• Research in Mathematical Education
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• v.13 no.3
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• pp.217-233
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• 2009

The purpose of this study is to describe how dynamic geometry systems can be useful in proof activity; teaching sequences based on the use of dynamic geometry systems and to analyze the possible roles of dynamic geometry systems in both teaching and learning of proof. And also dynamic geometry environments can generate powerful interplay between empirical explorations and formal proofs. The point of this study was to show that how using dynamic geometry software can provide an opportunity to link between empirical and deductive reasoning, and how such software can be utilized to gain insight into a deductive argument.

• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.39-53
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• 2003

We study the dynamic geometry software suitable for the Internet Environment. First, we look into the necessity of dynamic geometry software and compare the functions and the features of commercial softwares, GSP, Cabri and Cinderella. Secondly, we introduce the process of development and the structure of the new software DRC(Digital Ruler and Compass) designed by authors and discuss the learning program with DRC and Internet, and view the upgrade of the software in the future.

• The Mathematical Education
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• v.41 no.3
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• pp.341-360
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• 2002

The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.419-438
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• 1999

This paper explored the impact of dynamic geometry software such as CabriII, GSP on student's understanding deductive justification, on the assumption that proof in school mathematics should be used in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. The following results have been drawn: Dynamic geometry provided positive impact on interacting between empirical justification and deductive justification, especially on understanding the necessity of deductive justification. And teacher in the computer environment played crucial role in reducing on difficulties in connecting empirical justification to deductive justification. At the beginning of the research, however, it was not the case. However, once students got intocul-de-sac in empirical justification and understood the need of deductive justification, they tried to justify deductively. Compared with current paper-and-pencil environment that many students fail to learn the basic knowledge on proof, dynamic geometry software will give more positive ffect for learning. Dynamic geometry software may promote interaction between empirical justification and edeductive justification and give a feedback to students about results of their own actions. At present, there is some very helpful computer software. However the presence of good dynamic geometry software can not be the solution in itself. Since learning on proof is a function of various factors such as curriculum organization, evaluation method, the role of teacher and student. Most of all, the meaning of proof need to be reconceptualized in the future research.

• Education of Primary School Mathematics
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• v.9 no.1 s.17
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• pp.59-64
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• 2005

The purpose of this study is to find out how to use dynamic geometry software such as the Geometer's Sketchpad in elementary math classroom. Fist of all, I reviewed dynamic geometry software's property. Then I considered methods to improve geometry education using this software. Some researchers proposed three types of using the software. But I think using the software and developing instructional materials is different. So, I proposed two types of developing instructional materials using the software and two representative examples.

• School Mathematics
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• v.2 no.1
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• pp.111-144
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• 2000

The purpose of this study is to develop instruction sequence and teaching units for secondary school geometry using dynamic computer software like CabriII, GSP, Wingeom, Poly. For this purpose, literature was reviewed on various issues of geometry education and geometry curriculum using dynamic software. By the literature review, instructional sequence for teaching geometry in middle schools was designed. And, based on the newly developed instructional sequence, one sample teaching unit was developed. The basic principles for the development were to connect intuition geometry and formal geometry, and to emphasize students' investigative experience. Finally, experiment to check out teachers' response to the newly developed material was conducted by using questionnaire.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.543-556
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• 2002

The purpose of this study is to find a method to improve geometry instruction. For this purpose, I have investigated aims and problems of geometry education. I also reviewed related literature about discovery methods as well as verification. Through this review, “Mathematising teaching and learning methods” by Freudenthal is Presented as an alternative to geometry instruction. I investigated the capability of dynamic software for realization of this method. The result of this investigation is that dynamic software is a powerful tool in realizing this method. At last, I present one example of mathematic activity using dynamic software that can be used by school teachers.

• The Mathematical Education
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• v.46 no.3
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• Research in Mathematical Education
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• v.27 no.3
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• pp.367-399
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• 2024

The goal of this study is to explore productive ways to engage students in groupwork using dynamic geometry tasks in online synchronous classroom environments. In particular, we aim to understand the social, mathematical, and technological aspects of student collaboration in virtual spaces. We analyzed how three online groups of students collaboratively worked on dynamic geometry tasks of exploring interactive kaleidoscope applets in Desmos and producing visual representations and written descriptions of geometric transformations used in the applets. The students shared their screens in Zoom as they shared their findings and discussed how to draw and write to represent the kaleidoscopes. We identified three emerging practices of the students collaboratively working on dynamic geometry tasks in online synchronous environments: (a) drawing in response, (b) co-construction, and (c) writing in real time. The emergent practices captured how students socially interacted with others, engaged in mathematical processes, and utilized technology tools. We also discuss inequity in students' participation in collaborative practices in an online environment and possible ways to ensure equitable learning opportunities for online students.