• Korean Journal of Logic
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• v.18 no.1
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• pp.39-64
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• 2015

The most difficult problem for mathematical Platonism is the epistemological problem raised by Paul Benacerraf and Hartley Field. Recently, Mark Balaguer argued that his version of mathematical Platonism, Full Blooded Plantonism (FBP), can solve the epistemological problem. In this paper, I show that there are serious problems with Balaguer's argument. First, I analyse Balaguer's argument and reveal a formal defect in his argument. Then I raise an objection based on an analogical argument. Finally, I disarm some potential moves from Balaguer.

• Educational Technology International
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• v.16 no.2
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• pp.183-200
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• 2015

This study investigated the effect of learning achievements and cognitive load according to different types of presenting learning materials and epistemological beliefs (EB). Learning achievements in this study were composed by retention and transfer of ill-structured problem. A total of 80 college students participated in the study. Prior to the learning, students were guided to fill out a questionnaire regarding epistemological beliefs and a prior knowledge test. The students of each group studied with a different type of reading material: full text (FT), full text including key questions (KeyFT) and full text including a concept map (CmFT). After a session of study was finished, they were asked to complete the posttest: retention and transfer. The results showed that there was a significant difference in transfer achievements. CmFT outperformed higher scores than the other types. There was no significant difference in retention among the groups. It is strongly believed that the types of presenting learning materials may have affected the understanding of ill-structured problem solving skills. Students with sophisticated EB showed higher achievements on retention and transfer than naive-EB and mixed-EB. Even though the data showed decrease of the cognitive load on the type of materials and EB, there were no significant differences on the cognitive load. We should consider a positive effect of types of presenting learning materials and EB enhancing capabilities of solving ill-structured problems in real life.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.341-349
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• 2001

Infinity is one of the important concept in mathematics, science, philosophy etc. In history of mathematics, potential infinity concept conflicts with actual infinity concept. Reason that mathematicians refuse actual infinity concept during long period is because that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. Potential infinity concept causes difficulty like history of development of infinity concept in mathematics learning. Even though students team about actual infinity concept, they use potential infinity concept in problem solving process. Therefore, we must make clear epistemological obstacles of infinity concept and must overcome them in learning of infinity concept. For this, it is useful to experience visualization about infinity concept. Also, it is to develop meta-cognition ability that students analyze and control their problem solving process. Conclusively, students must adjust potential infinity concept, and understand actual infinity concept that is defined in formal mathematics system.

• Journal of The Korean Association For Science Education
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• v.40 no.4
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• pp.359-374
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• 2020

This study is a complex type consisting of survey study and self-study. The former investigated elementary teachers' epistemological beliefs on convergence knowledge and teaching. As a representative of the result of survey study I, as a teacher as well as a researcher, was the participant of the self-study, which investigated my epistemological belief on convergence knowledge and teaching and my execution of convergent science teaching based on family resemblance of mathematics, science, and physical education. A set of open-ended written questionnaires was administered to 28 elementary teachers. Participating teachers considered convergent teaching as discipline-using or multi-disciplinary teaching. They also have epistemological beliefs in which they conceived convergence knowledge as aggregation of diverse disciplinary knowledge and students could get it through their own problem solving processes. As a teacher and researcher I have similar epistemological belief as the other teachers. During the self-study, I tried to apply convergence knowledge system based on the family resemblance analysis among math, science, and PE to my teaching. Inter-disciplinary approach to convergence teaching was not easy for me to conduct. Mathematical units, ratio and rate were linked to science concept of velocity so that it was effective to converge two disciplines. Moreover PE offered specific context where the concepts of math and science were connected convergently so that PE facilitated inter-disciplinary convergent teaching. The gaps between my epistemological belief and inter-disciplinary convergence knowledge based on family resemblance and the cases of how to bridge the gap by my experience were discussed.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.181-192
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• 2002

There are various methods of proving a proposition. Among these, 'mathematical induction' is treated in school mathematics weightly. But many students have difficulty with the proof by 'mathematical induction'. To solve this problem, analysis needs to be attempted in various aspects This study attempts to compare the teaching methods of 'mathematical induction' in South and North Korea and to acquire the implication. In fact, many differences between South and North Korea are found. These differences are caused by epistemological and psychological premise. Therefore this study investigates the epistemological and psychological aspects in North Korea and compares the textbooks in South and North Korea. Through this study, some implications are found. First, the sequence of introducing the 'mathematical Induction' needs to be considered. Second, the rich context of applying the 'mathematical induction' is needed. Finally, disagreement between curriculum and textbook in South Korea needs to be reconsidered.

• Journal of architectural history
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• v.12 no.2 s.34
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• pp.61-69
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• 2003

Manfredo Tafuri's Ideological criticism in architecture has opened a new horizon to interpreting architecture in modern capitalist architecture for it views architecture not just as a style or formal invention, but in terms of socio-economical process. It offered a comprehensive understanding of a chaotic situation of contemporary architecture and historical meaning modern architectural movements in relation with capitalistic development. However, it has been criticized as architectural pessimism which does not allow any possibility for progressive architectural practice. It was also criticized of epistemological problem of how one could be outside ideology without assuming true consciousness against false consciousness of ideology. Tafuri solves this problem by assuming Althusserian activist concept of knowledge and suggest the concept of labor of writing history of critical historians, instead of a design for utopian society, as a possible critical architectural practice. However, I argue that ultimately ideological criticism does not deny architectural practice itself, nor researches on formal characteristics of architecture. The problem lies rather in the architectural Intellectuals' attachment to the traditional concept of architect as a form giver to the society. By rejecting this myth and broadening the concept of architectural practice from design to production, we can find that Ideological problem is not architectural pessimism, but rather it opens up a new way of approaching to the problem of architectural practice in modern capitalist society.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.389-400
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• 2013

The article makes a discussion to conceptualize a histo-genetic principle in the real historical view point. The classical histo-genetic principle appeared in 19th century was founded by the recapitulation law suggested by biologist Haeckel, but recently it was shown that the theory on it is no longer true. To establish the alternative rationale, several metaphoric characterizations from the history of mathematics are suggested: among them, problem solving, transition of conceptual knowledge to procedural knowledge, generalization, abstraction, circulation from phenomenon to substance, encapsulation to algebraic representation, change of epistemological view, formation of algorithm, conjecture-proof-refutation, swing between theory and application, and so on.

• Journal of English Language & Literature
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• v.64 no.3
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• pp.361-381
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• 2018

Shakespeare reflects/refracts the controversial spirit of his age in the epistemological and political skepticism of his Roman plays: Titus Andronicus, Julius Caesar, Coriolanus, and Antony and Cleopatra. Skepticism doubts all received truth and suspends judgment, and it often takes the form of mental jousting on both sides of a question. Renaissance skepticism was strengthened by rhetorical education. Arguing on both sides of the question (in utramquem partem) was a practice taught in Shakespeare's grammar school in order to enhance students' mental abilities in logic and dialectic. This rhetorical exercise seldom leads to a third-term resolution: it just reveals all the apparent and hidden aspects of a problem at issue. Shakespeare's Roman plays, especially his Julius Caesar, demonstrate this skeptical attitude, leaving the judgment to the audience.

• Journal of architectural history
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• v.11 no.4 s.32
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• pp.7-19
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• 2002

If we compare socio-cultural aspects of the two historical periods known as 'pre-modern' 'modern,' it would seem that the Aristotelian understanding of technology has difficulty explaining techno-cultural phenomenon of modern society. The problems are first that the discourse of scientific technology in the modern period has proceeded without a metaphysical base, and second that nothing in present culture regulates the limitations of scientific technology. The clear distinction between means and ends in the traditional approach is no longer valid in the jumble of interrelationships. Such complexity forces us to acknowledge that means and ends are relative and interchangeable, and that neither has a clear moral superiority over the other. Technology in modern society is no more a neutral means. The products of science do not always exist to serve human ends. In modem architecture and urban design, both its productive and destructive tendencies leave man and his society in an endless confusion of complexity and opposition. These problems of technology still result in unsolved question today. On this point, the discussion another currently prevalent attitude to technology, especially Heideggerian thinking in the below could give a somewhat clearer answer to the problem of modem architecture and technology, although it also comprises limited contemplation in itself.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.