• The Mathematical Education
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• v.48 no.2
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.297-312
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• 2009

We study the process of horizontal and vertical mathematization on the polyhedron problems through the history of mathematics, computer experiments, problem posing, and justifications. In particular, we explore the Hamilton cycle problem, coloring problem, and folding net construction on the Archimedean and Catalan polyhedrons. In this paper, we present our mathematical results on the polyhedron problems, and we also present some unsolved problems that we found. We found that the history of mathematics and mathematical experiments are very useful in such R&E exploration as polyhedron problem posing and solving project.

• Korean Journal of Logic
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• v.17 no.1
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• pp.71-109
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• 2014

Gila Sher believes that Tarskian definition of logical consequence is a conceptually and extensionally adequate explanation. She has tried to show this on the basis of Mostowskian conceptions of generalized quantifiers as being invariant under isomorphic structures and her own conceptions of models. In this paper I try to show that her attempt to justify the Tarskian definition is only partially successful. I admit that her conceptions of the logical as being invariant under isomorphic structures are enough to show the logical formality of logical consequence relations. But I think that since her conceptions of meanings of terms are quite inadequate for dealing with the problem of empty predicates, she fails to distinguish logically necessary truths from other kinds of truths.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.261-275
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• 2012

There are some geometry achievement standards presented indistinctly in middle school mathematics curriculum revised in 2011. In this study, indistinctness of some geometric topics presented indistinctly such as symbol $\overline{AB}{\perp}\overline{CD}$ simple construction, properties of congruent plane figures, solid of revolution, determination condition of the triangle, justification, center of similarity, position of similarity, middle point connection theorem in triangle, Pythagorean theorem, properties of inscribed angle are discussed. The following three agenda is suggested as conclusions for the development of next middle school mathematics curriculum. First is a resolving unclarity of curriculum. Second is an issuing an authoritative commentary for mathematics curriculum. Third is a developing curriculum based on the accumulation of sufficient researches.

• Korean Journal of Logic
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• v.18 no.3
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• pp.389-436
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• 2015

Epistemic dogmatism claims that if it seems P to you then you have immediate justification to believe P. The view has been faced with a problem that it is incompatible with Bayesianism, especially raised by Roger White(2006). James Pryor(2013), defending epistemic dogmatism, has given a reply for the problem. In this paper, first, I show some problems on Pryor's reply. Then, I present a new kind of suggestion to deal with the problem, which avoids problems Pryor's reply has. Finally, I suggest a different diagnosis on the problem.

• Korean Journal of Child Studies
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• v.36 no.5
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• pp.135-153
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• 2015

The purpose of this study was to investigate false belief understanding and justification reasoning according to information of reality amongst children aged 3, 4 and 5. Children aged 3 to 5 years (N = 176) participated in this study. Each child was interviewed individually and responded to questions designed to measure his/her false belief understanding. Every child responded to the false belief task under two different information conditions of reality(reality known vs reality unknown). For more specific analysis, children's reasoning responses were also recorded. The major findings of this study are as follows. Children could understand false belief more easily under reality unknown conditions. Specifically, the influences of information conditions were crucial to 3-year-olds but not to 4- and 5-year-olds. Although 3 year olds were able to avoid the systematical errors inherent in the false belief task, they still did not understand the false belief itself. This study provides specific aspects of false belief understanding and its relevance to general changes in cognitive development.

• School Mathematics
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• v.12 no.1
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• pp.79-95
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• 2010

The purpose of this study is to examine into how the mathematically gifted cope with ambiguity when they are encountered to learn via resolving ambiguity. In this study 6 gifted students are asked to resolve the ambiguity. Participant in this study appeared to experience the need of mathematical justification and the flexible change of perspective. The gifted have constructed unified mathematical knowledge by making a relation between two incompatible perspective in the process of resolving the ambiguity. We suggest that dealing with ambiguity in mathematics class can be a good opportunity for enhancing the gifted student mathematics education.

• Water for future
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• v.11 no.2
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• pp.54-61
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• 1978

An attemption of synthesizing and forecasting of monthly river flow has been made by employing a linear stochastic difference equation model. As one of the linear stochestic difference equation model, an ARIMA Type is tested to find the suitability of the model to the monthly river flows. On the assumption of the stationary covariacne of differenced monthly river flows the model is identrfield and is evaluated so that the residuale have the minimum variance. Finally a test is performed to finld the residerals beings White noise. Monthly river flows at six stations in Han River Basin are applied for case studies. It was found that the difference operator is a good measure of forecasting the monthly river flow.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.69-82
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• 2012

The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.

• Journal of Korean Philosophical Society
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• v.146
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• pp.79-114
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• 2018

In this article I investigate the critical fundamental truth of the practical philosophy of Kim Doo-Huhn who has not become known in our Korean society but should be paid respect at any cost in the history of practical philosophy, and whom we should take the important case of a philosophical lesson, focused on 'the Dialectic of Theory of Value' which makes up an essential framework of his practical philosophy.