• Communications of Mathematical Education
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• v.33 no.2
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• pp.47-66
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• 2019

The purpose of this study is followings. First, we develop and apply teaching and learning methods for conducting team projects in flipped calculus class. Second we collect data such as team reports, individual reviews, and surveys during class activities. Third we survey the impacts on participation in student team activities, advanced studying, communication and collaboration. A total of 120 engineering and science majoring students participated in the 16-week long class study administered in team project learning styles in Spring 2018. There were two characteristics of this class. First students studied concepts and examples with video in pre-class and did the team project learning in the classroom. Second we used Google Drive to record team project progress, and to make sure the instructor to intervene appropriately in team activities. We conducted a team project inside and outside the classroom. This could lead the instructor to advise students and so their participation in team activity increased. As a result, it not only had a good effect on communication and cooperation, but also had an effect on advanced learning.

• The Mathematical Education
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• v.61 no.4
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• pp.581-595
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• 2022

The purpose of this study is to specify the procedure for making item models based on ontology models using automatic item generation in the mathematics subject through the CAFA system, and to explore the generated item instances. As an illustration for this, an item model was designed as a part of formative assessment based on the content characteristics, including concepts and calculations, and process characteristics, including application, using the representative values and the measures of dispersion in Mathematics of the 9th grade based on the evaluation criteria achievement standards. The item types generated in one item model were a best answer type, a correct answer type, a combined-response type, an incomplete statement type, a negative type, a true-false type, and a matching type. It was found that HTML, Google Charts, TTS, figures, videos and so on can be used as media. The implications of the use of digital evaluation based on automatic item generation were suggested in the aspects of students, pre-service teachers, general teachers, and special education, and the limitations of this study and future research directions were presented.

• The Mathematical Education
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• v.62 no.2
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• pp.257-268
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• 2023

The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• The Mathematical Education
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• v.61 no.1
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• pp.29-45
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• 2022

This study tried to analyze the problems by critically examining how the chance is taught in relation to the concept of chance and randomness in the Korean elementary school mathematics curriculum. To this end, the concepts of chance and randomness were first examined, and problems were presented in based on this by the literature analysis on mathematics curriculum material and textbooks for elementary school in Korea. As a result, there was a lack of experience in reasoning based on data, and randomness instruction was not performed properly. In addition, as the teaching of the sample space was omitted, contradictory materials were being used. Moreover, it was pointed out that the teaching of chance is focused on a specific grade level. For the improvement of the teaching of chance, a teaching of the probability experiment and the sample space were mainly suggested, and it was also suggested that the contents of the data area be adjusted for the composition focused on a specific grade.

• East Asian mathematical journal
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• v.40 no.2
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• pp.183-207
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• 2024

This study is a case study that considered fractional senses and fraction operation abilities for 107 gifted students in elementary school classes. In order to find out the fractional sense, in the first question comparing the sizes of fractions 2/3 and 4/5, the students showed a variety of strategies, but the utilization rate of strategies excluding reduction to a common denominator did not exceed 50%. The second question can be solved by using the first question. It is a problem of finding two fractions by selecting four from six numbers 1, 3, 4, 5, 6, and 7 to create two fractions of which sum does not exceed 1. The percentage of correct answers to this question was about 27% (29 out of 107). Only 5 out of 29 students found answers using the first question, and the rest of the students sought answers through trial and error in various calculations. It shows that the item arrangement method from a deductive perspective has no significant effect on elementary school students. The percentage of correct answers was about 27% in the questions to find out the fraction operation ability-the question of drawing a 4/3 bar using a given 3/8-sized bar and 30.7% (23 out of 75) of the students who had wrong answers showed insufficient splitting operation. In addition, it has been shown that the operation of partitioning and iterating to form numerical senses and fractional concepts related to the fractions of the students has no significant impact.

• Journal of Korean Society for Geospatial Information Science
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• v.3 no.1 s.5
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• pp.45-54
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• 1995

The relational data model is based on mathematical concept of relations and is well formulated, and so there have been numerous practical applications and studies. However, it is not suitable for representing a complex hierarchical structure, which is the characteristic of most geographical objects. On the other hand, the object-oriented data model can naturally represent a complex hierarchical structure, but there is a difficulty in sharing data with the relational data model which is currently used by most commercial GIS users. Also it has no standard query language with standardized format. In this paper, we propose an Object Grouping based on RDBMS to use data from a traditional relational data model while supporting various concepts of the object-oriented data model, and we applied this data model to design a GIS.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.5
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• pp.798-806
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• 2003

Structural optimization has been carried out in continuous or discrete design space. Methods for continuous design have been well developed though they are finding the local optima. On the contrary, the existing methods for discrete design are extremely expensive in computational cost or not robust. In this research, an algorithm using tabu search is developed fur the discrete structural designs. The tabu list and the neighbor function of the Tabu concepts are introduced to the algorithm. It defines the number of steps, the maximum number for random searches and the stop criteria. A tabu search is known as the heuristic approach while genetic algorithm and simulated annealing algorithm are attributed to the stochastic approach. It is shown that an algorithm using the tabu search with random moves has an advantage of discrete design. Furthermore, the suggested method finds the reliable optimum for the discrete design problems. The existing tabu search methods are reviewed. Subsequently, the suggested method is explained. The mathematical problems and structural design problems are investigated to show the validity of the proposed method. The results of the structural designs are compared with those from a genetic algorithm and an orthogonal array design.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.399-407
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• 1998

This paper deals with a method for finding the physical structure of dynamic systems which shows reasonable response to a given specifiation. The method uses only four basic models of bond graph prototypes which have been originally proposed by the authors as a general model for dynamic systems, and then makes its procedure highly physical in the sense that it can synthesize a dynamic system through the structural transformation directly on bond graph models without any mathematical manipulation. Also, it is shown that this method has further advantages in optimizing parameters for an existing system rather than developing design concepts for a new device, the latter being more suitable using the so-called analytical synthesis method introduced by Park and Redfield. One example serves to trace the outlines of the direct synthesis method proposed in this paper for dynamic systems in terms of bond graph prototypes.

• Korean Journal of Logic
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• v.17 no.2
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• pp.349-358
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• 2014

Human being has attempted to solve the problem of imperfect knowledge for a long time. In 1982 Pawlak proposed the rough set theory to manipulate the problem in the area of artificial intelligence. The rough set theory has two interesting properties: one is that a rough set is considered as distinct sets according to distinct knowledge bases, and the other is that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or an event) may be understood as different ones from different perspectives, while different concepts (or events) may be understood as a same one in a certain perspective. This paper claims that such properties of rough set theory produce a mathematical model to support critical realism and theory ladenness of observation in the philosophy of science.