• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.459-479
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• 2006

The purpose of this study is to investigate the applicability of DGS(dynamic geometry software) for the assessment of reasoning ability and the influence of DGS on the process of assessing students' reasoning ability in middle school geometry. We developed items for assessing students' reasoning ability by using DGS in the connected form of 'construction - inductive reasoning - deductive reasoning'. And then, a case study was carried out with 5 students. We analyzed the results from 3 perspectives, that is, the assessment of students' construction ability, inductive reasoning ability, and justification types. Items can help students more precisely display reasoning ability Moreover, using of DGS will help teachers easily construct the assessment items of inductive reasoning, and widen range of constructing items.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.115-134
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• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.

• East Asian mathematical journal
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• v.37 no.4
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• Research in Mathematical Education
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• v.14 no.3
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• pp.219-231
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• 2010

Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).

• Journal for History of Mathematics
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• v.13 no.2
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• pp.73-86
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• 2000

This paper introduces an hypermedia program supportable for teaching secondary and upper secondary level geometry. This program links users to files written in other softwares and internet web sites to provide information and exploratory environments with softwares. The linkage with the interactive dynamic software(GSP) files to teach hyperbolic geometry is illustrated with sample screens.

• Research in Mathematical Education
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• v.7 no.1
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• pp.41-58
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• 2003

This study firstly examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions and the use of the dynamic geometry software Sketchpad to not only improve their understanding of definitions, but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognize uneconomical definitions, and improve them.

• Research in Mathematical Education
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• v.18 no.1
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.160-165
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• 1998

In this paper, We discuss the directional stability of a Mini-bus with varying suspension design parameters. We analyzed the vehicle behavior during the cornering in a transient steering condition. We made a vehicle model by use of DADS, which is dynamic analysis software, in order to carry out many cases of simulation with varying design parameters. The effect of toe-geometry change to vehicle stability is evaluated by computer simulation and the actual test. In order to reduce the under steer characteristics of a mini-bus, the amount of toe geometry change should be less than current value.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.139-159
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• 2000

The experimental software such as Cabri II, The Geometer's Sketchpad, etc. provides dynamic environment which construct and explore geometric objects interactively and inductively. It has the effects on mathematics itself differently from other technologies that are used in instruction. What is its characteristics\ulcorner What are the educational implication of it for the learning of geometry\ulcorner How is mental reasoning of geometric problems changed by transformation of the means of representation and the environment to manipulate them\ulcorner In this study, we answer these questions through the review of the related literatures and the analysis of textbooks, teaching materials using it and curricular materials. Also, we identify implications about how the criteria for choosing geometic content and the ways of constructing context, for orchestrating the students' exploration with the secondary geometry curriculum, can be changed.