• 대한수학회논문집
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• 제28권3호
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• pp.511-516
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• 2013

We establish an easy proof of an integral identity using the unitary invariance, which is applied to compare harmonicity and M-harmonicity.

• 교육시설 논문지
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• 제24권6호
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• pp.27-36
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• 2017

Educational facilities have an affect to make a decently learning environment. After constructed, it needs a maintenance plan to keep the performance or function which provide the repair time, repair scope and ratio. But the fundamental data are so insufficient that the field worker can't provide the maintenance plan and has no choice use the other data which concerned with apartment or office building. Above all, the service life is indispensible to make a repair plan because the repair time and scope would be provided within the service life. This study aimed at providing the method to make a service life of component in educational facilities and applying the method into the roof proof and floor finishing. Results are shown that first, it is important to set the $1^{st}$ repair time after constructed. when it proposes the three ways with the probability approach, choice probability model and cumulative cost function. Second, the service life of roof proof is provided with about 35 years. In addition, the service life of the floor finishing is about 40 years. These result would be utilized to conduct the repair plan under the service life.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권2호
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• pp.215-225
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• 2002

In this paper we consider some properties of. bisector of interior angle(theorem 1) and exterior angle(theorem 2) in triangle by using analogy. As a result of analyzing various mathematics textbooks we have known that they focused not on relation between two theorems, but on describing two theorems. We have seen that theorem 2 is able to be inferred from theorem 1 by using analogy. After proving theorem 1 by some methods we analyze proof process, extract proof ideas, and analogize some ideas for proving theorem 2. From this we are able to find relationships between theorem 1 and 2.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권4호
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• pp.597-612
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• 2007

For finding the optimal strategy in Blackout game which was introduced in the homepage of popular movie "Beautiful mind", we have developed and generalized a mathematical proof and an algorithm with a couple of softwares. It did require only the concept of basis and knowledge of basic linear algebra. Mathematical modeling and analysis were given for the square matrix case in(Lee,2004) and we now generalize it to a generalized $m{\times}n$ Blackout game. New proof and algorithm will be given with a visualization.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제27권1호
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• 충청수학회지
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• 제10권1호
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• pp.37-41
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• 1997

In this paper, we give a direct proof that the Perron and variational integrals are equivalent.

• 충청수학회지
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• 제31권3호
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• pp.321-324
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• 2018

We present a new and simple proof of improved Carleson's inequality.

• East Asian mathematical journal
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• 제34권1호
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• pp.17-20
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• 2018

Hardy-Bennett inequality is an inequality of Hardy-type having logarithmic weight. It appeared in 1973, and several generalizations followed. We, in this note, present another generalization with a simple proof.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권3호
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• pp.215-229
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• 2018

Despite the importance of learning to do mathematical proofs, researchers have reported that not only secondary school students but also undergraduate students have difficulties in learning proofs. In this study, we introduced a new toll for learning proofs and explored the reliability and the validity of peer assessment on proofs. In the course of a university in Seoul, students were given weekly proof assignments prior to class. After solving the proofs, each student had to assess other students' proofs. The inter-rater reliabilities of weekly peer assessment was higher than .9 over 90 percent of the observed cases. To examine the validity of peer assessment, we check whether students' assessments were similar to expert assessment. Analysis showed that the equivalence has been quite high throughout the semester and the validity was low in the middle of the semester but rose by the end of the semester. Based on these results, we believe instructors can consider the application of peer assessment on proving tasks as a tool to help students learn.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권1호
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• pp.83-98
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• 2015

By analysing the examination papers for geometry, we classified the errors occured in the proofs for geometric problems into 5 main types - logical invalidity, lack of inferential ability or knowledge, ambiguity on communication, incorrect description, and misunderstanding the question - and each types were classified into 2 or 5 subtypes. Based on the types of errors, answers of each problem was analysed in detail. The errors were classified, causes were described, and teaching plans to prevent the error were suggested case by case. To improve the students' ability to express the proof of geometric problems, followings are needed on school education. First, proof learning should be customized for each types of errors in school mathematics. Second, logical thinking process must be emphasized in the class of mathematics. Third, to prevent and correct the errors found in the proofs for geometric problems, further research on the types of such errors are needed.