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The Journal of Educational Research in Mathematics (JERM) was founded in 1991 as the official journal of the Korean Society of Educational Studies in Mathematics. The journal aims to serve as the scholarly venue for emerging research ideas and innovative pedagogical research developments in mathematics education across different cultures and global regions. The journal has earned a reputation as the premier national scholarly journal in Korea, and now looks to serve the interests and needs of the international research community of mathematics education. JERM is an international, peer-reviewed open access journal that publishes articles in Korean or English. Seekings to publish high-quality original research and scholarly articles, the scope of JERM focuses on various areas and topics in mathematics education, including (but not limited to): +More

Learningmathematics& psychology

Teachingmathematics& teacher education

History of mathematics & philosophy

Mathematicscurriculum& assessment

Educational policy& social systems

Instrument& technology

KORENG
  • 전자저널 논문 | 2021-08-31

    JeongSuk Pang1, Jin Sunwoo2

    2021; 31(3): 231-255

    https://doi.org/10.29275/jerm.2021.31.3.231
    Abstract

    Abstract : The purpose of this study was to analyze the changes in pre-service teachers’ noticing through an elementary mathematics methods course along with a practicum. For this purpose, the comments pre-service teachers made on an entire video-based mathematics lesson were collected three times over the semester. Their comments were analyzed in terms of topic, actor, stance, evidence, and alternative strategy. The results showed that the pre-service teachers’ noticing abilities were slightly changed after learning mathematical content and pedagogy related to teaching elementary mathematics. Substantial changes in their noticing occurred after a four-week practicum and subsequent discussions on their own lesson planning, implementation, and reflections. This study has implications for designing a mathematics methods course to develop teacher expertise and refining a teacher noticing analytic framework.

  • 전자저널 논문 | 2021-08-31

    Nilton Silveira Domingues1 , Marcelo C. Borba2

    2021; 31(3): 257-275

    https://doi.org/10.29275/jerm.2021.31.3.257
    Abstract

    Abstract : This paper aims to present how video production is impacting the classroom, mathematics students and teachers in Brazil, as well as mathematics knowledge production developed with this media. Digital video Festivals with mathematical content are being implemented in Brazil, locally and nationally. One of them is Mathematics Education Digital Video Festival, organized by the Research Group in Informatics, Other Media and Mathematics Education, GPIMEM. In this century, video is earning space as a pedagogical approach in either face-to-face or distance education, even before the COVID-19 pandemic. Currently, considering social distance, the use of videos became an imposed reality to students and teachers. Students and teachers with different level of experience or age started to realize possible positive effects regarding the reorganization of the classroom by the presence of mathematical videos. However, other aspects provided negative effects: for example, inequalities in homes and mobile access impacted equal opportunity to all. This paper will summarize the use of mathematical video in the last century and discuss what is happening this century. We will revise some research developed, mainly in Brazil, that shows how the classroom does not fit in a parallelepiped model. Internet, videos and software combined are "things" that have agency and are co-participating in learning and teaching mathematics. The organization of festivals of videos have become important not only in Brazil but elsewhere in many formats either nationally or internationally, in a way to create challenges, exhibitions, cultural mix that aim to show mathematics applications to the general public. In particular, this article reports on parts of a qualitative research that investigated participants of the first edition of the referred national festival. As a result, we look for the comprehension of following the discussions of qualitative transformations regarding the use of videos in classrooms and mathematics knowledge production, as this new setting suggests that digital technologies arrived in XXI century to collaborate with learning. This article will be supported by a theoretical perspective on technology based on the notion of humans-withmedia. In such a perspective knowledge is seen as being constructed by humans and different media and different artifacts. This article shows how such a perspective may help us to cope with the classroom of the XXI century, including the classroom that during the pandemic include students' and teachers' homes.

  • 전자저널 논문 | 2021-08-31

    Shu Zhang1, Man Ching Esther Chan2, David Clarke3, Yiming Cao4

    2021; 31(3): 277-297

    https://doi.org/10.29275/jerm.2021.31.3.277
    Abstract

    Abstract : In this paper we report on a case study involving four Chinese students; the aim of the study was to develop a conceptual framework for investigating student participation in a collaborative task in mathematics. Building on previous research on student participation, we defined student participation in a collaborative task in mathematics as the process of taking part in student interactions and task completions. A video recording and transcript of students involved with collaborative task in mathematics were analyzed. Four categories (initiation, response, evaluation, and non-interactive) were created for analyzing the students' interactions. The four students showed different approaches to communicating with other group members. The content of the group's discussion was examined in terms of the negotiation process. By looking at the content of the group's discussion, the process how the group work on the task could be revealed. We identified that students showed involvement in the group discussion by proposing and revisiting topics. It was found that through forming an interactive pair, students might be able to take up the leading role in working on the task and controlling the conversation of the group.

  • 전자저널 논문 | 2021-08-31

    Yeajin Ham1, Jihyun Hwang2

    2021; 31(3): 299-320

    https://doi.org/10.29275/jerm.2021.31.3.299
    Abstract

    Abstract : We examined the relationships between mathematics achievement and collaborative problem solving, which has been emphasized as the 21st century skills. Focusing on moderating effects of attitude toward working with others, we analyzed the PISA 2015 data for binational comparison between Korean and the U.S. Random-intercept linear models - where the intercepts vary across schools while slopes are fixed across schools - were applied to the data including 5,545 students in Korea and 5,564 in the U.S. The findings showed the positive linear relationships between mathematics achievement and collaborative problem solving as expected, but the slope was remarkably higher in the Korean model. However, we found no significant moderating effects of attitude toward working with others on the relationship between mathematics achievement and collaborative problem solving. Particularly, students in Korea and the U.S. are likely to have similarly low scores in mathematics achievement when their collaborative problem solving scores are low. However, Korean students would have even higher mathematics achievement scores if students in Korea and the U.S. have similarly high collaborative problem solving scores. The findings suggest the necessity for further scrutinies on attitude toward working with others and research on teaching and learning the 21st century skills in an integrated way.

  • 전자저널 논문 | 2021-08-31

    Ngan Hoe Lee1, June Lee2 , Zi Yang Wong3

    2021; 31(3): 321-356

    https://doi.org/10.29275/jerm.2021.31.3.321
    Abstract

    Abstract : Characterised by increased automation and digitalisation of work processes, the Fourth Industrial Revolution (4IR) has displaced and redesigned many existing jobs, and will create new occupations that are currently non-existent. To prepare a future workforce that is adaptive amid a volatile employment landscape, schools should provide the necessary learning experiences to help students today develop transferrable competencies, which encompass deep conceptual understanding of domain-specific knowledge and 21st century competencies in the cognitive, intrapersonal, and interpersonal domains. In this paper, we study this possibility in the context of mathematics learning and propose a constructivist learning design (CLD) that affords students to engage in deeper learning processes. In the proposed CLD, students first work collaboratively to solve a complex problem targeting a math concept that they have yet to learn, before being engaged in instruction that builds upon their solutions in the teaching of the concept, and practices that reinforce these ideas. Testing CLD in mathematics learning at secondary level via a quasi-experimental design, we found out that (1) CLD facilitates deeper learning as it encouraged students to apply their cognitive, intrapersonal, and interpersonal competencies, and (2) CLD students (n=23) outperformed their Direct Instruction counterparts (n=18) on mathematical conceptual understanding and transfer. Overall, this study suggests that the CLD has the potential to cultivate competencies that allow students to transfer in novel situations, rendering it as a possible learning environment to better prepare students for the 4IR.

  • 전자저널 논문 | 2021-08-31

    Yuichiro Hattori1 , Hiroto Fukuda2, Takuya Baba3

    2021; 31(3): 357-378

    https://doi.org/10.29275/jerm.2021.31.3.357
    Abstract

    Abstract : The purpose of this study is to propose socio-critically open-ended problems (SCOEPs) as a novel theoretical framework for nurturing students' critical mathematical literacy while respecting diverse values embedded in transscientific problems. First, we outline the socially open-ended problem─which is of current interest to Japanese researchers of critical mathematics education─and describe its nature and significance. Second, we derive issues from current research on social justice and ethics in mathematics education using a literature interpretive methodology and build a theoretical framework of SCOEPs to develop socially open-ended problems. We present several potential examples of classroom practices based on the SCOEPs framework that were implemented in Japanese schools to explore the impact of these questions on student's engagement and thinking processes. We found evidence that the objectives of nurturing both social judgment skills within an ethical framework, as well as fostering mathematically and socially diverse solutions for authentic problems are integrated in SCOEPs. The framework can be described as the coexistence of the process of fostering social decision-making through mathematical thinking and the process of critically considering mathematical thinking to achieve social justice. This proposal has significant implications for the future directions of mathematics education in the 21st century.

  • 전자저널 논문 | 2021-08-31

    Zahra Gooya1, Soheila Gholamazad2

    2021; 31(3): 379-392

    https://doi.org/10.29275/jerm.2021.31.3.379
    Abstract

    Abstract : World is divided into six continent and within each, there are many separate regions called “countries”. Some are called “first world”, trying to dominate the others whom are known as “third world” and rarely, people enquire about the “second world” in between (We are aware of this political/ideological division as aftermath of the World War II and the notion of “three worlds” suggested by Mao Zedong)! The claim is that this division has nothing to do with “ranking” the countries, but it is culturally weird to hear “ordinal numbers” and not giving them “values” of either “priority” or “inferiority”! And in the midst of everything, the world faced a horrible phenomenon called Covid-19 that soon became a pandemic! Within a short period of time, the whole world, despite of any ranking, felt how fragile and hopeless is in the battle with this monster! And yet, it is soon to expect that decision makers who govern the world, must be aware that without well- being of everyone, there is no other way to defeat the virus. This is an irony! Isn’t it? No matter how wealthy or poor, dominant or dominated, so- called developed or developing the countries are, in our view, they only have one solution to this devastating problem that is to know that the world is connected and no part of it is in joy while others are in pain! Hopefully, we are entering a new era of deeper understanding of what humanity is! A big lesson to be taught by the opportunity that Covid-19 created for human beings! Thus far, Corona and Covid-19 pandemic is not just a treat but a wake- up call for humanity to believe that “If you’ve no sympathy for human pain, the name of human you cannot retain!”

  • 전자저널 논문 | 2021-08-31

    Wee Tiong Seah1, Hee-jeong Kim2 , Dong-Joong Kim3

    2021; 31(3): 393-404

    https://doi.org/10.29275/jerm.2021.31.3.393
    Abstract

    Abstract : The 21st Century is characterised by technological advances which is the Fourth Industrial Revolution, climate change, and the COVID19 pandemic, for examples. The role of mathematics in each of these phenomena has been central and crucial. As such, it is an opportune time now to take stock of events that are (re-)shaping the world, so that we can better facilitate mathematics education in schools. Three themes are identified and discussed in this article, namely the convergence of mathematics pedagogical approaches, mathematics proficiencies, and students' mathematical wellbeing.

KORENG
  • 전자저널 논문 | 2021-08-31

    Nilton Silveira Domingues1 , Marcelo C. Borba2

    2021; 31(3): 257-275

    https://doi.org/10.29275/jerm.2021.31.3.257
    Abstract

    Abstract : This paper aims to present how video production is impacting the classroom, mathematics students and teachers in Brazil, as well as mathematics knowledge production developed with this media. Digital video Festivals with mathematical content are being implemented in Brazil, locally and nationally. One of them is Mathematics Education Digital Video Festival, organized by the Research Group in Informatics, Other Media and Mathematics Education, GPIMEM. In this century, video is earning space as a pedagogical approach in either face-to-face or distance education, even before the COVID-19 pandemic. Currently, considering social distance, the use of videos became an imposed reality to students and teachers. Students and teachers with different level of experience or age started to realize possible positive effects regarding the reorganization of the classroom by the presence of mathematical videos. However, other aspects provided negative effects: for example, inequalities in homes and mobile access impacted equal opportunity to all. This paper will summarize the use of mathematical video in the last century and discuss what is happening this century. We will revise some research developed, mainly in Brazil, that shows how the classroom does not fit in a parallelepiped model. Internet, videos and software combined are "things" that have agency and are co-participating in learning and teaching mathematics. The organization of festivals of videos have become important not only in Brazil but elsewhere in many formats either nationally or internationally, in a way to create challenges, exhibitions, cultural mix that aim to show mathematics applications to the general public. In particular, this article reports on parts of a qualitative research that investigated participants of the first edition of the referred national festival. As a result, we look for the comprehension of following the discussions of qualitative transformations regarding the use of videos in classrooms and mathematics knowledge production, as this new setting suggests that digital technologies arrived in XXI century to collaborate with learning. This article will be supported by a theoretical perspective on technology based on the notion of humans-withmedia. In such a perspective knowledge is seen as being constructed by humans and different media and different artifacts. This article shows how such a perspective may help us to cope with the classroom of the XXI century, including the classroom that during the pandemic include students' and teachers' homes.

  • 전자저널 논문 | 2021-05-31

    노정원1, 이경화2†, 문성재3

    Jeong-Won Noh1, Kyeong-Hwa Lee2, Sung-Jae Moon3

    2021; 31(2): 131-152

    https://doi.org/10.29275/jerm.2021.31.2.131
    Abstract

    Abstract : This study aims to reveal how diagramming in the everyday mathematics classroom supports students’ mathematical learning, based on the Châteletean perspective. To this end, we analyzed the diagramming of two 9th grade students who participated in the task of proving the Pythagorean theorem through diagrams in a geometry lesson. In particular, we focused on the epistemic distance as well as the material directness between the students and the diagrams. As a result, the students discovered mathematical ideas while they engaged in direct or indirect diagramming; they actualized virtual mathematical objects and relationships that were not visible in the given diagrams. During diagramming, the epistemic distance between the students and the diagrams was also dynamically changing. The findings suggest that diagramming in mathematics classrooms is not just a static representational activity, but an indeterminate and mobile engagement, which materially interacts with diagrams at varying degrees of epistemic distance.

  • 전자저널 논문 | 2021-08-31

    Ngan Hoe Lee1, June Lee2 , Zi Yang Wong3

    2021; 31(3): 321-356

    https://doi.org/10.29275/jerm.2021.31.3.321
    Abstract

    Abstract : Characterised by increased automation and digitalisation of work processes, the Fourth Industrial Revolution (4IR) has displaced and redesigned many existing jobs, and will create new occupations that are currently non-existent. To prepare a future workforce that is adaptive amid a volatile employment landscape, schools should provide the necessary learning experiences to help students today develop transferrable competencies, which encompass deep conceptual understanding of domain-specific knowledge and 21st century competencies in the cognitive, intrapersonal, and interpersonal domains. In this paper, we study this possibility in the context of mathematics learning and propose a constructivist learning design (CLD) that affords students to engage in deeper learning processes. In the proposed CLD, students first work collaboratively to solve a complex problem targeting a math concept that they have yet to learn, before being engaged in instruction that builds upon their solutions in the teaching of the concept, and practices that reinforce these ideas. Testing CLD in mathematics learning at secondary level via a quasi-experimental design, we found out that (1) CLD facilitates deeper learning as it encouraged students to apply their cognitive, intrapersonal, and interpersonal competencies, and (2) CLD students (n=23) outperformed their Direct Instruction counterparts (n=18) on mathematical conceptual understanding and transfer. Overall, this study suggests that the CLD has the potential to cultivate competencies that allow students to transfer in novel situations, rendering it as a possible learning environment to better prepare students for the 4IR.

  • 전자저널 논문 | 2021-08-31

    Yuichiro Hattori1 , Hiroto Fukuda2, Takuya Baba3

    2021; 31(3): 357-378

    https://doi.org/10.29275/jerm.2021.31.3.357
    Abstract

    Abstract : The purpose of this study is to propose socio-critically open-ended problems (SCOEPs) as a novel theoretical framework for nurturing students' critical mathematical literacy while respecting diverse values embedded in transscientific problems. First, we outline the socially open-ended problem─which is of current interest to Japanese researchers of critical mathematics education─and describe its nature and significance. Second, we derive issues from current research on social justice and ethics in mathematics education using a literature interpretive methodology and build a theoretical framework of SCOEPs to develop socially open-ended problems. We present several potential examples of classroom practices based on the SCOEPs framework that were implemented in Japanese schools to explore the impact of these questions on student's engagement and thinking processes. We found evidence that the objectives of nurturing both social judgment skills within an ethical framework, as well as fostering mathematically and socially diverse solutions for authentic problems are integrated in SCOEPs. The framework can be described as the coexistence of the process of fostering social decision-making through mathematical thinking and the process of critically considering mathematical thinking to achieve social justice. This proposal has significant implications for the future directions of mathematics education in the 21st century.

  • 전자저널 논문 | 2021-08-31

    JeongSuk Pang1, Jin Sunwoo2

    2021; 31(3): 231-255

    https://doi.org/10.29275/jerm.2021.31.3.231
    Abstract

    Abstract : The purpose of this study was to analyze the changes in pre-service teachers’ noticing through an elementary mathematics methods course along with a practicum. For this purpose, the comments pre-service teachers made on an entire video-based mathematics lesson were collected three times over the semester. Their comments were analyzed in terms of topic, actor, stance, evidence, and alternative strategy. The results showed that the pre-service teachers’ noticing abilities were slightly changed after learning mathematical content and pedagogy related to teaching elementary mathematics. Substantial changes in their noticing occurred after a four-week practicum and subsequent discussions on their own lesson planning, implementation, and reflections. This study has implications for designing a mathematics methods course to develop teacher expertise and refining a teacher noticing analytic framework.

  • 전자저널 논문 | 2021-08-31

    Wee Tiong Seah1, Hee-jeong Kim2 , Dong-Joong Kim3

    2021; 31(3): 393-404

    https://doi.org/10.29275/jerm.2021.31.3.393
    Abstract

    Abstract : The 21st Century is characterised by technological advances which is the Fourth Industrial Revolution, climate change, and the COVID19 pandemic, for examples. The role of mathematics in each of these phenomena has been central and crucial. As such, it is an opportune time now to take stock of events that are (re-)shaping the world, so that we can better facilitate mathematics education in schools. Three themes are identified and discussed in this article, namely the convergence of mathematics pedagogical approaches, mathematics proficiencies, and students' mathematical wellbeing.

  • 전자저널 논문 | 2021-05-31

    이동근

    Donggun Lee

    2021; 31(2): 153-177

    https://doi.org/10.29275/jerm.2021.31.2.153
    Abstract

    Abstract : This study investigates the way students perceive and express change in an exponential situation with different reasoning methods for continuous change - for example, students, who use chunky reasoning, construct a new function representing the change of exponential distance-time function. Using case study approach, the study presents the results of teaching experiments conducted on three high school freshmen students. It may be difficult to generalize the results since the sample size was limited; however, the findings have the potential to inform researchers in mathematics education about students’ conceptual knowledge of continuous change. The information about the process of constructing the speed-time function from the distance-time function based on the students' understanding of continuous change may also be helpful in interpreting student thinking in differential concept.

  • 전자저널 논문 | 2021-08-31

    Yeajin Ham1, Jihyun Hwang2

    2021; 31(3): 299-320

    https://doi.org/10.29275/jerm.2021.31.3.299
    Abstract

    Abstract : We examined the relationships between mathematics achievement and collaborative problem solving, which has been emphasized as the 21st century skills. Focusing on moderating effects of attitude toward working with others, we analyzed the PISA 2015 data for binational comparison between Korean and the U.S. Random-intercept linear models - where the intercepts vary across schools while slopes are fixed across schools - were applied to the data including 5,545 students in Korea and 5,564 in the U.S. The findings showed the positive linear relationships between mathematics achievement and collaborative problem solving as expected, but the slope was remarkably higher in the Korean model. However, we found no significant moderating effects of attitude toward working with others on the relationship between mathematics achievement and collaborative problem solving. Particularly, students in Korea and the U.S. are likely to have similarly low scores in mathematics achievement when their collaborative problem solving scores are low. However, Korean students would have even higher mathematics achievement scores if students in Korea and the U.S. have similarly high collaborative problem solving scores. The findings suggest the necessity for further scrutinies on attitude toward working with others and research on teaching and learning the 21st century skills in an integrated way.

  • 전자저널 논문 | 2021-05-31

    최인용

    Inyong Choi

    2021; 31(2): 179-210

    https://doi.org/10.29275/jerm.2021.31.2.179
    Abstract

    Abstract : The purpose of this study is to propose and discuss the pedagogical idea of introducing conditional probability with the relative frequency approach. This study developed a learning activity and simulation using the frequency tree diagram and implemented them. The first-year high school students (n=14) were able to construct the concept of conditional probability through a frequency perspective of sequentially obtaining the conditional relative frequency, the limit of the relative frequency, and the theoretical probability. The implications for teaching and curriculum were presented.

  • 전자저널 논문 | 2021-08-31

    Shu Zhang1, Man Ching Esther Chan2, David Clarke3, Yiming Cao4

    2021; 31(3): 277-297

    https://doi.org/10.29275/jerm.2021.31.3.277
    Abstract

    Abstract : In this paper we report on a case study involving four Chinese students; the aim of the study was to develop a conceptual framework for investigating student participation in a collaborative task in mathematics. Building on previous research on student participation, we defined student participation in a collaborative task in mathematics as the process of taking part in student interactions and task completions. A video recording and transcript of students involved with collaborative task in mathematics were analyzed. Four categories (initiation, response, evaluation, and non-interactive) were created for analyzing the students' interactions. The four students showed different approaches to communicating with other group members. The content of the group's discussion was examined in terms of the negotiation process. By looking at the content of the group's discussion, the process how the group work on the task could be revealed. We identified that students showed involvement in the group discussion by proposing and revisiting topics. It was found that through forming an interactive pair, students might be able to take up the leading role in working on the task and controlling the conversation of the group.

  • 전자저널 논문 | 2021-05-31

    옥보명1, 이창연2, 고상숙3†

    Bo-myoung Ok1, Changyeon Lee2, Sang S. Choi-Koh3

    2021; 31(2): 211-230

    https://doi.org/10.29275/jerm.2021.31.2.211
    Abstract

    Abstract : This study evaluates the factorial structure of the Mathematics Anxiety Scale for Students (MASS) using data from 1,272 high school students. To this end, we used the mathematical anxiety rating scale for middle and high school students developed by Ko and Yi (2011). An exploratory factor analysis of the response data from the first sample (636 students) eliminated 31 of the 65 items of the original MASS, generating the MASS-Short Version (MASS-SV), a mathematical anxiety scale for high school students with four factors-mathematical problem solving, mathematical learning methods, mathematics test, and mathematics class. A confirmatory factor analysis of the MASS-SV using the responses of the second sample (636 students) revealed that the model fit indices were acceptable and did not differ significantly from those of the original MASS. The MASS-SV derived from this study is a valid and reliable mathematical anxiety measurement tool for high school students; it also helps the students save time and provide quality responses. Future research on the progress of math anxiety in students should identify trends in math anxiety or the relationship between variables such as achievement, attitude toward mathematics, and career path in relation to math anxiety.

  • 전자저널 논문 | 2021-08-31

    Zahra Gooya1, Soheila Gholamazad2

    2021; 31(3): 379-392

    https://doi.org/10.29275/jerm.2021.31.3.379
    Abstract

    Abstract : World is divided into six continent and within each, there are many separate regions called “countries”. Some are called “first world”, trying to dominate the others whom are known as “third world” and rarely, people enquire about the “second world” in between (We are aware of this political/ideological division as aftermath of the World War II and the notion of “three worlds” suggested by Mao Zedong)! The claim is that this division has nothing to do with “ranking” the countries, but it is culturally weird to hear “ordinal numbers” and not giving them “values” of either “priority” or “inferiority”! And in the midst of everything, the world faced a horrible phenomenon called Covid-19 that soon became a pandemic! Within a short period of time, the whole world, despite of any ranking, felt how fragile and hopeless is in the battle with this monster! And yet, it is soon to expect that decision makers who govern the world, must be aware that without well- being of everyone, there is no other way to defeat the virus. This is an irony! Isn’t it? No matter how wealthy or poor, dominant or dominated, so- called developed or developing the countries are, in our view, they only have one solution to this devastating problem that is to know that the world is connected and no part of it is in joy while others are in pain! Hopefully, we are entering a new era of deeper understanding of what humanity is! A big lesson to be taught by the opportunity that Covid-19 created for human beings! Thus far, Corona and Covid-19 pandemic is not just a treat but a wake- up call for humanity to believe that “If you’ve no sympathy for human pain, the name of human you cannot retain!”

  • 전자저널 논문 | 2021-02-28

    송륜진, 주미경

    송륜진, 주미경

    2021; 31(1): 83-107

    https://doi.org/10.29275/jerm.2021.02.31.1.83
    Abstract

    Abstract : This research aims to investigate the teachers’ pedagogical design capacity for multicultural mathematics education. For the purpose, we collected teaching plans developed by inservice teachers who registered in a multicultural mathematics teacher education course of graduate level. The analysis focused on how the teachers reorganized mathematical contents and adapted instructional strategies in order to achieve the instructional goals. The analysis shows that the teachers applied the ‘Principle of Equity’ most frequently compared to other principles of multicultural mathematics education. This means that it is necessary to provide teacher education programs to enhance teachers’ understanding of ethnomathematics and to develop PCK to reorganize curricula contents by integrating ethnomathematics. Second, it was observed that the teachers experienced difficulty in adapting the levels of multicultural mathematics education coherently. This suggests that when teachers tried to design lessons from a new perspective, they often turned back to teacher-centered teaching practices that they had been used to. Third, in the teaching plans adapting the ‘Principle of Transformation’, although Level 4 appeared most frequently, mathematical contents and social issues were placed separately without being integrated. Although the course helped the teachers recognize the relationship between mathematics and human practice, the teachers might keep their previous beliefs about mathematics as academic knowledge separated from human life. Thus, this limitation may persist without a change of the teachers’ beliefs regarding the cultural origin of mathematics. Based on the results, we draw implications for the future development of multicultural mathematics teacher education.

  • 전자저널 논문 | 2019-11-30

    방정숙, 선우진, 조선미, 이유진, 김은경, 김윤영, 박예진, 김경훈, 황지남, 이하늬

    방정숙, 선우진, 조선미 et al.

    2019; 29(4): 709-739

    https://doi.org/10.29275/jerm.2019.11.29.4.709
    Abstract

    Abstract : An analysis of domestic research in the field of mathematics education over the past decades shows that there has been a steady growth in this field of research for both qualitative and quantitative analyses. The main aim of this study is to analyze the trends of domestic research on mathematics education in terms of the publication periods, research topics, research methods, and target research population. In this respect, a total of 4559 research articles dealing with mathematics education in seven professional journals published from 1963 to the present were analyzed. The results of this study showed that the number of articles on mathematics education has been rapidly increased since the 1990s. With respect to the topics, studies on instruction and, learners’ abilities or characteristics have been the most frequent. However, there has been lack of research on assessment and technology, or manipulative materials. With respect to the research methods, analytic study of literature, case study, and survey have been most frequently applied methods. With respect to the target research population, the main participants were either elementary or secondary school students. In conclusion, this paper identifies important implications for future research directions on mathematics education in Korea.

  • 전자저널 논문 | 2020-05-31

    이수진, 신재홍

    이수진, 신재홍

    2020; 30(2): 245-279

    https://doi.org/10.29275/jerm.2020.05.30.2.245
    Abstract

    Abstract : The aim of this study is to analyze students’ units-coordinating activities and operations in their proportion problem solving, and to investigate how quantitative structures corresponding to ratios are constructed with different levels of units coordination. As a result of our clinical interviews with three seventh grade students who were at units coordination stage 2 and 3, we found that the use of operations relevant to whole number division was crucial to solving mixed-juice problems and only the stage 3 students assimilated the problem situations involving ratios as three-levels-of-units structures consisting of composite units of indefinite numerosity. Given the importance of units coordination in solving proportion problems, implications for further research are discussed.

  • 전자저널 논문 | 2020-08-31

    편집부

    편집부

    2020; 30(3): S

  • 전자저널 논문 | 2019-11-30

    권미선

    권미선

    2019; 29(4): 741-760

    https://doi.org/10.29275/jerm.2019.11.29.4.741
    Abstract

    Abstract : Time and elapsed time are concepts that are applicable in everyday life and thus directly affect students" lives. This is because students study the concepts in the lower grades of elementary school. Unlike other aspects of measurement, time is characterized by continuous flow and it uses a number system that is unfamiliar to students such as base-12 and 60 system. With such specificity, lower grade students may have difficulty in understanding time and elapsed time. In this respect, this study analyzed the concepts of time and elapsed time in the 2015 revised mathematics curriculum and textbooks and examined 108 second-grade elementary school students" responses. The results show that students are struggling to grasp these concepts. To be specific, many students had difficulty recognizing the movement of the minute and the hour hand over time. Moreover, they also had difficulty finding the elapsed time using the time band. This study provides guidance on how to teach time and elapsed time when learning occurs in the classroom.

  • 전자저널 논문 | 2020-08-31

    Gila Hanna, Christine Knipping

    Gila Hanna, Christine Knipping

    2020; 30(3): 1-13

    https://doi.org/10.29275/jerm.2020.08.sp.1.1
  • 전자저널 논문 | 2019-11-30

    황희정, 이수진

    황희정, 이수진

    2019; 29(4): 687-708

    https://doi.org/10.29275/jerm.2019.11.29.4.687
    Abstract

    Abstract : 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.

  • 전자저널 논문 | 2020-11-30

    손태권, 황성환

    손태권, 황성환

    2020; 30(4): 601-624

    https://doi.org/10.29275/jerm.2020.11.30.4.601
    Abstract

    Abstract : Research into assessments in mathematics education has broadened from summative assessments focusing on students achievement to those focusing on students’ cognition, curriculum, teaching and learning, teacher knowledge and quality, and affective domains. Considering these changes in assessment research, we examined the characteristics of domestic assessment research in mathematics education by comparing 237 articles published in KCI journals with 857 articles published in SSCI journals from 2000 to 2020 August. We used LDA topic modeling to examine research trends over time. The findings indicated that there were different keyword distributions by period between domestic and international mathematics education journals. There were nineteen research topics in both journals; five topics were similar while nine topics were different. In addition, the hot topics in international and domestic mathematics education journals were found to be curriculum assessment and student competency assessment, respectively. Based on these findings, we discussed practical implications for the development of assessment research in domestic mathematics education.

  • 전자저널 논문 | 2020-05-31

    유재근, 이정아, 박문환, 장혜원

    유재근, 이정아, 박문환 et al.

    2020; 30(2): 353-374

    https://doi.org/10.29275/jerm.2020.05.30.2.353
    Abstract

    Abstract : The purpose of this study was to explore the possibility of interconnection between non-fractional representation and non-circular decimal representation in irrational teaching and learning of school mathematics and to examine the possibility of field application. First, through the analysis of previous studies, it was found that the core of understanding irrational concepts is the intuitive perception of convergence and the inference of acyclicity. And through mathematical analysis, we confirmed that finite decimal sequences and approximate fractional sequences should be learning contents. In this regard, we applied engineering tools in teaching and learning activity of irrational numbers and analyzed the process by which engineering tools become learners’ mathematical tools and then learning occurs, that is, instrument genesis. As a result, in the activity of finding finite fractions of square roots, students gained a meaningful understanding by focusing on the meaning of square root symbols and square roots as objects from inputting functions and operations and using drag. And in the activity to solve the task ‘Can a graph cross a grid point?’, Students could infer the acyclicity of the decimal representation of irrational numbers by observing the approximate fraction as the slope. Thus, this study is expected to be a basic reference of teaching and learning of irrational numbers to construct a mental image of real numbers completeness axiom.

  • 전자저널 논문 | 2020-08-31

    Deborah Schifter, Susan Jo Russell

    Deborah Schifter, Susan Jo Russell

    2020; 30(3): 15-28

    https://doi.org/10.29275/jerm.2020.08.sp.1.15
  • 전자저널 논문 | 2020-11-30

    황지남, 방정숙

    황지남, 방정숙

    2020; 30(4): 625-648

    https://doi.org/10.29275/jerm.2020.11.30.4.625
    Abstract

    Abstract : In order to understand the research trends in mathematical reasoning since 2000, this study analyzed 262 papers published in seven KCI journals and 381 papers published in five SSCI journals via topic modeling. The overall research topics were compared and contrasted between domestic journals and international journals. A more detailed analysis was conducted by considering different publication periods. The results showed that the main domestic research topics included, in order, geometry proof, mathematical justification, problem solving, pattern generalization, proportional reasoning, and statistical reasoning, whereas the main international research topics included, in order, proof and argument, teacher education, geometric reasoning, pattern generalization, problem solving, and statistical reasoning. The results of this study also showed that gifted students represented the most popular research target of domestic studies, while the process of mathematical reasoning was the main focus of international studies. This paper closes with implications on research targets including teachers, attention to the mathematical reasoning process, diversity of research topics, and new research topics that may guide future research on mathematical reasoning.

  • 전자저널 논문 | 2020-02-28

    김정하

    김정하

    2020; 30(1): 67-88

    https://doi.org/10.29275/jerm.2020.02.30.1.67

    Abstract : To analyze how fraction division is used in Korean mathematics textbooks, this study examined the various situations in which fraction division is applied and how the fraction division algorithm is developed. In the textbooks from the 1st curriculum to the 2015 revised curriculum, we analyzed how and in what situations fraction division is being developed, and present the results of the analysis and discussion points.

  • 전자저널 논문 | 2019-11-30

    이지현, 이기돈

    이지현, 이기돈

    2019; 29(4): 481-506

    https://doi.org/10.29275/jerm.2019.11.29.4.481
    Abstract

    Abstract : The purpose of this case study was to explore seven high school students’ understanding of derivatives at a point in terms of multiple contexts (symbolic, graphic, numerical/verbal, physical, applied contexts) and also the process-object layers. Student participants who demonstrated a structural conception of the ratio layer in symbolic, graphic, and physical contexts revealed a weak understanding of rate values as the results of comparing two quantities multiplicatively. As for the limit layer, some participants failed to think of the limit process, or could only think of the partial limit process. The analysis of students’ understanding may suggest, in terms of multiple contexts and the process-object layers, which aspects are lacking in current high school teaching and learning practices of derivatives.

  • 전자저널 논문 | 2020-08-31

    Yeon Kim

    Yeon Kim

    2020; 30(3): 185-198

    https://doi.org/10.29275/jerm.2020.08.sp.1.185
  • 전자저널 논문 | 2020-08-31

    박지현

    박지현

    2020; 30(3): 553-573

    https://doi.org/10.29275/jerm.2020.08.30.3.553
    Abstract

    Abstract : The purpose of this study was to examine the outcomes of the National Assessment of Educational Achievement (NAEA) 2015-2018 when the 2009 Revised National Curriculum was applied and suggested for future curriculum revisions. The characteristics of students’ academic achievement were analyzed based on the results of evaluating test items developed by the achievement standards of the 2009 Revised National Curriculum. The analysis showed that students’ academic achievement was low in the ‘Function’, ‘Probability and Statistics’, and ‘Geometry’ domain. In addition, many achievement standards could be mastered only by the above average group of students. Accordingly, it is necessary to reinforce customized teaching and learning activities in relation to achievement standards which were under achieved. To improve the achievement characteristics, it is necessary to specify detailed achievement standards and to strengthen the linkage between achievement standards.

  • 전자저널 논문 | 2020-08-31

    김선희, 안세인

    김선희, 안세인

    2020; 30(3): 445-463

    https://doi.org/10.29275/jerm.2020.08.30.3.445
    Abstract

    Abstract : This study analyzed the features of the IB"s mathematics assessment and proposed methods to settle the mathematics process-focused assessment in schools. According to the difficulties of teachers investigated in the previous studies, solutions were derived by the documents related to assessment in the IB MYP and DP curriculum and interviews with teachers in IB schools. As a result, research and policy were proposed to support teachers. First, design an assessment frame that has the curriculum competency as an assessment element, and suggest the approaches toward reflecting competencies. Second, provide examples of typical assessment tasks and scoring rubrics, and the achievement level of each assessment criterion to detail the task, and engage students in the TSC process. Third, present an objective assessment method to produce the result and a feedback method. Fourth, to improve the fairness of teachers’ autonomous assessment, provide external organization inspections, teacher training, and feedback on teacher assessment. Additionally, it is suggested that criterion-referenced assessment, assessment framework development study, change of student"s view on the assessment, and reduction of teacher’s workload would be necessary as conditions for mitigating teachers’ difficulties.

  • 전자저널 논문 | 2020-08-31

    GwiSoo Na, Dong-Won Kim

    GwiSoo Na, Dong-Won Kim

    2020; 30(3): 135-152

    https://doi.org/10.29275/jerm.2020.08.sp.1.135
  • 전자저널 논문 | 2020-11-30

    이지현, 이규희

    이지현, 이규희

    2020; 30(4): 649-673

    https://doi.org/10.29275/jerm.2020.11.30.4.649
    Abstract

    Abstract : The function concept arose from analyzing the relationships between co-varying quantities to model change. From the covariation perspective of function, we analyzed the responses of 13 pre-service teachers to the tasks to interpret rates of change or reason the corresponding change of one quantity from the changes of the other using the given rate of change; by using the rate of change, a change of one quantity can be directly deduced from the given change of the other quantity. Most of the pre-service teachers reasoned the change correctly. However, a portion of pre-service teachers reflexively calculated the formula of the function and the difference between the two values of the function. In addition, some teachers revealed their insufficient understanding of the slope of the linear function. The conceptions of pre-service teachers help elucidate what and how students might learn and might not learn about functions from the school mathematics curriculum.

KORENG

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Korea Society of Education Studies in Mathematics

Vol.31 No.3
August, 2021

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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Article

전자저널 논문

2021; 31(2): 131-152

Published online May 31, 2021 https://doi.org/10.29275/jerm.2021.31.2.131

Copyright © Korea Society of Education Studies in Mathematics.

A Case Study on Learning Proofs of the Pythagorean Theorem through Diagramming: Based on the Châteletean Perspective

Jeong-Won Noh1, Kyeong-Hwa Lee2, Sung-Jae Moon3

1Graduate Student, Seoul National University, 2Professor, Seoul National University, 3Lecturer, Gyeongin National University of Education, South Korea

Correspondence to:Kyeong-Hwa Lee, khmath@snu.ac.kr
ORCID: https://orcid.org/0000-0002-2784-3409

Received: March 25, 2021; Revised: April 30, 2021; Accepted: April 30, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

    Fig 1.

    Figure 1. Generative mode of interaction (Herbst, 2004, p. 134)1)
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 2.

    Figure 2. (a) The task applied in the 1st class (b) The task applied in the 2nd class
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 3.

    Figure 3. Euclidean proof in animation (Iwamoto, 2006)3)
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 4.

    Figure 4. S1 and S2’s final answer to Task 1-1
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 5.

    Figure 5. S1’s diagramming-C while discovering Method 1
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 6.

    Figure 6. S2’s diagramming-R and diagramming-C related to Method 1
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 7.

    Figure 7. S2’s diagramming-D and diagramming-C related to Method 2
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 8.

    Figure 8. S1’s diagramming-R and diagramming-C related to Method 2
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 9.

    Figure 9. S2’s diagramming-R changing both the spatial relationship between his body and the diagram and the direction of his gaze
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 10.

    Figure 10. Triangles included in S1 and S2’s final answer to Task 1-2
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 11.

    Figure 11. S1’s diagramming-R while S2 sharing his answer
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 12.

    Figure 12. S1’s diagramming-C and diagramming-D while actualizing the triangle BHI
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 13.

    Figure 13. S1’s diagramming while actualizing the triangle CHK
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 14.

    Figure 14. S1’s diagramming while actualizing the triangle ACK
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 15.

    Figure 15. S2’s diagramming-D while actualizing the triangle BCG
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Fig 16.

    Figure 16. (a) While S1 was tracing the triangle ACG (diagramming-D), the tip of S2’s pencil was flying obliquely in the air over S1’s worksheet (diagramming-C). (b) S1 actualized the triangle CGH (diagramming-D) after sweeping the line segment AH (diagramming-C).
    Journal of Educational Research in Mathematics 2021; 31: 131-152https://doi.org/10.29275/jerm.2021.31.2.131

    Table 1 Analysis code of diagramming according to the degree of directness

    분석 코드설명예시
    Diagramming-D다이어그램 자체에 직접적인 변형을 가할 때연필로 주어진 다이어그램 내에 기존에 없던 새로운 요소를 도입하거나, 선 위를 덧칠한다
    Diagramming-C다이어그램 가까이에 위치한 손 또는 연필 등을 이용하여 다이어그램에 포함된 요소들을 가리키거나 그 위를 움직이는 제스처를 취할 때다이어그램과 바로 위의 공중에서 연필로 도형의 변을 따라 훑듯이 움직인다
    Diagramming-R다이어그램과 학습자의 신체 사이의 공간적인 위치 관계를 변화시킬 때다이어그램이 포함된 활동지의 방향을 변경하거나, 자세를 조정해 다른 각도에서 다이어그램을 바라본다4)

    Table 2 Analysis code of diagramming according to epistemic distance

    분석 코드예시인식론적 거리
    DD- 다이어그래밍과 함께 “아, 알겠다!” 등의 높은 음조의 감탄사를 외친다감소
    - 다이어그래밍 직후 형식화 된 언어로 활동지에 답안을 작성하거나 진술한다
    ID- 다이어그래밍과 함께 “음…”, “어...”, “모르겠다.” 등의 머뭇거리거나 의문을 표시하는 발화를 언급한다증가
    - 다이어그래밍 직후 답안 작성이나 관련 진술 없이 또 다른 다이어그래밍으로 옮겨간다