• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.267-276
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• 2004

이 글은 초등학교 학생들을 대상으로 상호변화적(covariational) 개념으로 변화율에 대한 교수실험을 담고 있다. 기하적 문맥에서 함수의 그래프를 자연스럽게 도입하고, 함수의 변화율에 대한 상호변화적 질적 접근의 예를 제시한다. 또한 언어적 명령을 통하여 스스로 함수의 그래프를 만들어보도록 하고 함수의 그래프를 분석하는 경험을 가지게 하여 이후 함수와 그 역함수와의 개념을 마이크로월드에서 경험하도록 하는 환경과 그 역할에 대하여 논의한다. 이 과정을 통한 마이크로월드, 학생, 연구자의 역할과 상호작용을 알아보고 이 후의 대수식의 도입에 대한 문제를 논의한다.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.1-24
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• 2001

어떤 유향그래프 D의 경쟁그래프란 D와 같은 꼭지점들의 집합을 갖고 두 개의 꼭지점 x와 y가 변으로 연결되어있는 것과 동치인 조건이 D에서 어떤 꼭지점 z에 대하여 유향변(x,z)와 (y,z)가 존재하는 것인 그래프로 정의된다. 어떤 그래프 G의 경쟁수란 G에 첨가하여 생기는 그래프가 유향 회로가 없는 유향그래프의 경쟁그래프가 되도록 하는 고립된 꼭지점의 최소수로 정의된다. 갱쟁그래프의 개념은 생태학적 위상공간의 최소차원을 결정하는 수단으로 1968에 Cohen에 의하여 도입되었다. 경쟁그래프와 그것의 변형들은 잡음이 많은 통신로 상에서의 교신, 라디오 송신기에 주파수 부어하기, 복잡한 경제 체계와 에너지 체계에 응용된다. 이 논문에서는 경쟁 그래프와 그 변형들, 경쟁수와 그 변형들에 대하여 소개하며 그것들에 대한 중요한 결과들을 개관하고 미해결 문제들을 제시하고자 한다.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.477-493
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• 2018

The six core competencies included in the mathematics curriculum Revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the creativity and convergence competency is very important for students' enhancing much higher mathematical thinking. Based on the creativity and convergence competency, this study selected the five elements of the creativity and convergence competency such as productive thinking element, creative thinking element, the element of solving problems in diverse ways, and mathematical connection element, non-mathematical connection element. And also this study selected the content(chapter) of the graph in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the five elements of the creativity and convergence competency were shown in each textbook.

• 한국HCI학회:학술대회논문집
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• 2009.02a
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• pp.422-427
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• 2009

We present a real-time graph drawing tool for mathematics education. We developed a sketch-based graph drawing interface that recognizes the schematic sketch of a graph. Our system generates figures displaying useful supplementary information such as auxiliary lines, abscissas, and ordinates. The resulting graphs are very similar to the graphs commonly found in textbooks. We also developed a graph retrieval system that makes rapid graph drawing feasible.

• Education of Primary School Mathematics
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• v.17 no.2
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• pp.113-125
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• 2014

The purpose of the study is to examine how the 6th graders interpret graphs, and on basis of the research, to seek for guidance on ways to improve their analysis capabilities. All the students from two classes of D elementary school in Busan became the target to examine how to interpret graphs. On the basis of the result, 6 students who characterized by graph interpretation got an in-depth interview and the outcome was analyzed in detail. The students are able to understand both quantitative and qualitative meaning of graphs and they learned practicality while they think of graphs connecting with real life, most of all they have been interested in interpreting the meaning of graphs.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.289-301
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• 2010

This study discovered that instructional objectives of graphs which are dealt with in Math I of the revised curriculum are not matched with those of Discrete Mathematics in the 7th Curriculum. Based on the findings, this study analysed didactic transposition method of trail in graph and matrix of Math I and students' understanding about trail. Then this study discovered that though the concept definition of trail in Math I of the revised curriculum, some textbooks and students tend to consider it as the path. The concept definition of trail is significant in systems that deal with Euler Circuits(Euler Closed trail) and Hamilton Cycle. Then it is not easy to find the value of trail in Math I of the revised curriculum.

• The Mathematical Education
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• v.58 no.3
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• pp.403-422
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• 2019

As the informal graph was introduced newly in the area of function in middle school mathematics curriculum revised in 2015, ten publishing company became to have a concern on how to represent the graph content uniquely and newly. At this time, it may be meaningful and useful to compare and analyze the content of the graph unit shown on each textbook published by publishing companies. To accomplish this, on fundamentally the basis of diverse prior researches this study tried to select the elements of expression and interpretation of the graph and establish an analytic frameworks of expression and interpretation of the graph respectively. This study executed the frequency analysis and cross analysis by textbook system, textbook, and the number of the graph drawn on a coordinate plane on the representation and interpretation of the graph. As a result, the textbook contains more items on interpretation than the representation of the graph, and students showed a learning effect on the graph unit but showed a neutral response to the impact of learning. This basic and essential paper shed light on developing the practical and more creative textbook which has diversity and characteristic respectively, while adjusting the scope of the elements of the graph's representations and interpretations and providing proper level and quality content.

• 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.

• Communications of Mathematical Education
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• v.10
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• pp.519-528
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• 2000

최근 10 여년 동안 교육 현장의 각 부분에 여러 가지 종류의 테크놀로지가 도입되면서, 교육의 내용과 방법에 있어서 점진적인 변화가 나타나고 있다. 예를들어, 수학 과목에 있어서는 그래픽 계산기, 도형 및 기하 학습 프로그램, 스프레드 시트, 함수 그래픽 프로그램 등의 도입으로 교과 과정 전반에 걸친 변화가 일고 있는데, 처음에는 이들 테크놀로지가 단순히 기존의 수업에서 수많은 반복을 요하거나, 지필식 방식으로는 정확하게 나타내기 어려운 도형이나 그래프를 빠르고 정확하게 그려내주는 보조수단으로 사용되었지만, 시간이 지나면서 이들 테크놀로지에 대한 활용도가 높아지게 되고, 이들 테크놀로지에 대한 교사들의 활용능력이 증대됨에 다라서, 이러한 테크놀로지가 단순한 보조수단에 머무르지 않고 주지에 기술이나 개념을 설명하는 방법 자체를 변화시키고 있다. 예를들어, 함수 교육에 있어서 그래픽 프로그램이 사용될 때에도, 초기 단계에서는 이들 함수의 개념을 설명할 때에는 거의 집합론이나 대수학적인 방법을 이용하였고, 최종 단계로 이들 함수를 좌표계 위에 표현하기 위한 보조수단으로 잠깐씩 사용되는 경우가 대부분이었으나, 최근들어서는 함수 학습의 초기과정부터 곧바로 이들 그래프 프로그램을 적극적으로 도입하여 학습자로 하여금 다양한 그래프 조작을 하게 함으로써, 어려운 집합론이나 대수학적인 개념을 도입하지 않고서도 함수에 대한 개념을 시각적으로 직관적으로 파악하도록 하는 학습 방안들이 제시되고 있는 것이다. 본 고에서는 현행 중고등학교 함수 교육 과정에서 그래프에 대한 다양한 조작 기능을 제공함으로써 학습자로 하여금, 제시되는 함수에 대한 시각적이고 직관적인 이미지를 가질 수 있도록 하기 위해서 개발된 ‘그래프 마법사’라는 프로그램을 소개하고자 한다.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.169-192
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• 2019

This study investigates how well grade 4, 5, and 6 students understand graphs before formal education is done on graphs. For this, we analyzed students' understanding of graphs by classifying them into 'reading data', 'finding relationships between data', 'interpreting data', and 'understanding situations' based on previous studies. The results show that the students have good understanding of graphs that did not have formal education. This suggests that it is necessary to consider the timing of the introduction of the graph. In addition, when we look at the percentage of correctness of each graph, it is found that the understanding of the line graph is weaker than the other graphs. The common error in most graphs was that students relied on their own subjective thoughts and experiences rather than based on the data presented.