• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.585-604
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• 2013

This study is based on the problem that most middle school students cannot recognize the generality of geometrical theorems even after having proved them. By considering this problem from the point of view of empirical verification, the particularity of geometrical representations, and the role of geometrical variables, we suggest that some experiences in dynamic geometry environment (DGE) can help students to recognize the generality of geometrical theorems. That is, this study aims to observe students' cognitive changes related to their recognition of the generality and to provide some educational implications by making students experience some geometrical explorations in DGE. To do so, we selected three middle school students who couldn't recognize the generality of geometrical theorems although they completed their own proofs for the theorems. We provided them exploratory activities in DGE, and observed and analyzed their cognitive changes. Based on this analysis, we discussed the effects of DGE on studensts' recognition of the generality of geometrical theorems.

• Journal for History of Mathematics
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• v.36 no.4
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• pp.61-78
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• 2023

By virtue of the characteristics inherent in diagrams, diagrammatic reasoning has potential and limitations that distinguish it from general thinking. It is natural that diagrams rarely appeared in Joseon mathematical books, which were heavily focused on computation and algebra in content, and preferred linguistic expressions in form. However, as the late Joseon Dynasty unfolded, there emerged a noticeable increase in the frequency of employing diagrams, due to the educational purposes to facilitate explanations and the influence of Western mathematics. Analyzing the role of diagrams included in Jo Taegu's 'JuseoGwangyeon', an exemplary book, this study includes discussions on the utilization of diagrams from the perspective of mathematics education, based on the findings of the analysis.

• The Southeast Asian review
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• v.20 no.3
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• pp.147-182
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• 2010

The purpose of this study is to examine the population changes in the nine Southeast Asian countries, including Cambodia, Lao People's Democratic Republic, Philippine, Indonesia, Malaysia, Myanmar, Singapore, Vietnam, and Thailand. According to the demographic transition theory which described the transition from high birth and death rates to low birth and death rates, the demographic changes in less developed countries, including the Southeast Asian countries, follow the general pattern of the population changes that the Western countries had experienced. However, this theory does not consider the fact that the demographic behaviors such as fertility and mortality tend to be ethnocentric (or particular). Therefore, I examine in this paper both the generality and particularity of the population changes in the Southeast Asia . The analytic results are consistent with my assumptions. Every country in the Southeast Asia will soon reach the third phrase of the demographic transition and meet population ageing process. However, the timings arriving at the third phrase can differ. Singapore which is the most developed country had firstly passed through the demographic transition and the highest level of population ageing. Cambodia and Lao People's Democratic Republic, the least developed countries, will lastly arrive at the third phrase and the ageing society. In addition, among the three countries which had experienced war or civil war, only Cambodia had experienced babyboom.