• Journal for History of Mathematics
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• v.20 no.4
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• pp.61-70
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• 2007

Combinatorics, often called the 21 st century mathematics, has turned out a very important subject for the present information era. Modern combinatorics has started from some mathematical works, for example, Pascal's triangle and the binomial coefficients, and Euler's problems on the partitions of integers and Konigsberg's bridge problem, and so on. In this paper, we investigate the origin of combinatorics by looking over some interesting ancient combinatorial problems and some important problems which have started various subfields of combinatorics. We also discuss a little on the role of combinatorics in mathematics and mathematics education.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2002.06a
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• pp.392-407
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• 2002

컴퓨터의 발달은 정보의 축적, 처리, 분석과 전달능력을 기하급수적으로 증대 시키면서 사회전반의 효율성과 생산성을 획기적으로 향상시켰다. 그러나, 다른 한편으로는 이에 못지 않은 다양한 사회적 병리현상과 이와 관련된 윤리적 딜레마들을 양산하고 있다. 본 논문에서는 최근 정보사회로의 이행과정에서 제기되고 있는 정보통신 윤리상의 문제점 및 대응방안들을 검토하고, 그 중에서 자율적 규제방안의 하나인 윤리강령을 중심으로 다음과 같은 방법을 통해 향후 바람직한 컴퓨터 윤리 체계의 방향을 모색해 보았다. 첫째, 정보통신 윤리의 탄생 배경을 살펴보았다. 둘째, 현재 행해지고 있는 사회적, 제도적 대응 방안들과 그 현실적 한계점들을 검토하였다. 셋째, 그 중에서 자율적 규제방안의 하나인 윤리강령으로 논의의 범위를 좁혀서 현재 윤리강령들의 내용을 분석하고 바람직한 윤리강령의 조건들을 모색하였다. 끝으로 이상의 논의들을 토대로 향후 바람직한 윤리체계의 확립을 위한 종합적인 방안을 제시하였다. 본 논문은 정보통신망에서 벌어지고 있는 다양한 윤리적 문제점들을 극복하기 위해서 다각도로 모색되어야 할 대응방안들을 제시하였다. 또한, 본 논문은 단기적 차원의 법적 규제나 장기적 차원의 교육적 대응을 보완하면서, 동시에 자율적 합의에 의해 윤리적 원칙을 세워 갈 수 있는 윤리강령의 수립과 그 적극적 활용을 강조함으로써, 현재 우리나라의 컴퓨터 윤리 확립을 위한 구체적이고도 효과적인 대응방안을 제시하였다는데 의의가 있다.

• Journal of The Korean Association For Science Education
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• v.24 no.3
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• pp.612-620
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• 2004

The purpose of this study was to investigate how middle and high school students represent circuit diagrams with different shapes but electrically same. What prototypes of circuit which students possessed were, how students represented the connection of resistors, and what criteria used while grouping the circuit diagrams were investigated. The participants were 10 middle and 10 high school students. The results show that they represented the circuit diagrams by the geometrical resistor configurations rather than physics principles, not considering the presence of a junction or a battery on the branch. This representation was constrained by the circuit prototypes. Middle and High school students seems to have the own way of representing circuit diagrams without considering physics principles.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.701-722
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• 2010

Students have to investigate, experiment and inquire using the manipulative materials and real-world thing for studying Geometry. Manipulative materials activities encourage to understand mathematical concept and connection of symbol. Experiment activities using the computer focused the student's intuitive and inquisitive activities because of visualization of an abstract mathematics concept. This study developed a workbook through the use of manipulative materials and computer for operating and experimenting, and suggested a method for inquiry of geometrical properties and proved an effect. Manipulative materials-experiment activities was proven effective to middle level and lower level students in understanding the geometrical properties, and was proven effective to high level and lower level students when it comes to mathematical communication ability. When students operate, at first, they have to know about the feature and information of the materials, and the teacher has to make an elaborate plan and encourages the students to discuss about this.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.8
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• pp.455-476
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• 2006

An avatar script language consists of commands set which is used to control avatar behaviors in cyberspace. The script language should be abstract from complex low-level concepts, so that a user can write down a scenario script easily without concerning about physical motion parameters. Also, the script should be defined in a standard format and structure to allow reusing in various implementation tools. In this paper, a layered script language is proposed for avatar behavior representation and control, which consists of task-level behavior, high-level motion and primitive motion script language. The script language of each layer represents behavior elements for a scenario scripting interface, an avatar motion sequence, and geometric information of implementation environment, respectively. Therefore, a user can create a scenario script by abstract behavior interface and a script can be applied to various implementations by the proposed translating process. A presentation domain is chosen for applying the proposed script language and the implementation result shows that the script is flexibly applied in several applications.

• Journal of Science Education
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• v.38 no.1
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• pp.182-195
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• 2014

Ray drawing in geometrical optics is an effective method for visible imagery of light. In this study, we developed peer instruction materials for in-service teachers' training concepts on the refraction of light including drawing rays. And then we applied these programs to 29 pre-service teachers and 21 in-service primary teachers and evaluated the degree of conceptual change in correct points from the pretest and the post one. As a result of pretesting, in spite of experiences for learning this topic in elementary and secondary education courses, most participants in the study did not well understand the path of refracted light before instructions. However, the result of post testing after the application of peer instruction materials shows that they have practiced ray drawing, which is helping visible imagery. Accordingly, in learning geometrical optics, we suggest that peer instruction with ray drawing activity for teachers' training program would be effective. We also suggest that similar approaches would be applied to other context.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.55-73
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• 2018

The purpose of this study is to investigate the effects of cognitive activity on cognitive activities that students imagine and cope with continuously changing quantitative changes in functional tasks represented by linguistic expressions, table of value, and geometric patterns, We identified covariational reasoning levels and investigated the characteristics of students' reasoning process according to the levels of covariational reasoning in the elementary quantitative problem situations. Participants were seven 4th grade elementary students using the questionnaires. The selected students were given study materials. We observed the students' activity sheets and conducted in-depth interviews. As a result of the study, the students' covariational reasoning level for two quantities that are continuously covaried was found to be five, and different reasoning process was shown in quantitative problem situations according to students' covariational reasoning levels. In particular, students with low covariational level had difficulty in grasping the two variables and solved the problem mainly by using the table of value, while the students with the level of chunky and smooth continuous covariation were different from those who considered the flow of time variables. Based on the results of the study, we suggested that various problems related with continuous covariation should be provided and the meanings of the tasks should be analyzed by the teachers.

• School Mathematics
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• v.19 no.2
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• pp.319-343
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• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.

• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.157-170
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• 2017

Mathematics was the main domain of PISA 2012, and both paper-based and computer-based assessment of mathematics (CBAM) were conducted. PISA 2012 was the first large-scale computer-based mathematics assessment in Korea, and it is meaningful in that it evaluated students' mathematical literacy in problem situations using dynamic geometry, graph, and spreadsheet. Although Korea ranked third in CBAM, the use of ICT in mathematics lessons appeared to be low. On the other hand, this study focused on Singapore, which ranked first in CBAM. The Singapore Ministry of Education developed online programs such as AlgeTools and AlgeDisc, and implemented the programs in classes by specifying them in mathematics curriculum and textbooks. Thus, this study investigated influential factors on computer-based assessment of mathematics by comparing the results of Korea and Singapore, and aimed to provide meaningful evidence on the direction of Korea's ICT-based mathematics education. The results showed that ICT use at home for school related tasks, attitudes towards computers as a tool for school learning, and openness and perseverance of problem solving were positively associated with computer-based mathematics performance, whereas the use of ICT in mathematics class by teacher demonstration was negatively related. Efforts are needed to improve computer use and enhance teaching techniques related to ICT use in Korean math classes. Future research is recommended to examine how effectively teachers use ICT in mathematics class in Singapore.

• The Mathematical Education
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• v.62 no.1
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• pp.79-93
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• 2023

This study used metaphors as a analysis tool to investigate elementary school students' formation and development of angle concepts. For this purpose, the students were asked to write words associated with angle, right angle, acute angle and obtuse angle and to explain why. In case of angle and right angle, responses of 268 students from 3rd to 6th graders were analyzed and for acute angle and obtuse angle, those of 192 students from 4th to 6th graders were examined. As the results of categorizing the metaphors, they can be classified into categories such as; (1) qualitative aspects: 'things metaphor', 'personality metaphor', 'emotions metaphor' etc., (2) quantitative aspects: 'motions metaphor', 'changes metaphor', 'emotions metaphor' etc., and (3) relational aspects: 'shape relations metaphor.' The metaphoric expressions were prominent in 'qualitative aspects' associated with shapes. As for the other aspects, 'quantitative aspect'- the size of angles and the amount of spread and 'relational aspects' - elements of angle and relationship with another shapes, the frequency increses were shown to as grade levels were up. In case of right angle and acute angle, 'qualitative aspects' associated with shapes were outstanding and the frequency of the metaphoric expressions of obtuse angle was distributed similarly in three aspects. As the figure strand and the measurement strand are integrated to an strand in the 2022 revised curriculum, we need more discussion of multifaced aspects of angle and the learning sequences in the 'figure and measurement' strand.