• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.465-479
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• 2012

For $0<p{\leq}{\infty}$ and a convex body $K$ in $\mathbb{R}^n$, Lutwak, Yang and Zhang defined the concept of dual $L_p$-centroid body ${\Gamma}_{-p}K$ and $L_p$-John ellipsoid $E_pK$. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $K$, there exist an ellipsoid $E$ and a parallelotope $P$ such that for $1{\leq}p{\leq}2$ and $0<q{\leq}{\infty}$, $E_qE{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$; For $2{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, $2^{-1}{\omega_n}^{\frac{1}{n}}E_qE{\subseteq}{\Gamma}_{-p}K{\subseteq}{2\omega_n}^{-\frac{1}{n}}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$. (ii) For any convex body $K$ whose John point is at the origin, there exists a simplex $T$ such that for $1{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, ${\alpha}n(nc_{n-2,p})^{-\frac{1}{p}}E_qT{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qT$ and $V(K)=V(T)$.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.681-691
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• 2011

Mathematics curriculum according to 2009 Revised National Curriculum suggests that school mathematics must cultivate interest and curiosity about mathematics in addition to creative thinking ability of students, and ability and attitude of observing and analyzing many things happening around. Centroid of a triangle in 2007 Revised National Curriculum is defined as 'an intersection point of three median lines of a triangle' and it has been instructed focusing on proof study that uses characteristic of parallel lines and similarity of a triangle. This could not teach by focusing on the centroid itself and there is a problem of planting a miss concept to students. And therefore this writing suggests centroid must be taught according to its essence that centroid is 'a dot that forms equilibrium', and a justification method about this could be different.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.255-279
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• 2015

Educating for character was emphasized in 2009 reformed Korea national mathematics curriculum. Thus, in this study we basically conducted to realize the character education. This study aimed to develop the teaching and learning materials for character education in middle school. For the purpose of this study, the following study was carried out. First, we investigated the concept of character education. Second, based on this, we extracted the three factor(altruism, rationality, course orientation) for character education in mathematics teaching and learning. Third, we developed five teaching and learning models for character education. The five kinds of models are 'Respect model', 'Self-directed model', 'Cooperation-centered model', 'Self-interest model, 'Story sympathy model'. Finally, We have developed a teaching and learning materials in accordance with the models. And, we applied to the classroom and confirmed its effectiveness.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.59-75
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• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• School Mathematics
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• v.16 no.1
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• pp.57-81
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• 2014

This study was to investigate how the underachievers of mathematics in a non-leveling excellent high school would overcome the errors through the lessons based on the inductive thinking model in the equation of a circle. The results showed that when there were many stages to solve the problem, the students gave it up or forgot the stage they reached. In this case, if they had a revisit-opportunity to review their thinking process by planning ahead the stage to solve the problem and recording it, the omission error of the solving process and the error of wrong conclusions would be dramatically decreased. Moreover, they understood the mathematical concept, principle, and formula and remembered the learning contents extremely well through thinking by themselves in exploration-based activities and by using visualization for the problem and could solve the problem through these pictures besides algebraic expressions.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.37-58
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• 2011

The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.1-18
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• 2011

The purpose of this study was to investigate the effects of estimation strategy on placing decimal point in multiplication and division of decimals. To examine the effects of improving calculation ability and reducing decimal point errors with this estimation strategy, the experimental research on operation with decimal was conducted. The operation group conducted the decimal point estimation strategy for operating decimal fractions, whereas the control group used the traditional method with the same test paper. The results obtained in this research are as follows; First, the estimation strategy with understanding a basic meaning of decimals was much more effective in calculation improvement than the algorithm study with repeated calculations. Second, the mathematical problem solving ability - including the whole procedure for solving the mathematical question - had no effects since the decimal point estimation strategy is normally performed after finishing problem solving strategy. Third, the estimation strategy showed positive effects on the calculation ability. Th Memorizing algorithm doesn't last long to the students, but the estimation strategy based on the concept and the position of decimal fraction affects continually to the students. Finally, the estimation strategy assisted the students in understanding the connection of the position of decimal points in the product with that in the multiplicand or the multiplier. Moreover, this strategy suggested to the students that there was relation between the placing decimal point of the quotient and that of the dividend.

• School Mathematics
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• v.7 no.4
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• pp.445-467
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• 2005

The purpose of this study was to investigate mathematics teaching of an elementary school teacher and to understand the meaning of it. This study was a qualitative case study using by analyzing metaphors. The notion of metaphors was newly set up. Traditionally, it had been regarded as a mere tool for better understanding, but it was recognized as the primary source of all of our concept(Sfard, 1998). The subject of this case study was a researcher 'I' and also an elementary school teacher. The three selves named Mee1, Mee2, Mee3, respectively. Mee1 was the 'I' who developed the 4th graders' activities on mathematical patterns in 1996 and wrote mathematics textbook for the 4th graders in 1998-1999. Mee2 was the 'I' who taught mathematical patterns to her students in 2002. Mee3 was the 'I' who criticized the teaching of Mee2 in 2005. [ADVENTURE], [HIDE-AND-SEEK], and [FIREWORKS DISPLAY] were deter-mined to be key metaphors of mathematics teaching. [ADVENTURE] of Mee] was focused on profound understanding of mathematics, [HIDE-AND-SEEK] of Mee2 on construction of mathematics, and [FIRE-WORKS DISPLAY] of Mee3 on making meaning and participating in communities. Studies of metaphors give us the power of understanding mathematics teaching and also generate it. And viewing mathematics teaching via metaphors makes teaching studies open to new ways.