Korean Mathematics Research Articles

A survey on Students' Understanding of Pure Korean Mathematics Terminologies Used in North Korea

우리나라 학교 수학 용어의 대부분이 한자어인 것과는 달리 북한에서는 여전히 ‘씨수’, ‘곁수’, ‘마디’, ‘같기식’, ‘늘같기식’, ‘안같기식’과 같은 순우리말 수학 용어를 보존하여 사용하고 있다. 본 연구에서는 순우리말 수학 용어를 포함한 북한의 수학 용어를 우리나라 학생들이 얼마나 친숙하게 혹은 이질적으로 인식하고 이해하는지 분석하였다. 그 결과 학생들의 인식에서 남북한 수학 용어의 이질화를 확인할 수 있었고, 저학년일수록 순우리말 수학 용어가 학생들에게 쉽게 받아들여질 가능성이 크다는 것을 확인하였다. 특히 우리가 일상생활에서 흔히 사용하는 순우리말이 포함된 수학 용어는 용어 그 자체가 개념을 풀어 쓴 설명으로 받아들여져 학생들이 쉽게 그 의미를 이해하는 것으로 나타났다.This paper attempted to examine students` comprehensive understanding of pure korean mathematics terminologies in North Korea. Survey items were developed based on mathematics terminologies seen in North Korean mathematics textbooks and researches on understanding of mathematics terminologies were conducted. Through the researches on understanding of North Korean mathematics terminologies, it gave an opportunity to identify the heterogeneity in mathematics terminologies between South and North Korea and rediscover the necessity of integrating mathematics terminologies between South and North Korea. Furthermore, it is expected that mathematics terminologies that allow future Korean students in unified Korea to have an mathematically appreciative eye and mathematical thought.

비정형 그래프에 대한 예비 중등 수학교사 세 명의 교수를 위한 수학적 의미 분석

The informal graph is ‘a graph showing real-life contexts and irregular changes without being bound by the definition of a function or algebraic equation’, and is a new concept that was introduced in the first year of middle school by the 2015 revised Korean mathematics curriculum. According to previous studies, some teachers do not have a high level of understanding of informal graph. This raises the need to analyze in detail how teachers understand informal graph and reflect it in teacher education, given that the way teachers understand mathematical ideas closely influences the way students form mathematical ideas. The present study analyzes the mathematical meaning for teaching of prospective mathematics teachers on the informal graph to provide specific implications for one area of school mathematics taught in pre-service teacher education. Specifically, we examined three of the 15 prospective participant teachers' ways of reasoning with two items all of which required them to draw and interpret informal graph through questionnaire and semi-structured interview. We paid attention to mathematical meaning for teaching of each the three teachers, who were chosen due to the distinctive ways they coordinated two quantities, brought forth in reasoning with informal graph. Finally, the conclusions and the implications for teacher education were discussed.

점그래프와 상자그림의 교수학적 분석: 통계적 추리 지도를 위한 교육적 효용성 고찰

This study analyzes the characteristics of dot plots and box plots that have been identified to be effective in developing the understanding of distribution and variability. Moreover, the study examines the use of dot plots and box plots in statistical teaching and learning and discusses the utility in Korean mathematics curriculum. With respect to the results obtained, the dot plot is firstly expected to bridge the gap between the elementary and middle school curriculum since the dot plot has a very simple system that can be used to construct and express a distribution by dealing with numerical data even at the elementary school level. Secondly, box plots aid in comprehensive understanding of distribution concepts and summary concepts. These concepts are expected to help establish links of statistical content elements that are currently perceived segmentally within the middle school curriculum. Third, dot plots and box plots provide an experience of an informal inferential reasoning for data sets at the elementary and middle school levels, and are expected to be a springboard for learning formal statistical reasoning that will be addressed later in high school.

A Generalization of Semidetached Subalgebras in BCK∕BCI-algebras

Generalization of the paper [Y. B. Jun and S. Z. Song, Semidetached subalgebras in [Formula: see text]-algebras, to appear in Bulletin of the Korean Mathematical Society] is discussed. Several conditions for a semidetached structure in [Formula: see text]-algebras to be a semidetached subalgebra are provided. The concepts of ([Formula: see text])-fuzzy subalgebra, [Formula: see text]-left ([Formula: see text]-right) [Formula: see text]-fuzzy subalgebra, ([Formula: see text])-fuzzy subalgebra and ([Formula: see text])-fuzzy subalgebra are introduced, and relative relations and properties are discussed.

교사용 지도서의 교육적(Educative) 수업 지원 양상 및 개선 방안

Korean mathematics curriculum has undergone multiple cycles of reforms. Recent reforms emphasize teachers' role as who enact the written curriculum to their students. Teachers' guide is one of the resources that support teachers with enacting a given curriculum. Therefore, the potential teachers' guide has as a space for teacher professional development is worth an in-depth examination. To this end, this study explored the potential of Korean mathematics teachers' guides as educative curriculum materials. Nine guides for first year high school students were examined based on the coding scheme derived from literature. In addition, qualitative approach was applied to identify exemplary cases that contribute to increasing educativeness of teachers' guides. The examination revealed that the guides support assessment the most while providing limited guides for classroom instruction. The study provides various examples from the nine guides to enhance the quality of teachers' guides. The study ends with suggestions for teacher educators, curriculum writers, and researchers.

A Comparative Study on the Mathematics Epistemological Beliefs of Mongolian and Korean Pre-service Teachers

본 연구는 한국과 몽골 수학 예비교사들의 수학인식론적신념을 비교함으로써 심도있는 이해를 도모하기 위하여 수행되었다. 이를 위하여 기존의 수학인식론적신념 검사 도구(박철영, 2012)를 이중번역(double translation) 방법을 통하여 몽골어로 번안하였으며, 각국 언어로 구성된 검사를 실시하여 양국 수학 예비교사들의 검사 결과를 비교하였다. 번안된 검사의 타당화 검증 과정에서 원래의 38 문항 중 8개 문항이 제외되고, 30개 문항으로 구성된 도구로 본 검사를 실시하였다. 몽골과 한국 수학 예비교사들의 수학인식론적신념을 비교하기 위하여 국가, 성별, 학년 간 삼원변량분석을 실시하였다. 연구 결과, 전체적으로 몽골 수학 예비교사들의 평균(3.16)이 한국 수학 예비교사들의 평균(3.06)보다 유의미하게 높게 나타났다. 하위 요인별로 살펴보면, 선천적 능력, 수학학습효능감, 학습속도, 수학적지식의구조의 네 개 요인들에서 몽골 수학 예비교사들의 평균이 한국보다 유의미하게 높았다. 한국 수학예비교사들은 수학의 유용성, 수학적 문제해결의 두 요인에서 몽골보다 통계적으로 유의미한 수준에서 높게 나타났다. 상호작용효과는 국가와 성별 간에만 유의미한 것으로 나타났으며, 하위요인별로는 수학적문제해결 요인에서만 유의미했던 것으로 나타났다.This study was carried out to understand the mathematical epistemological beliefs of Mongolian pre-service teachers and to provide implications for the development of Mongolian mathematics teachers. For this purpose, the study developed Mongolian mathematical epistemological belief measure and compared it with Korean mathematics pre-service teachers. The test tool was translated into Mongolian using the mathematical epistemological belief test (6 factors, total 38 items) presented by Park(2012). In order to validate the Mongolian measure, the study conducted a pilot study of 304 Mongolian pre-service teachers and conducted exploratory factor analysis and reliability analysis. In this process, out of the original 38 items, excluding 8 items, the measure composed of 30 items, was developed and utilized. In order to compare the mathematical epistemological beliefs of Mongolian and Korean mathematics pre-service teachers, the study conducted a three-way ANOVA between countries, sex, and grade. As a result, the average of Mongolian pre-service teachers (3.16) was higher than the average of Korean mathematics pre-service teachers (3.06). In terms of sub-factors, the average of Mongolian pre-service teachers was higher than that of Korea in four factors of innate ability, mathematics learning efficacy, learning speed, and mathematical knowledge structure. Korean mathematics pre-service teachers were higher than that of Mongolian in two factors of mathematical usefulness and mathematical problem solving. Interaction effects were significant only between country and gender, and sub-factors were significant only in mathematical problem solving factors. Finally, based on the results of the study, practical and theoretical implications for Mongolian pre-service teacher education were discussed.

Limiting behaviour for arrays of rowwise widely orthant dependent random variables under conditions of R − h-integrability and its applications

ABSTRACTIn this paper, we mainly study the convergence, complete convergence and complete moment convergence for arrays of rowwise widely orthant dependent (WOD, for short) random variables under some conditions of R-h-integrability. The results in this paper generalize and improve the corresponding ones of Sung et al., Weak laws of large numbers for arrays under a condition of uniform integrability, Journal of the Korean Mathematical Society 45 (2008), pp. 289–300, Wang and Hu, Weak laws of large numbers for arrays of dependent random variables, Stochastics: An International Journal of Probability and Stochastic Processes 86 (2014), pp. 759–775, and Wu et al., Limiting behaviour for arrays of rowwise END random variables under conditions of h-integrability, Stochastics: An International Journal of Probability and Stochastic Processes 87 (2014), pp. 409–423. As applications of the complete convergence that we established, we present some results on complete consistency for the estimator in a nonparametric regression model based on WOD errors.

Possibilities and Limitations of Secondary Pre-Service Teacher Education Program for Interdisciplinary Teaching Proficiency: Focusing on Fusion of Korean language, Mathematics, and Science

Possibilities and Limitations of Secondary Pre-Service Teacher Education Program for Interdisciplinary Teaching Proficiency: Focusing on Fusion of Korean language, Mathematics, and Science

국제 교실수업 어휘 프로젝트

Discourses about classrooms provide clear insights into pedagogical principles and practices in a cultural context. Human thinking is not independent of the use of language, and thinking may form language, and at the same time language may shape human thinking. In particular, it is important to investigate the pedagogical terms named and used by teachers because the classroom activities and principles can be objectified and further developed after that. This paper reports what Korean teachers see and name classroom activities in Korean middle school mathematics classrooms as a part of the International Classroom Lexicon Project that 10 countries collaborate on identifying and documenting own country’s pedagogical terms in their middle school mathematics classrooms. Using 9 video stimulus materials, which support ways of which teachers see and name pedagogical phenomena using particular pedagogical terms and languages, we identify and list the pedagogical terms. The initial pedagogical terms were 112, but after conducting a national-wide survey, we finalized and identified the total 105 numbers of Korean pedagogical terms in mathematics classrooms. Issues with regard to the Korean pedagogical terms are also discussed. Our study will be further analyzed to compare each country’s lexicon in collaboration with the other 9 countries. We expect that this Korean pedagogical lexicon can be used to identify Korean mathematics classroom culture as well as be the groundwork for analyzing classroom practices both in Korea and in comparison with other participant countries.

남한과 북한 초등학교 수학 교과서의 구성 체제 및 학습 내용 비교 -1,2,3학년을 중심으로-

In this study, we analyzed the elementary school mathematics textbooks are used in 1st to 3rd grade in South Korea and North Korea. Specifically, the textbooks were compared in terms of unit and lesson frameworks, and the learning contents of mathematics covered in the 1st grade textbooks were compared and analyzed. As the results, some implications on the similarities and differences between the two textbooks were derived. First, we identified the emphasis on the textbooks for the South and North Korean mathematics, as well as similarities and differences in the composition of the textbooks, the structure of textbooks, and the system of teacher’s guidebooks. Second, South and North Korean mathematics textbooks share the largest proportion of units in the number and operation domain, and differ in the number of units and presentation of names. Third, both textbooks contain the introductions are composed of illustrations and the lessons are comprised of play activities, while there are differences in terms of the use of icons. Fourth, among the learning contents covered in the 1st grade mathematics textbooks, we identified the contents covered in thr 1st grade of South Korea and in the 1st grade of North Korea.

History, tradition, and development of journals of the Korean Mathematical Society

History, tradition, and development of journals of the Korean Mathematical Society

중학교 기울기 개념에 대한 학습경로와 그에 따른 한국 수학 교과서와 미국의 CMP 교과서 비교

The understanding of the concept of slope in terms of the rate of change serves as the foundation for developing meaningful calculus concepts. The purpose of our study was two-fold: Firstly, we attempted to develop a learning trajectory for the slope of a linear function using the rate of change; secondly, we used the trajectory to compare Korean mathematics textbooks with those of the U.S. standard-based curriculum CMP. After developing a learning trajectory of slope for the linear function via an in-depth analysis of the past literature, we compared and contrasted the textbooks of the two countries. Specifically, we analyzed how the textbooks of the two countries defined and described the terminologies, how they introduced the slope concept including the way how slope was represented (e.g., double number line and strip diagram), and finally the affordance of the two different perspectives of proportional relationships. Our results suggest that a careful consideration of the method to introduce the slope concept, the consistency of the terminology usage and explanations, and the devising of instructional materials that enhance the student awareness of the invariant relationship between two quantities using proportional reasoning are imperative for students’ meaningful development of more advanced mathematics.

The Asian Mathematical Conference 2016 (AMC 2016)

PrefaceThis volume consists of the refereed papers presented at 2016 Asian Mathematical Conference (AMC2016) held on July 25-29, 2016 at Bali Nusa Dua Convention Center (BNDCC), Nusa Dua Bali Indonesia. This conference was hosted by the Indonesian Mathematical Society (IndoMS) and the Southeast Asian Mathematical Society (SEAMS). The AMC2016 was co-organized by Institut Teknologi Bandung (ITB), Universitas Padjadjaran (Unpad), Universitas Gadjah Mada (UGM), Universitas Indonesia (UI) and Universitas Udayana (Unud).The conference was attended by around 700 participants from all over the countries: Japan, China, Korea, India, Singapore, Malaysia, Vietnam, Thailand, Philippines, Pakistan, Australia, USA, Netherland, France, UK, Iran, Germany, Turkey, Spain and Indonesia. There were 9 plenary speakers, 3 special lecture speakers and 64 invited talks in this conference. Especially, Professor Martin Hairer (University of Warwick, 2014 Fields Medallist) gave a plenary talk.The organizers are grateful to the Korean Mathematical Society (KMS), Mathematical Society of Japan (MSJ), Korea Institute for Advanced Study (KIAS), International Mathematical Union (IMU), Commission of Women in Mathematics IMU, Centre International de Mathematiques Pures et Appliquees (CIMPA), the Ministry of Research Technology and Higher Education, the Ministry of Tourism, Badan Keamanan Laut (BAKAMLA), Persatuan Aktuaria Indonesia (PAI), PT Komatsu Indonesia for their invaluable supports. In particular, we also thank to IOP conference series for being a technical co-sponsor for this publication.We also thank all steering, scientific, organizing and program committee members and referees for the excellent work. Our high appreciation is to all the plenary speakers: James Maynard, Sudhir R. Ghorpade, Martin Hairer, Narutaka Ozawa, Sug Woo Shin, Hendra Gunawan, Wee Teck Gan, Van H. Vu, Zhou Xiangyu, and to all special lecture speakers, invited and contributed speakers as well as to all the participants for making this conference successful and enjoyable.

융복합 수학수업의 실행 방향 탐색1)2)

The 2015 revised Mathematics Curriculum stated integrated mathematics education through fostering competences like creativity, convergence, attitude and action. From 2018, every secondary school will sequentially implement this each year. This study explored the direction how to practice integrated mathematics instruction in the mathematics classroom and it is based on the perspective that Yungbokhap education in mathematics can facilitate students’ integrative ability to solve diverse tasks and social issues creatively as members of world civil society. For this purpose, this study reviewed preceding research on theories of integrated education, Korean Mathematics Curriculum, and domestic and international programs of integrated education to deduct constituting implementation plan. As a result, this study discussed how to practice teaching plans for Yungbokhap education in mathematics and how important is the competence of the teacher to enhance the effectiveness of the mathematics class.

Concept of Ratio in South Korean, Japanese, and Singaporean Mathematics Textbooks

Understanding ratio and its related mathematical concepts are crucial in upper grade elementary school mathematics and in later learning mathematics as well as science. There might be no controversies about the importance of the ratio concept, however, there are many different ways of describing it. Among them, Beckmann and Izsak’s (2015) recent study of ratio provides insights for viewing ratio concept. This paper investigated how do textbooks of South Korea, Japan, and Singapore view the concept of ratio. English version of Japanese and Singaporean mathematics textbooks were collected and Korean mathematics textbook was translated into English. Textbook analysis was conducted in macro level and micro level. The textbook analysis shows each country introduces ratio differently and emphasizes different aspects. Implications for South Korean mathematics textbook were discussed at the end of the paper.

MiC 교과서의 함수 과제에 대한 의사소통의 유형별 요소에 관한 탐색

우리나라 2015 개정에 따른 수학과 교육과정의 가장 주목할 만한 특징 중 하나는 창의적 역량을 갖춘 융합 인재로 성장할 수 있는 기반을 제공할 것을 제안하며 이를 위하여 수학 교과 역량을 강조하였는데, 이 중 하나가 의사소통이다. 본 연구에서는 김상화 방정숙(2010)이 제안한 D.R.O.C 유형을 근간으로 의사소통의 유형별 요소를 마련하고자 하였다. 의사소통 요소를 탐색을 위하여 Mathematics in Context 교과서를 선정하여 총 34개의 함수 내용 관련 과제에 속한 316개 문항을 대상으로 하였다. 해당 교과서는 수학적 의사소통의 유형별 요소에 따른 과제 중심의 수업 활동으로 구성되어 있으며, 함수 내용의 특성상 주로 그래프로 나타내거나 해석하는 것과 같은 표현에 해당하는 문항들이 많음을 보였다. 또한 자신이 접한 내용, 문제 풀이 과정, 또는 자신의 판단이나 생각들을 언어를 통해 말하고, 동료들과 서로 설명해 보게 하는 담화 유형과 구체물을 이용하는 조작 유형들을 다룸으로써 처음 접하는 용어나 개념에 친숙하게 접근하도록 이끌고 있었다. 한 마디로, 의사소통 유형 및 요소를 통해 학습자로 하여금 함수 관련 내용을 습득할 수 있도록 과제들이 비교적 풍부히 구성되어 있음을 알 수 있었다. Communication is one of 6 core competencies suggested newly in mathematics curriculum revised in 2015 in Korea. Also, it's importance has been emphasized through NCTM and CCSSI. By the subject of Mathematics in Context(MiC) textbook, this study planned to explore the communication elements according to the types of communication such as discourse, representation, operation. Namely, this study dealt with 316 questions in a total of 34 tasks relevant to function content in the MiC textbook, and this study explored the communication elements on the questions of each task. To accomplish this, this study first of all was to reconstruct and establish an analytic framework, on the basis of 'D.R.O.C type' of communication developed by Kim & Pang in 2010. In addition, based on the achievement standards of function domain in mathematics curriculum revised in 2015 in Korea, this study basically compared with the function content included in MiC textbook and Korean mathematics curriculum document. Also, it tried to explore the distribution of communication elements according to the types of communication.

교과서 실생활 문제 분석 - 미국 Precalculus 교과서를 중심으로 -

본 논문은 수학 교과서에 사용되는 실생활 관련 문제들에서 '사람의 존재 (Human presence)' 가 얼마만큼 실제적 또는 현실적으로 묘사되는지를 조사한 연구이다. 연구에 사용된 교과서는 미국 동부 지역 고등학교 Precalculus 수업에 많이 이용되는 Addison Wesley에서 출판된 Precalculus: Graphical, Numerical, Algebraic, Seventh Edition (2006) 이다. 본 논문에서는 실생활 관련 문제에서의 '사람의 존재 (Human presence)' 유무와 특성을 분석하기 위해 개발된 분석틀과 이 분석틀을 사용하여 분석한 결과들을 소개하고 시사점을 제언한다. In order to determine the message that is communicated to students about people who use math, this study analyzes contexts, human presence in particular, used in problems presented in a U. S. high school mathematics textbook. A framework was developed to analyze the human presence and was used to determine both the degree to which humans are present in the curriculum as well as characteristics of the present humans. One outcome of this study is the framework itself which can be used to analyze the human presence in any mathematics curriculum. Other outcomes include the determination that the particular mathematics textbook under study contains an overwhelming lack of humans, a surprising lack of named humans, and a disappointing presence of humans in math-related careers. These findings raise concerning questions about the message that is communicated to students about the usefulness of school mathematics and missing a valuable opportunity to inspire students to pursue degrees in mathematics. Additionally, it is hoped that these findings would inform the work of the Korean mathematics education communities on the textbook development.

중학교 수학교과서에 제시된 사회과제재의 가교성 분석1)2)

중학교 수학교과서에 제시된 사회과제재의 가교성 분석1)2)

수학교육 관점에서 본 MST 교육에서 STEAM 교육까지 통합교육의 흐름 분석

In this study, we investigate integrated educations as an alternative educational method. I look around the developments of the integrated educations from MST education through STEAM education, especially in mathematics education. I analyzed integrated educations such as MST, STS, STEM, STEAM educations and compare them to each other, in mathematics education. And I discuss how to apply STEAM education to Korean mathematics education. I suggest a proper integrated education, in particular, STEAM education, as one that is suitable for Korean mathematics education.

우리나라 유아수학교육사 연구

In this paper, we explore about Korean early childhood mathematics education history. Actually, mathematics education history is mathematics education curriculum`s history. Korean education curriculum has been influenced by the US and European prominent educators: Montessori, Piaget, Bruno, and Dewey, etc. We investigate how those philosophy and thoughts were adopted in Korean early childhood mathematics education curriculums from 1st to 2015 amended curriculum. Also, we can see that NCTM`s content standards and Korean Nuri curriculum are the same in the basic concepts: number and operations, space and shapes, measurement, understanding of patterns and data collection.