• East Asian mathematical journal
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• 제39권2호
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• pp.119-139
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• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• East Asian mathematical journal
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• 제39권4호
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• pp.437-454
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• 2023

The core of the change in the era of the 4th industrial revolution is the change in the base of 'digital technology'. These changes are incomparably large and are expected to have a more important impact on our lives than ever before. One of the major inflection points in the transition to the digital era is the education field, and IT technology has become an essential element in the educational field. Accordingly, this study examines domestic research trends related to the educational environment based on digital technology. Then, we would like to provide implications for the establishment of a digital-based educational environment that will change in the future. To this end, Semantic network analysis has been conducted to quantitatively structure text data obtained from studies related to digital technology in the field of mathematics education over the past 10 years, and the discussion will continue based on the results.

• East Asian mathematical journal
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• 제39권4호
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• pp.479-492
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• 2023

Although Euclidean plane geometry is implemented in the middle school course, there are three major problems in high school space geometry that can be intuitively taken for granted or misinterpreted as circular arguments. In order to solve this problem, this study proved three major problems using sets, Euclidean plane geometry, and parallel line postulates. This corresponds to a logical sequence and has mathematical and mathematical educational values. Furthermore, it will be possible to configure spatial geometry using sets, and by giving legitimacy to non-Euclidean spatial geometry, it will open the possibility of future research.

• East Asian mathematical journal
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• 제40권1호
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• pp.75-83
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• 2024

For a reduced, irreducible and nondegenerate curve C ⊂ ℙ^r of degree d, it was shown that the arithmetic genus g of C has an upper bound π₀(d, r) by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll S(0, 2) ⊂ ℙ³ which attain the maximal arithmetic genus.

• East Asian mathematical journal
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• 제23권1호
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• East Asian mathematical journal
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• 제36권4호
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• pp.475-492
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• 2020

This study is to establish the items on class critiques based on the mathematical competencies according to the mathematics curriculum revised in 2015. Namely, this study deals with the items on how pre-service or in-service teachers understand and comment on mathematics instruction on their own instruction or peers' instruction. To accomplish this, first of all the draft items on instructional reviews was developed by researchers of this study on the basis of the previous study(Hwang, 2018). In order to revise and develop the draft items, the experimental study was executed. The experimental study was done by the subject of 11 groups who are undergraduate students in the educational college of C University. The subject was supposed to watch an in-service middle school mathematics teacher's excellent instruction(study) video and to comment the instruction video on the draft items on class critiques. While analyzing the comments of the subject, the revised items on the class critiques were to be develop. Based on this study, from now on, the final and ideal items on the class critiques would be establish to reflect and comment teachers' instruction.

• East Asian mathematical journal
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• 제30권4호
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• pp.509-526
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• 2014

The mathematics has moved toward the independence from unit. However, is this tendency also kept up in teaching and learning mathematics? This study starts from this question. We have illuminated this question in respects of a character of unit operation, an essential probability of unit operation and a didactical application of unit. As results, addition and subtraction are operations on identical objects and the result of operation does not also get out of operation's object. On the other hand, multiplication and division are operations on both identical objects and different objects. And the result of operation can generate new unit. We proposed a hypothesis which multiplication and division are transcendental operations from this analysis. The unit operation is not possible essentially. It seems only like unit operation is possible superficially by operational definition on unit. We could discuss on a didactical application of unit from above analysis. And we could deduct implications that the direction of developing mathematic does not necessarily match with the direction of teaching and learning mathematics.

• East Asian mathematical journal
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• 제38권1호
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• East Asian mathematical journal
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• 제38권2호
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• pp.187-214
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• 2022

This study compares the functions of the Learning Management Systems (LMS) in three widely used Edu-Tech platforms, that support students' individualized learning by using the learning characteristics of the students. The rapid advances in artificial intelligence (AI) are broadening their impacts in the education industry, and play a broad role in supporting student learning. In many countries, online classes have become a norm due to the COVID-19 crisis, and the demand for Edu-Tech in classes has increased rapidly. As a result, many countries, including South Korea, are now preparing and implementing various policy measures to adopt Edu-Tech in the class setting. Therefore, in this study, we analyze and compare the structures and characteristics of the three widely used Edu-Tech platforms that support individualized mathematics learning. In particular, we compare the LMSs of the three platforms by considering the elements such as learning design, learning management, learner analysis, learning result analysis, and student management functions. The results of this study give implications in the future directions to take on how to build Edu-Tech platform models that promote students' individualized mathematics learning in public education.

• East Asian mathematical journal
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• 제25권3호
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• pp.299-320
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• 2009

In mathematics, the education of the geometry proof has been playing an important role in promoting the ability for logical thinking by means of developing the deductive reasoning. However, despite of those importance mentioned above, considering the present condition for the education of the geometry proof in middle schools, it is still found that most of classes are led mainly by teachers, operating the cramming system of eduction, and students in those classes have many difficulties in learning the geometry proof course. Accordingly this thesis suggests the other method that is distinguished from previous proof educations. The thesis of Kai-Lin Yang and Fou-Lai Lin on 'A Model of Reading Comprehension of Geometry Proof (RCGP)', which was published in 2007, have various practical examples based on the model. After composing classes based on those examples and instructing the geometry proof, found out a problem. And then advance a new teaching model that amendment and supplementation However, it is considered to have limitation because subjects were minority and classes were operated by man-to-man method. Hopefully, the method of proof education will be more developed through performing more active researches on this in the nearest future.