• 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.

• 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.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.

• 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 Crystal Growth and Crystal Technology
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• v.32 no.6
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• pp.246-250
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• 2022

An estimation method of glass viscosity using Lakatos model is one of the best way to calculate the viscosity of soda-lime glass. The glass viscosity is obtained by inputting a glass composition consisting of SiO₂, Al₂O₃, Na₂O, K₂O, CaO and MgO to the Lakatos model. A series of composition of glass bottles was obtained once a month for 10 months from a soda-lime glass bottle fabrication line and isokom temperatures at the viscosity of log η = 3, 6.6, 10 and 12.3 were calculated. It was found that the isokom temperature at log η = 3 and log η = 6.6 was closely related to the value of (Si+Al)/O and 1/Na, respectively.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.57-70
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• 2012

In this study, a teaching unit for mathematically gifted students is designed, based on Lakatos's perspective. First, students appreciated the exceptions of Desargue theorem and introduced the point at infinity to remove the exceptions. Finally students were guided to realize that the exceptions and the general case of Desargue theorem have equal status. Exploring Desargue theorem with other viewpoints, gifted students experienced the growth of mathematical knowledge due to exceptions of the theorem.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.33 no.1
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• pp.7-14
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• 2023

Forty Viscosity data of glass bottles fabricated in a glass bottle manufacturing plant for 4 years were calculated using Lakatos model. The relationship between the glass bottle compositions and viscosities at log η of 3, 6.6, 10 and 12.3 Pa·s was analyzed. MgO that was a component of the glass bottle showed the maximum coefficient of variation of 0.89, but it gave a very small change in the viscosity. CaO that was another component of the glass bottle lowered the isokom temperature because it tended to reduce the number of non-bridging oxygen at temperature below a softening point.

• 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 of the Korean Crystal Growth and Crystal Technology
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• v.32 no.3
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• pp.103-106
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• 2022

The effect of Al₂O₃ on isokom temperatures in soda-lime glass is estimated by comparing calculated isokom temperatures using viscosity model proposed by Lakatos. Substitution of SiO₂ with Al₂O₃ by 0.5 mol% raises the isokom temperatures by 3.1, 3.3, 3.6 and 7.2℃ at the viscosity of log η = 12.3, 10, 6.6 and 1 (Pa·s), respectively. Meanwhile, replacing 0.5 mol% of CaO with Al₂O₃ raises the isokom temperatures by 1.6, 2.3, 4.1 and 17.7℃ at the viscosity of log η = 12.3, 10, 6.6 and 1 (Pa·s), respectively.