Korean Mathematics Research Articles

한국의 국제수학올림피아드 참가의 성과 및 개선점 논의

In the present study, we review the history of the participations of the Korean national team in the International Mathematical Olympiad for 28 years. We identifiy three major events that highlighted the development of the Korean Mathematical Olympiad program: The first participation in the International Mathematical Olympiad, hosting of the International Mathematical Olympiad, and winning the first place in the International Mathematical Olympiad. We also propose some recommendations for next steps to facilitate the development of Mathematical Olympiad in Korea.

예비 초등교사의 한국수학사 활용에 대한 인식

본 연구는 예비 교사교육에서 한국수학사의 교육적 적용을 탐색하는 일련의 연구로서, 그 목적은 예비 초등교사의 한국수학사 활용에 대한 인식을 조사하는 것과 조선산학 프로그램이 한국수학사 활용에 대한 교사인식에 미치는 영향을 살펴보는 것이다. 이를 위해 조선산학 프로그램에 참여한 학생 88명을 포함한 총 174명의 예비교사들을 대상으로 한국수학사 활용의 실태, 효과, 개선방안과 관련된 설문을 실시하였다. 분석 결과, 예비교사들은 한국수학사의 활용을 수학사의 활용보다 더 중요하게 인식하는 것으로 나타났으며, 수학교육에 한국수학사 도입이 필요하다는 의견이 많았다. 또한 예비교사들은 문화적 측면의 활용효과와 활용방식을 가장 높게 평가하였으며, 정의적 측면과 인지적 측면은 후순위로 조사되었다. 한편 교사교육 참여집단과 비참여집단의 인식 차이를 분석한 결과, 두 집단 간에 통계적으로 유의미한 차이가 나타난 문항은 전체 54개 문항 중 25개 문항으로 나타났다. 무엇보다도 교사교육 참여경험이 인지적 측면의 활용효과와 활용방식에 대한 인식에 긍정적인 영향을 미쳤음을 확인하였다. 이는 교사교육이 한국 수학사 활용에 대한 교사들의 인식과 한국수학사를 활용한 수학수업의 활성화에 주요 변수임을 의미한다. This study analyzed the perception of prospective elementary school teachers in relation to using the history of Korean mathematics. The results of this study showed that the pre-service teachers realized using the history of Korean mathematics more importantly than the history of mathematics. They thought that the contents of the history of Korean mathematics should be increased in mathematics education and pre-service teacher education. The participation experience in teacher education about the history of Korean mathematics had a positive effect on the perception of pre-service teachers. Finally, this paper asserted that teacher education is the key to the teacher perception on and using of the history of Korean mathematics.

수학 학습 평가틀 비교 분석 -NAEP 2015, TIMSS 2015, PISA 2015를 중심으로-

The purpose of this study was to provide insights on making Korean mathematics framework by analytical comparison of three major assessments such as the NAEP 2015, the TIMSS 2015 and the PISA 2015. This study focused on the key differences and common themes of mathematics frameworks among three major assessments. In order to achieve this purpose, mathematical frameworks of the NAEP 2015, the TIMSS 2015, and the PISA 2015 were analyzed and compared. The criteria of the comparison were content domain and cognitive domain. The comparing criteria of content domain were based on NCTM content standards and cognitive domain were used the three understanding levels of Jan de Lange's pyramid model. Based on these comparisons, researchers discussed that Korea mathematical framework was needed to have a set of content categories that reflect the range of underlying mathematical phenomena and a set of cognitive levels which contain the range of underlying fundamental mathematical capabilities including consideration of contexts.

History of Mathematics in Korean Mathematics Textbooks: Implication for Using Ethnomathematics in Culturally Diverse School

From a multicultural perspective, this research investigated to what extent Korean mathematics textbooks use history of mathematics. The results show even though educational use of history presented in Korean mathematics textbooks may provide a rich outlook, it does not encourage a fundamental change in the educational practice of school mathematics that has traditionally been entrenched in the Eurocentric narrative of mathematics. This suggests that the mathematics textbooks were not organized effectively to promote students’ understanding of diversity. Based on the results, we discuss the implications for the development of mathematics textbook from multicultural perspectives.

초등학교 교과서의 각의 크기에 따른 삼각형 분류에 관한 고찰

This study focused on the classification of triangles by angles in elementary school mathematics. We examined Korean national mathematics curriculum from the past to the present. We also examined foreign textbooks and the Euclid`s . As a result, it showed that the classification is not indispensable from the mathematical and the perceptual viewpoint. It is rather useful for students to know the names of triangles when studying upper level mathematics in middle and high schools. This study also suggested that the classification be introduced in elementary school mathematics in the context of reasoning and inquiring as shown foreign textbooks, and example topics for the reasoning and inquiring.

Exploring Teaching Strategies to Attain High Performance in Grade Eight Mathematics: A Case Study of Chungcheongbuk Province, South Korea

This paper reports on a study conducted to investigate the teaching strategies used in the South Korean mathematical classroom and establish how they attain high performance in mathematics in comparison with other countries. The study focused mainly on the grade eight mathematics classroom and the teaching strategies used by the teachers as well as the students’ perspective of the teaching strategies used. This was a case study in which both quantitative and qualitative research methods were used to collect data. Questionnaires consisting of a total of fifty closed questions to establish teaching strategies used, preferred learning styles from the students and how they felt about mathematics and the mathematical classroom were administered to two hundred and two grade eight students in sampled schools. An interview consisting of ten open questions to get feedback from the mathematics teachers on what teaching strategies they use in the classroom and what they think is the best strategy to use regarding mathematics were conducted with six grade eight teachers from those schools. The results showed that in the South Korean mathematics classroom a combination of direct instruction, practice and teacher guidance help the students to learn problem solving skills and to master mathematics. It was also revealed that students preferred that the teachers use mostly chalkboard instruction and that they practice solving problems with worksheets, exam paper questions and homework or private study. Also the study revealed that the average student studies mathematics about 6 hours a week and most of them go to afterschool academies to study more mathematics. DOI: 10.5901/mjss.2014.v5n23p1106

수학자 족보 프로젝트의 과거와 현재 그리고 한국

본 원고에서는 수학자 족보 프로젝트(MGP, Mathematics Genealogy Project)의 과거와 현재에 대해 소개하고, 힐베르트와 저자의 경우를 예를 들어, 우리가 MGP를 어떻게 활용할 수 있을지 연구한다. MGP를 통하여 한국의 주요 수학자들(한국 수학사에 기여한 5명, 역대 한국과학상 수학부문 수상자, 대한수학회 학술상 수상자 등)의 뿌리에 대해 조사해 본 결과 MGP의 데이터베이스에는 그들의 기록이 누락되었거나 부실한 경우가 대부분이었다. 따라서 본 논문에서는 자신의 수학적 뿌리에 대한 정보를 프로젝트에 입력하는 방법을 구체적으로 소개하였다. 이 작업은 한국인 수학자들 자신의 학문적 뿌리를 정리하고 또한 한국 근대 수학사의 이해 및 한국 수학의 미래를 전망하는 데 도움이 된다. In this paper, we introduce the history and the present status of the Mathematics Genealogy Project (MGP). The cases of David Hilbert and the first author were used to show how it works. As an example, we explain how to gain useful information such as the granting year of mathematics Ph. D degree holders, the title of dissertation, advisors and descendants from the MGP website. Through a survey of three different groups in MGP on 20~30 significant Korean mathematicians, we found that Korean records in the academic genealogy project are missing or poorly presented in the database of the MGP website. In conclusion, we found a way to improve the situation and provide instructions to submit our information to MGP. We expect our effort can help Korean mathematics and mathematicians to become better exposed to the world. It will help others to understand both the modern history and the future prospect of Korean mathematics.

Mathematical Canons in Practice: The Case of Nineteenth-Century Korean Scholar Nam Pyŏng-Gil and His Evaluation of Two Major Algebraic Methods Used in East Asia

Which texts should be canonized, and what mathematical knowledge could be considered “standard,” were important issues for practitioners of mathematics in premodern East Asia. The Jiuzhang suanshu had been listed as one of the mathematical canons in Korea since the seventh century before it was lost by the fifteenth century. The canons were replaced by texts from China's Song-Yuan period. Those texts introduced an algebraic method called Tianyuan shu (the “old” method), which was well kept in Korea after its introduction to the peninsula but lost in China from the fifteenth century until its recovery in the eighteenth century. So the Tianyuan shu became a distinctive mark of traditional Korean mathematics. Since the mid-eighteenth century, the imperially composed Shuli jungyun was recognized as the mathematical canon in Qing China and Chosŏn Korea, and the main algebraic method Jiegenfang (the “new” method), a kind of cossic algebra introduced by the Jesuits, was used by both Chinese and Korean scholars. The works of Korean mathematician Nam Pyŏng-Gil (1820–69) include some of the most interesting examples of “dialogues” between the two algebraic methods. At first he believed that the two methods were identical. After he studied the newly recovered Siyuan shu, also originating in the Song-Yuan period, Nam realized that it could be seen as a generalization of the Tianyuan shu, thus enabling the “old” method to solve a wider range of problems than the “new” one. Influenced by the evidential studies in China and the trend of “practical learning” in Korea, Nam changed his mind, favoring the “old” method for its practical usefulness and its status as a distinctive mark of Korean scholarship. He tried to make the “old” method a standard in his country, and he did it in a subtle way. Nam wrote a compendium of mathematics, suggesting that it was a “standard,” and in the text he used the “new” method in the imperial canon to endorse the “old” one, and then solved problems with the “old” method. Nam Pyŏng-Gil's case provides an interesting example of the interaction between mathematical knowledge and its social context.

발도르프 수학교육 방법을 적용한 우리나라 대안학교 기하단원 교수·학습에 관한 사례연구

The purpose of this research is to find out if it is possible to apply the Waldorf School's mathematics education method to Korean alternative schools which are run under the national curriculum. To achieve this, the researcher conducted class on geometry for three weeks with ten 7th graders(four girls and six boys) from Apple Tree Waldorf alternative school in Busan, which has adopted Valdorf education courses. For the first two weeks, the class was about 'fundamental geometrical construction', and then it was evaluated. On the third week, the lesson was on plane figures, followed by a test with 9 plane figure questions that are based on general middle school mathematics curriculum. The result shows that most of the students understood 'fundamental geometrical construction'. When it comes to the test on 'plane figures', seven students got 8 out of 9 right, two students got 6 out of 9 right, and one of them had difficulty solving the questions. According to the results of this research, it is thought that there will be no problem for students to understand mathematical concept even if the Waldorf School's mathematics education method is applied to Korean alternative schools. Also, the Waldorf School's mathematics education method is considered to be a good teaching model for the Korean mathematics curriculum which places emphasis on 'mathematical creativity' in regard to the curriculum and contents.

South Korean Elementary Teachers' Mathematics Teaching Efficacy Beliefs Implications for Educational Policy and Research

It is known that teacher efficacy is associated with mathematical instructional quality and student confidence (Gresham, 2009). To think more about ways to promote teacher efficacy, we examined South Korean elementary teachers' mathematics teaching efficacy beliefs and what factors increase their efficacy beliefs. A translated and adapted version of the mathematics teaching efficacy belief instrument was used to gather information on teachers' mathematics teaching efficacy beliefs and their background information (n=283). Based on statistical analyses (ANOVA and the multiple regression model), we found that South Korean mathematics teaching efficacy beliefs differ by educational level in mathematics education, certification level, and range of teaching experience. For example, teacher efficacy beliefs increase with experience, on average, with the highest occurring in teachers with between eleven and fifteen years of experience, then decline after fifteen years, possibly because of a reduction in certification and professional development participation after that time. The findings imply that elementary teachers' mathematics teaching efficacy beliefs might be increased with teachers' professional development programs focusing on mathematics education.

국어ㆍ수학 통합 교과 원리로서 ‘정당화’에 대한 탐구 - 툴민의 논증 구조에 따른 분석을 중심으로

국어ㆍ수학 통합 교과 원리로서 ‘정당화’에 대한 탐구 - 툴민의 논증 구조에 따른 분석을 중심으로

Empirical Investigations of Creativity and Giftedness in Mathematics: An International Perspective

The idea for this book originated at the first joint meeting of the Korean Mathematical Society and the American Mathematical Society, held in Seoul, South Korea, on December 16–20, 2009. Contributing authors from Sweden, Norway, Turkey, Israel, Iran, China, Canada, South Korea, and the United States provide international perspectives on creativity and giftedness in mathematics education. The vast majority of the book is comprised of reports from empirical studies. In this respect, the book is not theory driven, per se. Instead, the focus is on reporting findings from studies in an attempt to elucidate the relationship between giftedness and creativity in mathematics. In this review, I provide a brief synopsis of each chapter (except Chapter 1, which outlines the book) and discuss the relevance of the work to the literature on mathematical creativity and giftedness. The overview of the chapters is followed by general remarks on the state of mathematics education research on creativity and giftedness and final thoughts about the contribution of this book to the field.

수학교육 선진화 방안의 중학교 교과서 적용 실태 분석

The Ministry of Education Science and Technology represented National Mathematics Education Advance Plan in 2012. The plan is focused on reinforcing mathematics education, improving understanding about mathematics, and enhancing self-guided learning. After the National Mathematics Education Advance Plan new middle school mathematics textbooks have been developed and they will be used from 2013. The purpose of this study is to analyse those mathematics textbooks to find how the National Mathematics Education Advance Plan is affected to the mathematics textbooks. This study found some important aspects affected from the Advance Plan to those textbooks and some implications for the future Korean mathematics education.

An Eastern Learning Paradox: Paradoxes in Two Korean Mathematics Teachers’ Pedagogy of Silence in the Classroom

Eastern philosophies of education such as Confucianism and Taosim advocate the use of silence in the teacher–pupil tradition of pedagogy. We investigate contemporary classrooms in Korea, and study whether teachers in Korea today incorporate this method implicitly or explicitly in their classrooms. Empirical data in the form of video-taped classroom lessons and the analysis of the videos reveal the learning paradoxes that arise from a rote adherence to constructivism by teachers that are trained within a larger Confucian society.

Special Features of Korean Mathematics Education

Special Features of Korean Mathematics Education

A NEW AGE IN MATHEMATICS EDUCATION IN THE U.S.: INTERPRETING THE COMMON CORE STATE STANDARDS FOR MATHEMATICS

For the first time ever in its history, the United States has a national version for K-12 mathematics programs, the Com-mon Core State Standards for Mathematics. Since its final version appeared in 2010 in the United States, the Common Core State Standards have started getting much attention from the Korean mathematics and mathematics education communities. Although attempts have been made to translate the original text of the stan-dards, the information such as the paradigm shift that led to the development of the standards, design principles and a comparison with the NCTM Standards would aid understating the standards in the intended way and avoiding unnecessary confusion.

Korean Language, English, and Mathematics Teachers' Perceptions on Selecting Textbooks

Korean Language, English, and Mathematics Teachers' Perceptions on Selecting Textbooks

수학교과서 연구 동향 분석 - 2006년부터 2011년에 게재된 국내 학술지 논문을 중심으로 -

The purpose of this study was to analyze recent research trends of mathematics textbooks to provide implications for textbook research and development. For this purpose, 90 out of 1121 research papers published between 2006 and 2011 in seven prestigious domestic journals were selected. The papers dealing with only Korean mathematics textbooks were analyzed by school levels (i.e., elementary or secondary), mathematics content areas, analytic methods, and implications. The papers comparing our mathematics textbooks with foreign counterparts were analyzed by reasons for the comparison, school levels, subjects for analysis, and implications. The results of this study urge us to pay more attention to secondary mathematics textbooks, least studied content areas, and various but inconsistent analytic methods. This paper also suggests close connections between textbook analysis and textbook development.

Two faces of mathematics lessons in Korea: conventional lessons and innovative lessons

This study identifies the characteristics of mathematics classrooms in Korea. First, conventional Korean mathematics lessons are analyzed from the perspective of “theory of variation”. Second, an innovative lesson for gifted children is reported in detail and analyzed from the perspective of “Lakatos’ proofs and refutations”. Third, the classroom characteristics identified in both the conventional lessons and the innovative lesson are interpreted in terms of the underlying cultural values that they share with other East Asian countries. The study concludes that although the two faces of Korean mathematics lessons look different, they may flow from the same “heart”—that of the common Confucian heritage culture culture, and in particular East Asian pragmatism.

Balance between foundations and creativity: features of Korean mathematics education

We are very pleased to write this introductory paper to the special issue of ZDM that provides readers with a glimpse of mathematics education in Korea. In July 2012 (7th–15th), the 12th International Congress on Mathematical Education (ICME-12) takes place at COEX in the center of Seoul, Korea. The ICME is the most important congress in the mathematics education community. It is held once every 4 years under the auspices of the International Commission of Mathematical Instruction (ICMI). The impetus for having this special issue during ICME-12 arose from the scarcity of literature on Korean mathematics education despite Korean students’ high achievement on international comparison studies. Korean students have consistently performed well in recent international assessments of mathematics achievement such as the Trends in International Mathematics and Science Study (TIMSS), the OECD Program for International Student Assessment (PISA), and the International Mathematics Olympiad. In addition, a recent study titled Mathematics Teaching in the 21st Century (MT21) compared prospective teachers’ knowledge and beliefs about teaching and learning in six participant countries, reporting that Korean prospective secondary mathematics teachers were better prepared than those in other countries (Schmidt et al., 2007; Schmidt, Blomeke, Tatto, 2011). Despite such outstanding performances of Korean students and prospective teachers, very little literature is available on factors that contribute toward it. In addition relatively little is also written about mathematics education in Korea. Many scholars, particularly in the West, are curious about Korea’s excellence in teacher quality and student achievement (e.g. Akiba, LeTendre, & Scribner, 2007; Kang & Hong, 2008). There are, however, a relatively small set of systematic studies that examine various aspects of Korean mathematics education substantively and carefully (Kwon, Park, & Park, 2011). Further, some studies on Asian education have even mistakenly assumed that mathematics education in Korea is almost the same as that in other East Asian countries (e.g., Leung, 2011). Considering teaching and learning as cultural practices (e.g., Alexander, 2000; Fernandez & Yoshida, 2004; Ma, 1999; Stigler & Hiebert, 1999), this could mislead readers to ignore the uniqueness of mathematics education in Korea. As a historical–cultural construct, educational practice of mathematics is situated in a specific cultural context of South Korean society, where there are a range of unique cognitive and normative assumptions around the functions and purposes of education, the kinds of knowledge pursued in school and society, the roles taken by teachers and students. Thus, this special issue not only overviews major aspects of Korean mathematics education, it also addresses the historical and cultural foundations of Korean mathematics education in order to foster an understanding of its practices. This issue, a thematic collection of studies, consists of nine papers that present and discuss emerging issues and challenges of Korean mathematics education with respect to various aspects of mathematics education such as curriculum, teaching practices, student learning, textbooks, assessment, and teacher education. It makes an important contribution by Korean mathematics educators to the international community. O. N. Kwon (&) S. J. Cho Department of Mathematics Education, College of Education, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul 151-748, Korea e-mail: onkwon@snu.ac.kr