• Journal for History of Mathematics
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• v.36 no.4
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• pp.61-78
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• 2023

By virtue of the characteristics inherent in diagrams, diagrammatic reasoning has potential and limitations that distinguish it from general thinking. It is natural that diagrams rarely appeared in Joseon mathematical books, which were heavily focused on computation and algebra in content, and preferred linguistic expressions in form. However, as the late Joseon Dynasty unfolded, there emerged a noticeable increase in the frequency of employing diagrams, due to the educational purposes to facilitate explanations and the influence of Western mathematics. Analyzing the role of diagrams included in Jo Taegu's 'JuseoGwangyeon', an exemplary book, this study includes discussions on the utilization of diagrams from the perspective of mathematics education, based on the findings of the analysis.

• Journal of the Korean School Mathematics Society
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• v.23 no.4
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• pp.509-521
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• 2020

This study began with the discovery of the concept of frequency density in Singapore textbooks and in a set of subject contents of the UK's General Certificate of Secondary Education. To understand the mathematical meaning of frequency density, the mathematical connection of frequency density was considered in terms of mathematics internal connections and mathematics external connections. In addition, the teaching method of frequency density was introduced. In terms of mathematical internal connections, the connections among the probability density function, relative frequency density, and frequency density in high school statistics were examined. Regarding mathematical external connections, the connection with the density concept in middle school science was analyzed. Based on the mathematical connection, the study suggested the need to introduce the frequency density concept. For the teaching method of frequency density, the Singapore secondary mathematics textbook was introduced. The Singapore textbook introduces frequency density to correctly represent and accurately interpret data in histograms with unequal class intervals. Therefore, by introducing frequency density, Korea can consistently teach probability density function, relative frequency density, and frequency density, emphasizing the mathematical internal connections among them and considering the external connections with the science subject. Furthermore, as a teaching method of frequency density, we can consider the method provided in the Singapore textbook.

• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.169-186
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• 2020

The purpose of this study is to find new material for developing teaching and learning materials for the gifted class of elementary school students by using the rotatable tangram made by modifying the traditional tangram. Rotatable tangram can be justified by gifted students through mathematical communication. However, even gifted class students have some limitations in finding and justifying triangles and rectangles of all sizes unless they go through the 'symbolization' stage at the elementary school level. Therefore, students who need an inquiry process for letters and symbols need to provide supplementary learning materials and additional questions. It is expected that the material of rotatable tangram for the development of teaching and learning materials for elementary school gifted students will contribute to the development of mathematical reasoning and mathematical communication ability.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.259-282
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• 2010

In this paper, we introduce a modified Moore Method designed for the multivariable calculus course, and discuss about the effective teaching and learning method by observing the changes in the understanding of students' learning and the effects on students' learning in the class implemented by this modified Moore Method. This teaching experiment research was conducted with the 15 students who took the multivariable calculus course offered as a 3 week summer session in 2008 at H University. To guide the students' active preparation, stepwise course materials structured in the form of questions on the important mathematical notions were provided to the students in advance. We observed the process of the students' small-group collaborative learning activities and their presentations in the class, and analysed the students' class journals collected at the end of every lecture and the survey carried out at the end of the course. The analysis of these results show that the students have come to recognize that a deeper understanding of the subjects are possible through their active process of search and discovery, and the discussion among the peers and teaching each other allowed a variety of learning experiences and reflective thinking.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.545-561
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• 2020

The purpose of this study is to investigate the applications and possibilities of major programs that provide services using artificial intelligence in mathematics education. For this study, related papers, reports, and materials were collected and analyzed, focusing on materials mostly published within the last five years. The researcher searched the keywords of "artificial intelligence", "artificial intelligence", "AI" and "mathematics education" independently or in combination. As a result of the study, artificial intelligence for mathematics education was mostly supporting learners' personalized mathematics learning, defining it as an auxiliary role to support human mathematics teachers, and upgrading the technology of not only cognitive aspects but also affective aspects. As suggestions, the researcher argued that followings are necessary: Research for the establishment of an elaborate artificial intelligence mathematical system, discovery of artificial intelligence technology for appropriate use to support mathematics education, development of high quality of mathematics contents for artificial intelligence, and the establishment and operation of a cloud-based comprehensive system for mathematics education. The researcher proposed that continuous research to effectively help students study mathematics using artificial intelligence including students' emotional or empathetic abilities, and collaborative learning, which is only possible in offline environments. Also, the researcher suggested that more sophisticated materials should be developed for designing mathematics teaching and learning by using artificial intelligence.

• Smart Structures and Systems
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• v.31 no.1
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• pp.1-11
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• 2023

Assessment of the compressive strength of concrete plays a major role during formwork removal and in the prestressing process. In concrete, temperature changes occur due to hydration which is an influencing factor that decides the compressive strength of concrete. Many methods are available to find the compressive strength of concrete, but the maturity method has the advantage of prognosticating strength without destruction. The temperature-time factor is found using a LM35 temperature sensor through the IoT technique. An experimental investigation was carried out with 56 concrete cubes, where 35 cubes were for obtaining the compressive strength of concrete using a universal testing machine while 21 concrete cubes monitored concrete's temperature by embedding a temperature sensor in each grade of M25, M30, M35, and M40 concrete. The mathematical prediction model equation was developed based on the temperature-time factor during the early age compressive strength on the 1^st, 2^nd, 3^rd and 7^th days in the M25, M30, M35, and M40 grades of concrete with their temperature. The 14^th, 21^st and 28^th day's compressive strength was predicted with the mathematical predicted equation and compared with conventional results which fall within a 2% difference. The compressive strength of concrete at any desired age (day) before reaching 28 days results in the discovery of the prediction coefficient. Comparative analysis of the results found by the predicted mathematical model show that, it was very close to the results of the conventional method.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.97-130
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• 2014

The purpose of the study was to investigate the aspects of analogy of high school student's thinking process revealed in the inquiry activity with synthetic division. The case study method of qualitative research was conducted with two high school 10th grade students. Structure-mapping model(SMM) of Gentner and similarity frames which were proposed by other researchers were utilized to analyze the data. Two students used analogy as a tool and they could discover synthetic division of more than 2 degrees, but they revealed different levels of mathematics discovery depending on the different degree of analogical thinking. Surface similarity in the process of inquiry activity played a vital role in analogical thinking. We asked students to explore and discover analogy based on structure similarity. Analogy based on the systematic approach made it possible to predict upper domain. Analogy based on the procedure similarity induced internalization. We could conclude that analogy has instrumental, heuristic and reflective characteristics.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.731-744
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• 2010

Nowadays in school mathematics, the skill and method for solving problems are often emphasized in preference to the theoretical principles of mathematics. Students pay attention to how to make an equation mechanically before even understanding the meaning of the given problem. Furthermore they do not get to really know about the principle or theorem that were used to solve the problem, or the meaning of the answer that they have obtained. In contemporary textbooks the conic section such as circle, ellipse, parabola and hyperbola are introduced as the cross section of a cone. But they do not mention how conic section are connected with the quadratic equation or how these curves are related mutually. Students learn the quadratic equations of the conic sections introduced geometrically and are used to manipulating it algebraically through finding a focal point, vertex, and directrix of the cross section of a cone. But they are not familiar with relating these equations with the cross section of a cone. In this paper, we try to understand the quadratic curves better through the analysis of the discussion made in the process of the discovery and eventual development of the conic section and then seek for way to improve the teaching and learning methods of quadratic curves.

• The Mathematical Education
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• v.43 no.4
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• pp.419-440
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• 2004

The purpose of this paper is to know the effects on number and operation abilities of the 1st grade children of elementary school by applying teaching and learning activity throught communication. For this purpose, we have studied according to the following procedure. 1. We divised teaching and learning model through communication and applied in the actual teaching and learning activity. 2. We investigated the effects of number and operations abilities of the 1st grade children by applying teaching and learning activity through communication. To accomplish this purpose, we applied learning activity through communication to the 1st grade of 40 elementary school children for about six months(September 1, 1999 ～ February 20, 2000). In process of applying this model, we collected all sorts of cases in the children's learning activity and investigated children's response on learning activity through communication, interview with children and researcher's observation. We applied the model through communication in class and compared with the traditional learning. 1. In learning through communication, children could solve the problem in themselves with a sense of responsibility. 2. It was impossible to find out the degree of children's comprehension in the explanatory learning. But in the learning through communication, it was a great help to individualize and plan the learning because children express their ideas clearly. It has conclusion as follows. The learning activity through communication has effected on forming number and operations abilities of the 1st grade of elementary school children importantly. 1. Children have improved in the abilities through communication to express their own ideas. 2. Children have studied with a sense of responsibility not in the teacher-oriented learning but in the self-directed learning 3. Children could find out the mathematical concepts in themselves - correcting false concepts, reguiding concepts by errors, finding invisible errors, solving problems variously and knowing the easy method. 4. The activity through communication in mathematics was a base of children's individual learning and important data of next learning plan. 5. The mathematical concepts formed through communication had a high transfer of learning. 6. Children have taken pleasure of discovery and had affirmative attitude about mathematics learning. We can make sure that number and operations abilities of the 1st grade children are formed by applying teaching and learning activity through communication. However, help and control of teacher have to be with it.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.41-44
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• 2005

Cytokines play a crucial role in the immune and inflammatory responses. But because of the high evolutionary rate of these proteins, the similarity between different members of their family is very low, which makes the identification of novel members of cytokines very difficult. According to this point, a new bioinformatic strategy to identify novel cytokine of the short-chain and long-chain 4${\alpha}$ helix cytokine using hidden markov model (HMM) is proposed in the paper. As a result, two motifs were created on the two train data sets, which were used to search three different databases. In order to improve the result, a strict criterion is established to filter the novel cytokines in the subject proteins. Finally, according to their E-value, scores and the criterion, four subject proteins are predicted to be possible novel cytokines for each family respectively.