• Journal of the Korea Society of Computer and Information
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• v.23 no.12
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• pp.57-64
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• 2018

In this paper, a method to measure similarity between two graphs is proposed, which is based on centralities of the graphs. The similarity between two graphs $G_1$ and $G_2$ is defined by the difference of distance($G_1$, $G_{R_1}$) and distance($G_2$, $G_{R_2}$), where $G_{R_1}$ and $G_{R_2}$ are set of random graphs that have the same number of nodes and edges as $G_1$ and $G_2$, respectively. Each distance ($G_*$, $G_{R_*}$) is obtained by comparing centralities of $G_*$ and $G_{R_*}$. Through the computational experiments, we show that it is possible to compare graphs regardless of the number of vertices or edges of the graphs. Also, it is possible to identify and classify the properties of the graphs by measuring and comparing similarities between two graphs.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.353-372
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• 2008

This study looks around the goals of teaching statistical graphs that are introduced in the seventh Korean Curriculum for Elementary School and in the Principles and Standards for School Mathematics(NCTM, 2000), and these are compared. We compare how to transpose statistical graphs didactically between the Korean and MiC textbooks. For it, it examines the types of statistical graphs, the methods defining them, and the making connections and comparing among them, which are content components in the chapters on statistical graphs. The results show that in contrast to the Korean textbooks, NCTM(2000) has allowed students to develop their own expression for data, to compare results analysed within different graphs, and to consider a graph as a whole in the goals of teaching statistical graphs. MiC textbooks have introduced the number-line plot and the box plot more than Korean. Although both of Korean and MiC textbooks usually use extensive methods for defining individual graphs, the former use extensive methods together with synonymic methods and the latter use extensive methods with the characteristics of graphs. Also, the number-line plot is defined using operative method in the MiC textbooks. MiC textbooks contain various activities for connecting and comparing graphs, but there are comparatively few comparing activities in the Korean textbooks.

• KIPS Transactions on Computer and Communication Systems
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• v.2 no.8
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• pp.317-326
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• 2013

In this paper, we present an effective method for comparing control flow graphs which represent static structures of binary programs. To compare control flow graphs, we measure similarities by comparing instructions and syntactic information contained in basic blocks. In addition, we also consider similarities of edges, which represent control flows between basic blocks, by edge extension. Based on the comparison results of basic blocks and edges, we match most similar basic blocks in two control flow graphs, and then calculate the similarity between control flow graphs. We evaluate the proposed edge extension method in real world Java programs with respect to structural similarities of their control flow graphs. To compare the performance of the proposed method, we also performed experiments with a previous structural comparison for control flow graphs. From the experimental results, the proposed method is evaluated to have enough distinction ability between control flow graphs which have different structural characteristics. Although the method takes more time than previous method, it is evaluated to be more resilient than previous method in comparing control flow graphs which have similar structural characteristics. Control flow graph can be effectively used in program analysis and understanding, and the proposed method is expected to be applied to various areas, such as code optimization, detection of similar code, and detection of code plagiarism.

• School Mathematics
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• v.1 no.2
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• pp.555-569
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• 1999

The graph unit(chapter) is a good example of a topic in elementary school mathematics for which computer use can be incorporated as part of the instruction. Teaching graph can be facilitated by using the graphing utilities of computers, which make it possible to observe the property of many types of graphs. This study was concerned with utilizing an educational software Graphers as an instructional tool in teaching to help young students gain a better understanding of graph concepts. For this purpose, three types of instructional activities using Graphers were shown in the paper. Graphers is a data-gathering tool for creating pictorial data chosen from several data sets. They can represent their data on a table or with six types of graphs such as Pictograph, Bar Graph, Line Graph, Circle Graph, Grid Plot and Loops. They help students to select the graph(s) which are the most appropriate for the purpose of analyzing data while comparing various types of graphs. They also let them modify or change graphs, such as adding grid lines, changing the axis scale, or adding title and labels. Eventually, students have a chance to interpret graphs meaningfully and in their own way.

• Journal of the Korea Society of Computer and Information
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• v.24 no.7
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• pp.61-69
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• 2019

In this paper, a classification method of random graph models is proposed and it is based on centralities of the random graphs. Similarity between two random graphs is measured for the classification of random graph models. The similarity between two random graph models $G^{R_1}$ and $G^{R_2}$ is defined by the distance of $G^{R_1}$ and $G^{R_2}$, where $G^{R_2}$ is a set of random graph $G^{R_2}=\{G_1^{R_2},...,G_p^{R_2}\}$ that have the same number of nodes and edges as random graph $G^{R_1}$. The distance($G^{R_1},G^{R_2}$) is obtained by comparing centralities of $G^{R_1}$ and $G^{R_2}$. Through the computational experiments, we show that it is possible to compare random graph models regardless of the number of vertices or edges of the random graphs. Also, it is possible to identify and classify the properties of the random graph models by measuring and comparing similarities between random graph models.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.75-92
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• 2019

The 2015 revised mathematics curriculum encourages students to use graphs in newspapers and the Internet as materials when teaching graphs, and to experience a series of statistical problem-solving processes that collect, classify, organize, graph and interpret data. The graphs that the students learn through traditional textbooks were a single type of graphs. In particular, the graphs of the 5th and 6th grade groups were only increased in numbers, but the basic concepts were repeated in the 3rd and 4th grades. Fortunately, from the 2009 revision curriculum, it is possible to select the graph suitable for the situation while comparing the characteristics of some graphs. In most cases, the graphs used in the real world are presented in the form of a compounded infographics. The purpose of this study is to analyze and analyze the manifestations of information processing competence elements emphasized in the 2015 revised curriculum through the statistical project class using the informal graphic in the fifth grade of elementary school. And we suggested a concrete class plan.

• Journal of The Korean Association For Science Education
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• v.27 no.4
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• pp.285-296
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• 2007

Graph is a major aspect of science textbooks. In this study, we investigated graph types and characteristics used in high school earth science subject by comparative analysis of science textbooks. The results of the analysis revealed that line graph and contour map was the most widely used graph types in earth science. Among line graphs, multiple line graph and YX graph was dominant. Comparing earth science graphs with other science graphs, earth science graphs exhibited superior in the number and variety. In earth science graphs, the portion of line graph was small, but the portion of contour map and scatter graph was larger than that of other science graphs. YX graph was the most specific graph type in earth science textbooks. The results of our study have implications for reform in function and structure of graph. We suggest that future studies be focused on students' ability of earth science graph interpretation.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.559-587
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• 2022

The purpose of this study is to derive implications for the development of the next curriculum and textbooks by comparing and analyzing the textbooks of the 2015 revised high school mathematics curriculum <Mathematics for Economics> and social studies curriculum <Economics>. In the <Mathematics for Economics> textbooks, economic terms and function notations should be introduced. Additionally, the use of graphs for economic-related functions is different from the use of graphs in mathematics in the <Mathematics for Economics> textbooks. For these reasons, the usage of economic terms, function notations, and function graphs covered in the <Mathematics for Economics> textbooks were compared and analyzed with the usage in the <Economics> textbooks. In the <Mathematics for Economics> textbooks, economic terms that are highly related to mathematics are defined and presented. Contrary to the conventions of mathematics and economics, the function notations in the <Mathematics for Economics> textbooks were used inconsistently because uppercase and lowercase letters were mixed in the function notations. Function graphs in the <Mathematics for Economics> textbooks had differences in the range of values represented by the variables regarding axes and scaling. The <Mathematics for Economics> textbooks did not provide a mathematical interpretation of the translation or slope. In the course of <Mathematics for Economics>, it is necessary to specify considerations for teaching and learning, and assessment in the curriculum to promote students' understanding of mathematics and economics. The descriptions in the curriculum document and textbooks of <Mathematics for Economics> should be supplemented to provide learning opportunities for mathematical interpretation of economics-related contents.

• New Physics: Sae Mulli
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• v.68 no.11
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• pp.1231-1239
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• 2018

This study aimed at examining undergraduate students' writing about experiments related to the photoelectric effect and giving some implications for experiment education. Thus, this study analyzed 26 students' reports about three kinds of experiments: measuring Planck's constant, comparing the photocurrent and the photovoltage across the intensity of light, and comparing the photocurrent and the photovoltage across the frequency of light. In the measurements, less than 25% of the students expressed the data to the correct number of significant figures even though two-thirds of the students successfully obtained the data given in the manual. In terms of interpretation, the students were not aware of the physical meanings of the detailed parts in the graphs. Even though over 50% of the students drew a line relating photocurrent to voltage, no students compared the theoretical to the empirical data or made a judgment as to whether of not the background theory really fit the experiment. The research findings showed that insufficient knowledge and skills for physics inquiry may be an obstacle in performing the experiments well.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.4
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• pp.107-116
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• 2013

This algorithm suggests a method in which a minimum spanning tree can be obtained fast by reducing the number of an algorithm execution. The suggested algorithm performs a select-and-delete process. In the select process, firstly, it performs Borůvka's first stage for all the vertices of a graph. Then it re-performs Borůvka's first stage for specific vertices and reduces the population of the edges. In the delete process, it deletes the maximum weight edge if any cycle occurs between the 3 edges of the edges with the reduced population. After, among the remaining edges, applying the valency concept, it gets rid of maximum weight edges. Finally, it eliminates the maximum weight edges if a cycle happens among the vertices with a big valency. The select-and-delete algorithm was applied to 9 various graphs and was evaluated its applicability. The suggested select process is believed to be the vest way to choose the edges, since it showed that it chose less number of big edges from 6 graphs, and only from 3 graphs, comparing to the number of edges that is to be performed when using MST algorithm. When applied the delete process to Kruskal algorithm, the number of performances by Kruskal was less in 6 graphs, but 1 more in each 3 graph. Also, when using the suggested delete process, 1 graph performed only the 1st stage, 5 graphs till 2nd stage, and the remaining till 3rd stage. Finally, the select-and-delete algorithm showed its least number of performances among the MST algorithms.