• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Korean Journal of Cognitive Science
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• v.13 no.4
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• pp.80-80
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• 2002

The main thesis of this article is that the decisive point of creativity education is the cultivation of critical thinking capability. Although the narrow conception of creativity as divergent thinking is not subsumed under that of critical thinking, the role of divergent thinking is not so crucial in the science context of creative problem-solving. On the contrary, the broad conception of creativity as focusing on the reference to utility and the third conception of creativity as a process based on the variation and combination of existing pieces of information are crucial in creative problem-solving context, which are yet subsumed under that of critical thinking. The emphasis on critical thinking education is connected with the characteristics of contemporary knowledge-based society. This rapidly changing society requires situation-adaptive or situation-sensitive cognitive ability, whose core is critical thinking capability. Hence, the education of critical thinking is to be centered on the learning of blowing-how and procedural knowledge but not of knowing-that and declarative knowledge. Accordingly, the learning of critical thinking is to be headed towards the cultivation of competence but not just of performance. In conclusion, when a rational problem-solving through critical and logical thinking turns out consequently to be novel, we call it creative thinking. So, creativity is an emergent property based on critical and logical thinking.

• Korean Journal of Cognitive Science
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• v.13 no.4
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• pp.81-90
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• 2002

The main thesis of this article is that the decisive point of creativity education is the cultivation of critical thinking capability. Although the narrow conception of creativity as divergent thinking is not subsumed under that of critical thinking, the role of divergent thinking is not so crucial in the science context of creative problem-solving. On the contrary, the broad conception of creativity as focusing on the reference to utility and the third conception of creativity as a process based on the variation and combination of existing pieces of information are crucial in creative problem-solving context, which are yet subsumed under that of critical thinking. The emphasis on critical thinking education is connected with the characteristics of contemporary knowledge-based society. This rapidly changing society requires situation-adaptive or situation-sensitive cognitive ability, whose core is critical thinking capability. Hence, the education of critical thinking is to be centered on the learning of blowing-how and procedural knowledge but not of knowing-that and declarative knowledge. Accordingly, the learning of critical thinking is to be headed towards the cultivation of competence but not just of performance. In conclusion, when a rational problem-solving through critical and logical thinking turns out consequently to be novel, we call it creative thinking. So, creativity is an emergent property based on critical and logical thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• Journal of the Korean Institute of Gas
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• v.7 no.1 s.18
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• pp.19-23
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• 2003

The purpose of this thesis is to investigate the BLEVE probability of LP gas storage tanks which are relatively more dangerous, by the deductive calculating method using the results of Birk's pilot tank test and the required heat capacity of BLEVE. The result that BLEVEs can occur in only above 43.68 percent of liquid filling level under $600^{\circ}C$ of tank pate temperature and $53^{\circ}C$ of inner liquid temperature, was obtained and will be useful for preventing the BLEVE of LP gas storage tanks in fire sites. In addition, this research showed conditions of external leak and fire causing BLEVE, based on 15ton capacity of LP gas tank which has the same specifications as those in Puchon LP gas filling station accident. The result of the calculation is that the minimum pool fire conditions of BLEVE are above 7.2mm equivalent diameter under a liquid release condition and above 17.6mm equivalent diameter under a two-phase release condition. In the end, the result of calculating the pool size corresponding the above conditions using EFFECTS version 2.1, concludes that a minimum of 3.3 meters of diameter and 10.4 meters of height should be needed for BLEVE outbreak.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• (The)Study of the Eastern Classic
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• no.50
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• pp.89-120
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• 2013

The concept of virtue seems to be one of the rare cases where the European and the Chinese traditions coincide. The meaning of the Latin word virtus and of Greek $aret{\acute{e}}$ seems to be similar to the Chinese $d{\acute{e}}$德. Most striking in virtue is that it is a capacity for self-realisation through action which is unique to man. On the other hand, there is something physical about it. It is the strength to do something. This strength overcomes the resistance of what is naturally given, it transforms the world, turns the natural world into a human one. In the Chinese tradition, $d{\acute{e}}$ 德, i.e. virtue, is therefore always connected with $da{\grave{o}}$ 道, the totality of natural forces. In the Chinese tradition, as opposed to the European one, virtue is itself considered to be a natural force that is present in man. This force sustains man's connectedness, unity and harmony with the surrounding world. Things exist through the unity of principle理 and ether氣. But the knowledge of this unity is due to principle. Moral and legal norms are shifted totally to the sphere of principle. Therefore their have found the final dissolution from a heroic models. Above all the classical Confucians, but also the other schools, would reply to this that there is nothing more precise than a concrete successful action. Its result fits the world perfectly. The difference is due to the differing interest of ethical thought. In the case of the Confucians the path is more direct. The actor establishes a precise pattern for other actions. Education therefore lies in detailed knowledge about forms of behaviour, not so much in conceptual differentiation. It is quite possible that generalisation may be a methodical prerequisite for success in this endeavour. That problem, too, is discussed. But the success of conceptualisation lies in the successful performance of individual actions, not in shaping actions in accordance with normative concepts.

• Journal of Korean Philosophical Society
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• no.117
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• pp.139-167
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• 2017

This essay attempts to reveal how taste spontaneously cultivates and why it is necessary for cultivating taste to edify our personality and to develop culture. It is a key of the solution of the problems that taste always reflects its judgment through pleasure. Because the grounds of the universal validity of the judgment of taste are found, whenever taste tests the validity of its own judgment, the so-called 'delight of discovery' makes taste cultivate itself. For having the moral personality, we need to practice spontaneously the morality of our own behaviour and for judging whether an artwork to represent the period is succeeded or not, we need to have a high insight to select the cultural heritage. But the autonomous thinking can delightfully be made a habit, judging the beauty of artworks. In the main body of this essay, it is determined from the three examples of the negative judgment of taste which Kant suggested in deduction. According to Kant, the negative judgment of taste means that the beautiful work is displeased, but what it asserts is that taste is cultivated. I formalize the methods of reflection of taste revealed in three negative judgments of taste into'resisting', 'indicating of error', 'self-retracting'.(Chapter 2) And from this, I emphasize the necessity to cultivate taste in the way that these methods of the cultivation of taste can affect building our personality by stimulating our reason to have interest in moral(Chapter 3) and in the way that taste directly judges the product of cultural succession.(Chapter 4) In the end of last chapter, I examine further essentially the method of the reflection of taste, to inquire into how to enable it.(Chapter 5) Especially, I try to illuminate its grounds through Schiller's concept of the "impulse of amusement(Spieltrib)", because his explanation helps us to understand the dynamics of taste's delight of discovery. Although the abilities of mind conflict with each other, taste has the characters that it reflects to encourage them for each other and that it is vitalized by its own activity. We, as it were, can pleasantly handle two tasks, because taste makes the impulse of amusement from conflictive impulses in mind. In conclusion, I state that we have to experience directly the impulse of amusement like creative artist, because it is maximized from creation.