• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.737-760
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• 2016

This study analyzed the 2009 revised curriculum 6th grade math geometric domain and developed virtual operation tool contents based RME theory. These materials were examine to find out how to effect on the spatial sense and mathematical attitudes by applying it to teach the 6th grade students. The results were as follows. First, it is more effective for improving spatial sense to study mathematics based RME theory with virtual operation tool contents than normal one. This means that mathematics study based RME theory with virtual operation contents overcomes the limitations of flat learning environment. And it is great educational and effective method for students to improve their spatial sense. Second, it is more effective for improving mathematical attitudes to study mathematics based RME theory with virtual operation tool contents than normal one. This means that Mathematics study based RME theory with virtual operation contents makes student more participate learning actively. It helps the students who have passive learning habits to have self-directed learning habits, ability to cooperation and communicate. The results of this study suggest that mathematics study based RME theory is very helpful for student to improve their spatial sense and have positive effect on self-concept in mathematics, attitudes toward mathematics and improving study habits in mathematical attitudes.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.409-419
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• 2015

The concept of Cayley-symmetric semigroups is introduced, and several equivalent conditions of a Cayley-symmetric semigroup are given so that an open problem proposed by Zhu [19] is resolved generally. Furthermore, it is proved that a strong semilattice of self-decomposable semigroups $S_{\alpha}$ is Cayley-symmetric if and only if each $S_{\alpha}$ is Cayley-symmetric. This enables us to present more Cayley-symmetric semi-groups, which would be non-regular. This result extends the main result of Wang [14], which stated that a regular semigroup is Cayley-symmetric if and only if it is a Clifford semigroup. In addition, we discuss Cayley-symmetry of Rees matrix semigroups over a semigroup or over a 0-semigroup.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.351-367
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• 1999

This study aims to study the discourses influencing high school students' concept and attitude toward mathematics, and to examine how gender differences concerning mathematical aptitude are created. This study is based on the results of previous two studies which suggested that mathematical competence differs not only according to gender, region and school year, but also even within the same gender. For this study, 12 students ranking in the top 10% at two co-ed high schools were interviewed to find out 1) what discourses are related to gender and mathematics, 2) in what way these discourses are formulated and gain currency, and 3) how they have affected students in general. Common notions concerning mathematics may be summed up as follows: 1) Most of the students believe that gender difference in mathematical aptitude results because biologically men tend to be strong in mathematics and analytical skills while women tend to have better linguistic ability. This concept can help male students' studying to have a greater learning toward mathematics. 2) A large number of the students believe that male students' studying method is based on comprehension whereas female students' method is based on retention, and hence the former group tends to be better at applying their learning than the latter group. This notion seres to encourage male students and discourage female students from tackling difficult mathematical problems. 3) Many students believe that, although female students may surpass their male counterparts in middle school or the first year of high school, they will eventually fall behind by the 3rd year. Despite research which shows that these common beliefs are not grounded in scientific proof, high-school girls, who may be strong in mathematics, lose self-confidence and feel a sense of crisis. The mechanisms which produce and reinforce such concepts as those mentioned above can be summarized as follows: 1) Regarding the choice of majors and future career paths, parents show different attitudes toward sons and daughters, and this tends to influence high-school girls and hinders them from entering mathematics-related fields. 2) Teachers with value systems based on stereo-typed gender roles affect students a great deal, and give different advice according to gender of their students, for selecting their major fields - for instance, whether to study the natural sciences as opposed to humanities. 3) This study indicates that peer-group behavior, of either support or exclusion, also reinforces the process of internalizing notions of gender difference related to mathematical aptitude. 4) The gender-based notion that men are naturally more inclined to have better mathematical ability has caused male students to choose the natural science subjects and female students to turn to the humanities. The discourses discussed above, propagated in schools and homes, and in the mass media, are continually reinforced along with general gender inequalities in the society at large.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.97-109
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• 1998

The activities of teaching and learning are to try to reach the lesson object most closely in many ways. Considering that the lesson objects are to get the principle or law of a concept, to acquire the mathematical function, to master it through repeated exercises and to solve mathematical problems, we need many ways to reach such objects. Among the many ways, we can first think of one: the students will learn with curiosity and according to their own ability or advancing level in learning when teachers study and prepare necessary contents enough in advance by using computers, showing the right program to learners' needs. For example, defining definite integral by measuration by parts will help understand measuration by parts well and know the meaning of definite integral correctly, In teaching and learning by the use of this program, the educational effects are expected as follows. 1. It is thought that this program will stimulate the desire for and interest in learning because it used animation and acoustic effect. And voluntary and positive thinking activity will be shown. 2. It is expected that the conviction of formulas will be got and the concept of definite integral will be remembered firmly by showing how to measure the width of circle with the use of measuration by parts in various other ways instead of the ways used at present. 3. It is expected that students will feel the pleasure of mathematics in life when they recognize mathematical facts scattered really in our life rather than mathematical difficulties. 4. It is expected that the repeated review of programs already designed will remove the fear of incomplete parts and help review again. 5. It is certain that positive attitude in life will be formed as teacher-centered class is changed into learner-centered class and unwilling study is changed into self-oriented study. However, I think this program is insufficient for humanbeing-centered education given directly in contact with students on the ground of the variety in mathematical education and applications in many ways. And mechanically inhuman computers leave some solutions to be desired

• The Mathematical Education
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• v.60 no.4
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• pp.467-491
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• 2021

This study is a study on the coding mathematics curriculum that converges elementary and middle school mathematics and information subjects and a minimum coding game-based education method for this. For the past 3 years, the coding mathematics curriculum and educational methods to effectively operate the curriculum were studied by applying them to 6th graders of elementary school and 1st graders of middle school. As a result of the first year of research, the coding mathematics curriculum was modified to a coding environment including the mathematical concept of a three-dimensional coordinate space, and the three-dimensional object was improved to be output as a real 3D print. As a result of the 2nd year study, it was improved so that even low-level students can build buildings by introducing different level commands for each component of the building so that self-directed learning is possible. As a result of the 3rd year study, a teaching-learning strategy based on a minimal coding game was designed to induce an increase in the level of computational thinking, and evaluation and feedback for diagnosing computational thinking were developed. Educational methods to promote self-directed learning and computing thinking ability, and researched coding mathematics curriculum are meaningful for the research and practice of the convergence education of school mathematics and informatics.

• The Mathematical Education
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• v.41 no.1
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• pp.59-78
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• 2002

In a globalization and information society in the 21st century, the emphasis of education is on producing people who can create intellectual value. To meet the purpose in mathematics education, students should be taught to be able to understand basic logics and principles and exchange mathematical information each other. Also they had better be guided to study on their own at home in an effective way. In reality, however, most of the home study does not go beyond confirming the same homework. It is very difficult for students to plan systematic preparation and review of their lessons and study on their own. Moreover there seems to be no integration between the lessons students receive at school and in private classes. Therefore the need for more systematic home study in relation to school lessons is high to maximize the teaming effect. Studying through Web has little restriction in terms of time and space. Students can collect useful information inexpensively and share their learning assignment with each other. But mathematics education through Web has not yet been developed in such a way as to see a positive result from it. This research intends to develop a web site where students can study mathematics systematically in a self-guided way. The research methods applied included survey, student discussion and online home study. The questionnaires were designed to figure out students'and parents'changes in their concept of mathematics home study. The research also tried to look for ways to cut down the burden of expensive private lessons in mathematics. The student discussions were made up of problem-making and problem-solving. The discussion procedure was analysed so as to check if students used their creativity while they were working. As stated above, the research aims to develop a web site to support effective home study, enhance students' mathematical ability and reduce the burden of private lessons.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1051-1069
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• 2016

Combining the concept of self-certified public key and message recovery, Li-Zhang-Zhu (LZZ) gives the proxy signature scheme with message recovery using self-certified public key. The security of the proposed scheme is based on the discrete logarithm problem (DLP) and one-way hash function (OWHF). Their scheme accomplishes the tasks of public key verification, proxy signature verification, and message recovery in a logically single step. In addition, their scheme satisfies all properties of strong proxy signature and does not use secure channel in the communication between the original signer and the proxy signer. In this paper, it is shown that in their signature scheme a malicious signer can cheat the system authority (SA), by obtaining a proxy signature key without the permission of the original signer. At the same time malicious original signer can also cheat the SA, he can also obtain a proxy signature key without the permission of the proxy signer. An improved signature scheme is being proposed, which involves the remedial measures to get rid of security flaws of the LZZ et al.'s. The security and performance analysis shows that the proposed signature scheme is maintaining higher level of security, with little bit of computational complexity.

• School Mathematics
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• v.19 no.3
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• pp.593-615
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• 2017

The purpose of this study is to develop a mobile-based math learning application and explore its application. In order to develop a learning application, the present study included literature review on math education involving mobile learning, investigation of literature related to mathematics education conducted in a digital environment, and method of use and implementation environment of existing math learning applications by type. Based on these preliminary investigation and analysis, an android version application, 'Mathematics Classroom for Middle School 3rd Graders' was developed. This application can be used for learning units such as Quadratic Functions and Graphs, Representative Value, and Variance and Standard Deviation. For the unit on Quadratic Functions and Graphs, the application was constructed so that students can draw various graphs by using the graphic mode and discuss their work with other students in the chatting room. For the unit on Representative Value, the application was constructed with the mathematical concept of representative value explained through animation along with activities of grouping data acquired after playing archery games by points or arranging them according to size so that students can study when and how to use median value, mode, and average. The application for Variance and Standard Deviation unit was also constructed in a way that allowed students to study the concept of variance and standard deviation and solve the problems on their own. The results of this study can be used as teaching & learning materials customized for individual student in math classes and will provide anyone the opportunity to engage in an interesting self-directed learning of math at anytime. Developed in the format of real life study, the application will contribute to helping students develop a positive attitude about math.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.553-563
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• 1998

In this thesis, I examined Bruner's EIS theory from the viewpoint of epistemology based on Piaget's genetic epistemology. Although Bruner's ideal thought which insisted ‘to teach the structure’accepted Piaget's theory in the methodology of realization, it is different from Piaget in understanding knowledge. The difference is shown from understanding the meaning of ‘structure’. Piaget's concept of structure is something that has overcome the realistic viewpoint of the traditional epistemology and is reconstructed through endless self-regulative transformational process. However Bruner's is used as a realistic meaning as we can see in the Plato's recollection theory. Therefore Piaget's ‘stage of development’means the difference of structure which lies in the generative process and it includes the qualitive difference of level. On the other hand, Bruner, who is trying to translate and suggest the fixed structure to the children understood Piaget's stage of development as the difference in the ways of representation. Piaget's operational constructivism insists that the children should ‘construct’the knowledge through their activity, and especially in case of the lohico-mathematical recognition, the source should be internalized activity, that is, operation. In view of this assertion, Burner's idea which insists to accept the structure of knowledge as a fixed reality and to suggest the translated representation proper to the cognitive structure of the children to teach them, has a danger of emphasizing only the functional aspects to deliver the given knowledge ‘quickly’. And it also has the danger of damaging ‘the nature of the knowledge’in the translated knowledge.

• Journal of Engineering Education Research
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• v.25 no.5
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• pp.68-74
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• 2022

The purpose of this study was to develop an infographic-based STEAM program for high school students and test its effectiveness. In this study, we converged high school 'art' education with 'Korean language' and 'mathematics.' The program was divided into four phases. The effectiveness of the program was analyzed by conducting matched pair t-test for 377 students at a girl's high school in Seoul before and after the program. The study found that the students' self-concept on mathematics and their attitude towards choosing science and engineering career showed significant increases after the program. By connecting high school courses through data visualization based on cognitive information design, findings from this study suggest that our infographic-based STEAM program should be implemented more frequently at high schools.