• 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.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.193-206
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• 2001

This study was designed to develop investigation- and exploration- activities on Euclidean geometry with an exploratory type software, Geometer's Sketchpad, and to gain insights into the geometric reasoning abilities of college students working with the software. A package of Euclidean geometric activities with GSP was developed and four college students worked on the several activities with GSP and their geometric reasoning process were analyzed. Results indicated that GSP helped students solve problems in the several ways: to make conjectures and discover theorems by providing precise construction and measurement; to discover their proofs by providing the visual images and its manipulation; and to make students easily apply "what-if"strategies and expand and deepen their activities. Students' geometric reasoning was highly depended on analytic methods and their abilities with synthetic methods were shown very limited.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.299-314
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• 2008

The purposes of this study were to investigate what attitudes students have toward learning proofs and what difficulties they have in learning proofs, and to examine how the use of dynamic geometry software, the Geometer's Sketchpad, helps students' proof learning. The study involved 117 9th graders in 2 high schools. According to questionnaire data, over 50 percent of the total respondents(116) indicated negative attitudes toward learning proofs, on the other hand, only 16 percent of the total respondents indicated positive attitudes toward the learning. Memorizing and remembering many kinds of theorems, definitions, and postulates to use in proving statements was the most difficult part in learning proofs, which the largest proportion of the total respondents indicated. The study found that the use of the Geometer's Sketchpad played positive roles in developing students' understanding of proofs and stimulating students' interests in learning proofs.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.515-536
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• 2014

In the present study, we analyze four seventh grade students' recognition of geometric properties and the following justification processes while their adopting different construction approaches in GSP(Geometer's Sketchpad). As the students recognized dependency and level-1 invariants by dragging activities, they determined their own construction approaches. Two students, who preferred robust construction, immediately recognized the path of a draggable point and provided step-1 justification. The other students attempted soft construction followed by their recognition of level-2 invariants and the path, and came to step-2 justification.

• Journal of the Korean School Mathematics Society
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• v.20 no.3
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• pp.303-323
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• 2017

This is a multiple-case study of how preservice secondary mathematics teachers teach a particular mathematics using a technological tool. In a performance interview, the preservice teachers demonstrated how they would teach a specific mathematical topic using Geometer's Sketchpad. The results of this study showed that the preservice teachers designed diverse types of lesson plans and implemented different pedagogical and technological techniques in their teaching demonstrations. The findings suggest that preservice teachers' pedagogical content knowledge is an important factor in the integration of technology into their mathematics teaching. Thus, mathematics teacher educators should help preservice teachers gain a robust pedagogical content knowledge in order to effectively teach mathematics with technological tools.

• 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.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.249-255
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• 2004

본 논문에서는 컴퓨터 기하 프로그램으로 가장 널리 활용되고 있는 GSP(The Geometer's Sketchpad)를 사용하여 사영기하학의 성질을 반영하는 투시화법(perspective drawing)으로 펜션을 작도하였다. 2000년에 버전 3.1로 작도하였을 때 한 점 투시화법(one-point perspective drawing)으로만 완성된 집을 보였고, 두 점 투시화법(two-point perspective drawing)으로는 미완성된 집이었다. 새로운 버전 4.0은 그 기능이 탁월하게 향상되었으므로 어렵지 않게 두 점 투시화법으로 집을 완성하였고 또한 photo -shop 7.0을 사용하여 아름다운 펜션으로 장식하여 보았다.

• The Mathematical Education
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• v.50 no.2
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• pp.233-246
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• 2011

The geometry field in the current high school curriculum deals mainly with analytic geometry and the reference to logic geometry leaves much to be desired. This study investigated the construction on a heptagon by using conic sections as one of measures for achieving harmony between analytic geometry and logic geometry in the high school curriculum with the Geometer's Sketchpad(GSP), which is a specialized software prevalent in mathematics education field and is intended to draw an educational suggestion on it.

• The Mathematical Education
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• v.38 no.2
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• pp.179-187
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• 1999

Math teachers are very short of computer tools and manipulatives to use in geometry classes of middle schools for the development of spatial abilities. At most they can ask student to make regular polyhedrons for helping the students to understand by concrete experience, but this experience is not enough to develop spatial abilities in spatial figures including the regular polyhedrons. This article is to introduce instructional materials for development of spatical ability in the regular polyhedrons using computer software, Geometer's Sketchpad. In this article, students can imagine the whole figure through the parts of a plane figure and think of the parts from the solid figure by free movement from 2 dimensions to 3 dimensions, or from 3 dimensions to 2 dimensions. Also, the instructional materials devised in this article will be good to enhance spatial abilities because the relation of 1-1 correspondence in the movement of the parts can be conserved and observed precisely, which is very hard to demonstrate and visualize by paper-and-pencil. It is recommended that this kind of materials should be developed in various ways for teachers to use them directly in their geometry classes.

• 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.