• 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.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.361-372
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• 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 of Educational Research in Mathematics
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• v.14 no.2
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• pp.143-156
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• 2004

Lakatos's mathematical philosophy implies that the mathematical knowledge is quasi-empirical and provides the context where mathematics grows and develops. So, it is educationally significant. But, it is not easy to apply Lakatos's methodology to teaching elementary mathematics, because Lakatos's logic of the mathematical discovery is based on the proofs and refutations but elementary mathematics does not contain any proof. This study is to develop the schemes that apply Lakatos's methodology to teaching elementary mathematics and to provide the teaching examples. I devised the teaching process and the curriculum development method. And I developed the teaching examples.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.553-565
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• 2013

The purpose of this study was to examine how the Lakatos method works in the elementary teacher education program. Elementary preservice teachers were given a task in which they examined the Pick's theorem. The finding revealed that Lakatos method was usable in the elementary teacher education. They produced initial conjecture and found counterexamples, and finally made improved conjectures. These experience encourage them to change their belief of teaching and learning mathematics and to find alternative ways of teaching mathematics.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.19-32
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• 2006

We study on administration system and teaching of R &E(Research and Education) in Korea Science Academy(KSA) laying stress on Mathematics project No.7. We analyze in detail administration system of R&E in KSA(for example, aim, human constitution, practical execution), and draw some meaningful suggestions in order to receive successful results in R&E of KSA. And we describe mathematical topics, problems, and results which are received by students of KSA in the process of R&E(project No.7).

• Journal of The Korean Association For Science Education
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• v.20 no.1
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• pp.88-100
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• 2000

This study was to investigate high school students' philosophical views on science and positions of constructivists; Popper, Lakatos, Toulmin, and Kuhn. The results of this study were as follows: First, most students had the eclectic position(69%): similar percentages in sex(male 67%, female 75%), stream(liberal art 72%, science 74%), and of having experience on reading books or magazines related to the philosophy of science(ever 78%, never 64%). Second, in analysis of ANDVA of science philosphical perspectives by experience of reading books, magazines, and matters related to the philosophy of science, significant difference was revealed(p<.01). Students who had ever heard of or read about the philosophy of science were tend to have Empiricism. Third, ANDVA analysis of constructivist philosphical perspectives showed that male students were nearer to Kuhn's position than female(p<.05) and students in science stream were closer to Popper than in liberal art(p<.05). And male students in science party showed a great tendency to consent Popper's perspective(p<.01). This result seems to suggest that male students tended to think social aspects more deeply than female and held Kuhn's position.

• School Mathematics
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• v.11 no.1
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• pp.55-70
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• 2009

The purpose of this study is to implement Lakatos method in the teaching and learning of geometry for middle school students. In his landmark book , Lakatos suggested the following instructional approach: an initial conjecture was produced, attempts were made to prove the conjecture, the proofs were repeatedly refuted by counterexamples, and finally more improved conjectures and refined proofs were suggested. In the study, students were selected from the high achieving students who participated in the special mathematics and science program offered by the city council of Seoul. The students were given a contradictory geometric proposition, and expected to find the cause of the fallacy. The students successfully identified the fallacy following the Lakatos method. In this process they also set up a primitive conjecture and this conjecture was justified by the proof and refutation method. Some implications were drawn from the result of the study.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.21-33
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• 2013

In this study, We analyzed the mathematical thinking of sixth grade students showed mathematics lessons through the application of Lakatos' methodology and search for the role of their teachers in this lessons. We supposed to find the solution to the way of teaching-learning regarding the Lakatos' methodology for the elementary school level. According to the stages of presenting a problem situation, suggesting an initial conjecture, examining the conjecture, and improving the conjecture, we had lessons 8 times that are applied to Lakato's methodology. We gathered and analyzed data from lessons and interviews recording videotapes, documents for this study. The participants showed a lot of mathematical thinking. They understood the problem situation with the skill of fundamental thinking and suggested the initial conjecture by the skill of developmental thinking and they found a counter-example to be able to rebut the initial conjecture by critical thinking. Correcting the conjecture not to have counter-example, they drew developmental thinking and made their thinking generalize.

• Journal of The Korean Association For Science Education
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• v.18 no.3
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• pp.283-296
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• 1998

This study was to identify middle school and college of education students' preconceptions about dielectric polarization and explore the students' reponses on the supporting or conflictual evidences on their preconceptions by letting them observe the demonstrations using electroscope, charged material, six conductor rods and six insulator rods. Letting students select the demonstrations to be observed by themselves, students' evidence selection types were classified as two : to select the evidences to testify their uncertain preconceptions, and to obtain the confirmation evidences about their preconceptions. And each evidence selection types, again, could be subclassified as three and two respectively. When students observed the conflictual observations, all accepted the observation itself. For supporting observational evidences, almost of all students showed the error of 'acceptance of antecedent' in the syllogism, that is, they did not required the succeeding supporting observations. Students' reponses on the conflictual observational evidences were classified as two: to reject the hard core of preconceptions, and to modify the students' auxiliary ideas related to the hard core with preserving the hard core. The first type reponses were, again, could be classified as three subtypes but, in all cases, students introduced new concept to explain the conflictual evidences. This responses indicated that Lakatosian rather than Popperian view is more acceptable to understand the students' reponses on the conflictual evidences. The second type reponses also were classified as three subtypes, and it was found that more middle school students than college education students were involved in this second type. That is, students who did not have perfect understanding of auxiliary ideas related with the hard core of preconceptions were more apt to change or modify theses auxiliary ideas rather than reject the hard core, this means that the quality of understanding of auxiliary ideas also take an important role in the change of hard core concept.