• Communications of Mathematical Education
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• v.24 no.3
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• pp.627-658
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• 2010

The introduce and accurate understanding of the concept of tangent line is very important in Mathematics education and its applications. In this study, we investigated the introduction method in the textbook for tangent line and its concepts. And we studied the effective teaching methods for the accurate understanding using Lakatos learning theory, GSP and related precedence studies. Finally we suggest the teaching plan for the equation of for the tangent line in the high school and apply to the High school students.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.383-397
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• 2008

In problem solving, the necessity of mathematical thinking is absolute. In this paper, with an established theory about mathematical thinking, we will try to observe how the students can form mathematical thinking through a mathematical example in mathematical class by using Lakatos' process of proofs and refutations.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.17-30
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• 2011

This study inquires into the change between two method of indivisibles, which Cavalier suggested. To cope with the objection of use of indivisibles, he modified his first method of indivisibles. Through the analysis of this transition, this study reveals the feature that Cavalier changed into reflecting the density of the figures so as to avoid the paradox related to the indivisibles and this change has the aspect of incomplete lemma-incorporation method according to Lakatos' theory.

• Journal for History of Mathematics
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• v.30 no.1
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• pp.31-50
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• 2017

This study analyses on the history of uniform convergence, and discusses its educational implications. First, this study inspects 'overflowing of the Euclidean methodology' which was suggested by Lakatos as a cause of tardy appearance of uniform convergence, and reinterprets that cause in the perspective of 'symbolization'. Second, this study looks into the emergence of uniform convergence of Seidel and Weierstrass in this viewpoint of symbolization. As a result, of analysis, we come to know that the definition of uniform convergence had been changed into the theory of 'domain and graph' from that of 'point and function value' by the location change of the quantifier. As these results, this study puts forward an educational suggestion from an angle of epistemological obstacle, concept definition and concept image.

• 사회경제평론
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• v.29 no.1
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• pp.31-70
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• 2016

This study provides a comprehensive survey of Post Keynesian economics. The global financial crisis 2008-2009 has triggered an important debate concerning economic theory, policy and methodology. The most important thing that this economic crisis has done for economics is that it revealed mainstream economics was wrong. Mainstream economics has been unable to offer clear answers for the crisis. The economic crisis, at the same time, brought about a crisis in the field of economics. This study suggests that economics needs to be altered into a new form that can explain the real world economy. In this paper, it is argued that Post Keynesian economics can be understood as the alternative economics. The paper begins with the vision and the origins of several Post Keynesian ideas, leading to an examination of certain features of the various groups, including their methodology and their approaches to uncertainty, their pricing theories and their growth theories. The focus, however, is on the stage reflected in Post Keynesian economics which is concerned with the conception of Lakatos's 'Scientific Research Programmes'. It is recognized that more research is necessary in order to complete the post keynesian economics as a standard science or as a progressive Scientific Research Programmes in economics.

• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Journal of The Korean Association For Science Education
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• v.33 no.1
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• pp.144-160
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• 2013

This study is a proposal, which is the trial to explicate, in neurology, on how critical thinking as a creative method of sciences functions. The creative methods of sciences, even at present, are mostly the hypothetical insistences concerning with the logical processes of researches suggested from the philosophers of science; Popper, Kuhn, Hempel, or Lakatos. These insistences do excavate what process or approach can be scoped out of scientists' creativity. I call the tendency or approach of the researches, "Process Approach of Creativity (PAC)". From my view point, any PAC trial does not concern with how creative theories can actually be invented. On the other hand, this study is focused on the philosophical thinking abilities of scientists who invented new great theories. They mostly had some experiences to study philosophy while studying their science fields, thus had critical thinking abilities on their studies. From my point of view, critical thinking in philosophy raised questions as to their fundamental and basic (old) concepts and principles, and thus gave them new creative theories. I will try to explain this from the point of neurophilosophy. From the perspectives coming from "the state space theory of representation" of Paul & Patricia Churchland, the pioneers of neurophilosphy, the "creative theories" are the networks of topographic maps giving new comprehensive explanations and predictions. From these perspectives, I presuppose that the attitude of critical questioning revises the old networks of maps with back-propagation or feedback, and thus, is the generative power of searching new networks of maps. From the presupposition, I can say, it is important that scientists reflect on the basic premises in their academic branches for issuing out extraordinary creativity. The critical attitude of philosophy can make scientists construct the maps of new conceptual scheme by shaking the maps of the old basic premises. From this context, I am able to propose "Critical Thinking Approach of Creativity (CTAC)".

• Journal of Korean Philosophical Society
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• v.148
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• pp.157-181
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• 2018

The aim of this essay is to identify elements of methodologies to investigate the development of Newtonian dynamics. This methodology involves the transformation and synthesis of preceding theories. My essay attempts to confirm my assertion by analyzing historical case of Newton's discovery of his dynamics. While discovering his mechanistic theory, Newton reconstructed theoretical concepts and structures of intellectual predecessors, such as Aristotle, Descartes, Galileo, and Kepler. Newton's synthesis was possible only after carefully reconstructing the appropriate and useful ideas of previous natural philosophers' ideas. As a result, Newtonian dynamics are completed with these modified and integrated concepts incorporated into Newton's law of motion and space-time concepts. This study consists of two parts. First, Lakatos' research program has been applied in order to analyze the structure of Newtonian dynamics. Second, the aforementioned methodologies of discovery are distilled from the case study.