• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.32 no.1
• /
• pp.12-15
• /
• 2022

The effect of SiO₂, Na₂O and CaO on isokom temperatures in soda-lime glass is estimated by comparing calculated isokom temperatures using viscosity model proposed by Lakatos. The isokom temperatures at the viscosity of log η = 12.3, 10, 6.6 and 1 (Pa·s) are lowered by 6, 7, 10 and 24℃, respectively, by the substitution of SiO₂ with Na₂O by 1 mol%. Meanwhile, replacing 1 mol% of SiO₂ with CaO raises the isokom temperatures by 3~4 and 2℃ at the viscosity of log η = 12.3 and 10 (Pa·s), respectively, but lowers the temperatures by 1 and 21℃ at the viscosity of log η = 6.6 and 1(Pa·s), respectively.

• Journal of The Korean Association For Science Education
• /
• v.17 no.2
• /
• pp.209-224
• /
• 1997

In this study, the images of science education illustrated in the books written by six major modern philosophers of science (K. R. Popper, N. R. Hanson, T. S. Kuhn, I. Lakatos, P. Feyerabend and J. Ziman) were investigated. In this article, the parts, from the books investigated, which have direct relevance to science education are quoted and the discussions by the researchers on them are added. Particularly, the learning by trial and error (of Popper), the role of context in scientific thinking (of Hanson), science education through the history of science (of Lakatos), science education appreciating individualities and voluntary curiosity (of Feyerabend) and the social aspect of science as a source of its rationality (of Ziman) appear to be the main points which have direct relevances and meaningful implications to science education but which have not been considered or discussed in detail in science education.

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
• /
• v.32 no.4
• /
• pp.41-61
• /
• 2019

Background : The current medical statistics used in clinical research are the results of Fisher's significance test and the Neyman-Pearson hypothesis test, which were combined by psychologists. Also, in the philosophical background, it is related to Popper's falsificationism based hypothesis-deductive method and reduction to absurdity. Objectives : This study was designed to find complementary and alternative methods of null hypothesis and alternative hypothesis used for the clinical research methodology of Korean medicine otolaryngology. Methods : The body of this paper was divided into seven part. These are historical background, hypothesis test, hypothesis test method used in the design of clinical study, falsificationism and reduction to absurdity, problem and alternative method of the Neyman-Pearson hypothesis test, diagnosis example of sinusitis differentiation syndromes by Bayesian statistics. Through this process, we found out problems of frequentist statistics and suggested alternative methods. Result & Conclusion : As a solution to the problems of the null hypothesis and the alternative hypothesis, there are effects size, confidence interval, Bayesian statistics and Lakatos methodology of scientific research programmes.

• The Mathematical Education
• /
• v.41 no.3
• /
• pp.329-339
• /
• 2002

This study analyzes the epistemological meaning of‘social construction’in mathematical instruction. The perspective that consider the cognition of mathematical concept as a social construction is explained by a cyclic scheme of an academic context and a school context. Both of the contexts require a public procedure, social conversation. However, there is a considerable difference that in the academic context it is Lakatos' ‘logic of mathematical discovery’In the school context, it is Vygotsky's‘instructional and learning interaction’. In the situation of mathematics education, the‘society’which has an influence on learner's cognition does not only mean‘collective members’, but‘form of life’which is constituted by the activity with purposes, language, discourse, etc. Teachers have to play a central role that guide and coordinate the educational process involving interactions with learners in this context. We can get useful suggestions to mathematics education through this consideration of the social contexts and levels to form didactical situations of mathematics.

• Journal for History of Mathematics
• /
• v.15 no.1
• /
• pp.15-42
• /
• 2002

Dialectical Methods is the form in which thinking and being developed, according to Hegel. Every given definition removes itself necessarily and goes over to its contrary definition. The mutual struggle brings us to a new definition, which is richer and more concrete insofar as it embraces the original definition, but on a higher level. The purpose of this study is to enhancing student's creative thinking in mathematics by dialectical methods. The conclusions drawn from the results obtained in this study are as follows, First the introduction of dialectical methods to mathematics education had been made by Lakatos, Brousseau, Freudenthal. Second, the dialectical teaching methods in mathematics are developed from dialectical methods: the step of affirmation - the step of negation - the step of sublation. Third, the students who team mathematics by dialectical teaching methods are creative in its implications.

• Journal for History of Mathematics
• /
• v.26 no.4
• /
• pp.259-275
• /
• 2013

It has been proposed since modern times that we need to consult the history of mathematics in teaching mathematics, and some modifications of this principle were made recently by Lakatos, Freudenthal, and Brousseau. It may be necessary to have a direction which we consult when modifying the history of mathematics for students. In this article, we analyse the elements of the cognitive interest in Hamilton's discovery of the quaternions and in the history of discovery of imaginary numbers, and we investigate the effects of these elements on attention of the students of nowadays. These works may give a direction to the historic-genetic principle in teaching mathematics.

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

• Communications of Mathematical Education
• /
• v.20 no.3 s.27
• /
• pp.361-372
• /
• 2006

This study was extended as one of the properties of isosceles triangles to polygons(n-angles) by conjectures-proofs-reputations-reformations and developed teaching-learning materials which can be used in high-level classes for middle and high school students.

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

• Journal of Educational Research in Mathematics
• /
• v.25 no.4
• /
• pp.717-754
• /
• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, which is very similar to the pattern of 'Conjectures and Refutations'(Lakatos, 1976). Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as humility and courage (Lampert, 1990), which is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.