며 그들의 활동 결과에 대해 다른 사람들과 의사소통 함으로서 개념을 명확하게 다듬어지게 해줄 수 있을 것이다. 아울러 평가 활동들이 본고의 마지막 부분에 주어져있다. 그러한 활동들은 교사들에게 어린이들의 기하학적인 사고수준을 결정하게 해주며 학습자들로 하여금 수업시간 이외에 보다 높은 사고수준으로 나아가게 해줄 수 있을 것으로 기대된다.