• Research in Mathematical Education
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• v.19 no.4
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• pp.229-245
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• 2015

In this study, I investigated how pre-service teachers (PSTs) proved three geometric problems by using Geometer's SketchPad (GSP) software. Based on observations in class and results from a test of geometric reasoning, eight PSTs were sorted into four of the five van Hiele levels of geometric reasoning, which were then used to predict the PSTs' levels of reasoning on three tasks involving proofs using GSP. Findings suggested that the ways the PSTs justified their geometric reasoning across the three questions demonstrated their different uses of GSP depending on their van Hiele levels. These findings also led to the insight that the notion of "proof" had somewhat different meanings for students at different van Hiele levels of thought. Implications for the effective integration of technology into pre-service teacher education programs are discussed.

• 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.

• Research in Mathematical Education
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• v.18 no.2
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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.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.483-500
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• 2019

This study compared and analyzed the van Hiele levels of geometry contents in middle school mathematics textbooks and those of students' thinking. As the mathematics curriculum was revised recently, the amount of contents in the geometry area were reduced, but the van Hiele level did not change much, and the gap between the van Hiele level of geometric contents presented in the textbooks and the level of students' geometric thinking still remained unchaged. The van Hiele levels of the geometric contents in the textbooks were distributed in the levels of 1, 2, 3 in the first grade, and 2, 3, 4 in the second and third grade. In the case of the first grade, 69% of the students were less than or equal to level 2, and 73.7% and 47.6% of the students in the second and third grades were less than or equal to level 3, respectively. Especially, in the case of the second and third grade, the ratio of the 4th level of the contents presented in the textbook is higher than the problem, which can cause difficulties for the students.

• 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.

• Research in Mathematical Education
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• v.4 no.2
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• pp.63-77
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• 2000

The purpose of this article is to devise the activities based on van Hiele levels of geometric thought using computer software, Geometer\\\\`s Sketchpad(GSP) as a tool. The most challenging task facing teachers of geometry is the development of student facility for understanding geometric concepts and properties. The National Council of teachers of Mathematics(Curriculum and Evaluation Standards for School Mathematics, 1991; Principles and Standards for School Mathematics, 2000) and the National Re-search Council(Hill, Griffiths, Bucy, et al., Everybody Counts, 1989) have supported the development of exploring and conjecturing ability for helping students to have mathematical power. The examples of the activities built is GSP for students ar designed to illustrate the ways in which van Hiele\\\\`s model can be implemented into classroom practice.

• 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.

• 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.

• Research in Mathematical Education
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• v.14 no.3
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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.

• Research in Mathematical Education
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• v.15 no.1
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• pp.81-91
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• 2011

The aim of this study was to explore the grade 1-3 students' geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 1-3. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele's model merely level 0 (Visualization) across textbooks for grades 1-3.