Exploring fraction knowledge of the stage 3 students in proportion problem solving
이진아 Lee Jin Ah , 이수진 Lee Soo Jin
61(1) 128, 2022
이진아 Lee Jin Ah , 이수진 Lee Soo Jin
DOI: JANT Vol.61(No.1) 128, 2022
The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middlegrade students, each lasting about 30∼50 minutes, were carried out from May 2021 to August 2021. The present study focuses on two 7th grade students who exhibited their ability to coordinate three levels of units prior to solving whole number problems. Although the students showed interiorization of three levels of units in solving whole number problems, how they coordinated three levels of units were different in solving proportion problems depending on whether the problems required reasoning with whole numbers or fractions. The students could coordinate three levels of units prior to solving the problems involving whole numbers, they coordinated three levels of units in activity for the problems involving fractions. In particular, the ways the two students employed partitioning operations and how they coordinated quantitative unit structures were different in solving proportion problems involving improper fractions. The study contributes to the field by adding empirical data corroborating the hypotheses that students’ ability to transform one three levels of units structure into another one may not only be related to their interiorization of recursive partitioning operations, but it is an important foundation for their construction of splitting operations for composite units.

A study on the mathematics curriculum for elementary school in Korea to improve teaching of chance
고은성 Ko Eunsung , 탁병주 Tak Byungjoo
61(1) 2945, 2022
고은성 Ko Eunsung , 탁병주 Tak Byungjoo
DOI: JANT Vol.61(No.1) 2945, 2022
This study tried to analyze the problems by critically examining how the chance is taught in relation to the concept of chance and randomness in the Korean elementary school mathematics curriculum. To this end, the concepts of chance and randomness were first examined, and problems were presented in based on this by the literature analysis on mathematics curriculum material and textbooks for elementary school in Korea. As a result, there was a lack of experience in reasoning based on data, and randomness instruction was not performed properly. In addition, as the teaching of the sample space was omitted, contradictory materials were being used. Moreover, it was pointed out that the teaching of chance is focused on a specific grade level. For the improvement of the teaching of chance, a teaching of the probability experiment and the sample space were mainly suggested, and it was also suggested that the contents of the data area be adjusted for the composition focused on a specific grade.

A study on the contents related to the plane figures of Joseon Sanhak in the late 18th century
최은아 Choi Eunah
61(1) 4762, 2022
최은아 Choi Eunah
DOI: JANT Vol.61(No.1) 4762, 2022
This study investigated the contents related to the plane figures in the geometry domains of JoseonSanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problemsolving process, and the newly emerged mathematical topics. For this purpose, We analyzed < Gosasibijip >, < Sanhakipmun > and < Juhaesuyong > written in the late 18th century and < Muksajipsanbeop > and < Guiljip > written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. JoseonSanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

An action research on a middle school mathematics teacher’s lesson reflection: Focused on the teacher’s discourse capability to promote students’ participation
박진환 Park Jinhwan , 신보미 Shin Bomi
61(1) 6382, 2022
박진환 Park Jinhwan , 신보미 Shin Bomi
DOI: JANT Vol.61(No.1) 6382, 2022
The aim of this study was to analyze the changing process in a middle school teacher’s discourse capability through reflection to lessons, thereby providing the implications for activities to improve the quality of lessons. To that end, this study explored the characteristics of change in the teacher’s discourse capability of promoting students’ participation while the teacher repeated instruction implementation and meeting for reflecting the implementation. Through the reflection, the teacher noticed his own matters about dealing with the students’ responses and presentations. By attempting to address the matters in the instructions and reflecting the attempt, the teacher was able to accelerate the students’ participation in the lesson discourse through enhancing productivity and openness of the discourse. The result of this study demonstrated that lesson reflection beneficially influenced development of teaching profession related to discourse capability.

A case study for class improvement through online math class analysis and selfevaluation: Focusing on fair access, autonomy, initiative, and evaluation areas in the TRU analysis
박만구 Park Mangoo , 김지영 Kim Ji Young , 김민회 Kim Minhwe , 윤종천 Yoon Jong Chun , 이정민 Lee Jung Min
61(1) 83108, 2022
박만구 Park Mangoo , 김지영 Kim Ji Young , 김민회 Kim Minhwe , 윤종천 Yoon Jong Chun , 이정민 Lee Jung Min
DOI: JANT Vol.61(No.1) 83108, 2022
This research is a case study in which teachers tried to improve classes through online class analysis and selfevaluation in elementary school mathematics classes using a checklist of class reflection based on fair access, autonomy, initiative, and evaluation areas in the TRU analysis framework of Schoenfeld (2016). As a result, it was confirmed that the teacher's fair participation, student autonomy, initiative, feedback, and evaluation areas improved teaching methods during the short time. Therefore, if you want to improve classes in relatively short period of time, you can see the effect of some improvement only by selfevaluation. However, continuous improvement of teaching methods require the help of a teacher communities including experts or critical colleagues, and a longerterm case study.

An Analysis of Teachers’ Knowledge on the Strategies for Understanding and Solving Equations by Fourth Graders
방정숙 Pang Jeongsuk , 이유진 Lee Yujin
61(1) 109126, 2022
방정숙 Pang Jeongsuk , 이유진 Lee Yujin
DOI: JANT Vol.61(No.1) 109126, 2022
The purpose of this study is to explore how well teachers anticipate students to understand and solve equations. For this purpose, a questionnaire of the equal sign was developed, and 20 fourthgrade classes were selected as research participants. Teachers in each class were asked to predict various strategies on how their own students would respond to the questionnaire, and a total of 450 students from the 20 classes solved the questionnaire. As a result of the analysis, the teachers could predict students’ computational strategies and relational strategies easily but did not fully understand that some students used both strategies or employed incorrect computational or relational strategies. The students tended to use relational strategies better than the teachers expected. They also employed operational strategies more often than the teachers expected. The teachers predicted that students’ strategies would be influenced by the types of the problems such as equationstructure items and equationsolving items, whereas the students were more influenced by the forms of equations in the problems. Based on these results, several implications for the knowledge to which teachers needed to attend were discussed so that elementary school students could enhance the relational understanding of the equal sign.

Longitudinal analysis of the direct and indirect influence of academic selfconcept and academic support of teachers and parents on academic achievement in mathematics
김용석 Kim Yongseok
61(1) 127156, 2022
김용석 Kim Yongseok
DOI: JANT Vol.61(No.1) 127156, 2022
This study used the data of students from the 6th grade to the 3rd grade of middle schoolin the Korean Educational Longitudinal Study 2013 and classified them into subgroups with similar longitudinal changes in math academic achievement. In addition, the influence of longitudinal changes in the group's academic selfconcept and teachers and parents academic support on the longitudinal changes in math academic achievement were analyzed, either directly or indirectly. As a result of the analysis, it was found that the academic selfconcept of each group had a positive influence on the academic achievement in mathematics. In addition, the academic support of teachers and parents was found to have a positive influence on the academic achievement in mathematics through the mediating of the academic selfconcept. In terms of direct and indirect influence on academic selfconcept and math vertical scale scores, it was found that teachers' academic support had more influence than parents' academic support. The educational implications of these points were discussed.

Preservice teachers’ understanding of fraction multiplication through problem posing and solving in Korea and the United States
여승현 Yeo Sheunghyun , 이지영 Lee Jiyoung
61(1) 157178, 2022
여승현 Yeo Sheunghyun , 이지영 Lee Jiyoung
DOI: JANT Vol.61(No.1) 157178, 2022
Mathematics teachers’ content knowledge is an important asset for effective teaching. To enhance this asset, teacher’s knowledge is required to be diagnosed and developed. In this study, we employed problemposing and problemsolving tasks to diagnose preservice teachers’ understanding of fraction multiplication. We recruited 41 elementary preservice teachers who were taking elementary mathematics methods courses in Korea and the United States and gave the tasks in their final exam. The collected data was analyzed in terms of interpreting, understanding, model, and representing of fraction multiplication. The results of the study show that preservice teachers tended to interpret (fraction)×(fraction) more correctly than (whole number)×(fraction). Especially, all US preservice teachers reversed the meanings of the fraction multiplier as well as the whole number multiplicand. In addition, preservice teachers frequently used ‘part of part’ for posing problems and solving posed problems for (fraction)×(fraction) problems. While preservice teachers preferred to a area model to solve (fraction)×(fraction) problems, many Korean preservice teachers selected a length model for (whole number)×(fraction). Lastly, preservice teachers showed their ability to make a conceptual connection between their models and the process of fraction multiplication. This study provided specific implications for preservice teacher education in relation to the meaning of fraction multiplication, visual representations, and the purposes of using representations.

Study on the quality of instruction of two beginning mathematics teachers: Toward the above criteria
박미미 Park Mimi , 김연 Kim Yeon
61(1) 179198, 2022
박미미 Park Mimi , 김연 Kim Yeon
DOI: JANT Vol.61(No.1) 179198, 2022
Teaching is delicate, complicated, and demanding work, and especially beginning teachers set forth their difficulties in preparing and implementing mathematics instruction. It is important to ensure the quality of beginning mathematics teachers’ instruction above a consistent level because such affirmation justifies the national policy on teacher education as well as the individual efforts of preservice teachers in South Korea. The current study collected mathematics lessons of the two beginning teachers who graduated from the same teacher training institute and worked at the same high school. The findings reported what features their lessons have with regard to the learning environment, engaging students in learning, deepening student learning, and using representations of the edTPA in order to identify what can or cannot be expected in their mathematics instruction. The instruction of the one teacher was assessed middle or more than middle scores throughout the rubrics, but the other one had lower scores. Based on these findings, this study suggested the implications for teacher education in ways of improving the quality of instruction of beginning mathematics teachers.

A basic research for the development of Korean mathematics education standards for the next generation
권오남 Kwon Oh Nam , 김영록 Kim Young Rock , 고호경 Ko Ho Kyoung , 임해미 Rim Haemee , 박정숙 Park Jung Sook , 박지현 Park Jee Hyun , 박수민 Park Soomin , 이경원 Lee Kyungwon , 박진희 Park Jin Hee
61(1) 199220, 2022
권오남 Kwon Oh Nam , 김영록 Kim Young Rock , 고호경 Ko Ho Kyoung , 임해미 Rim Haemee , 박정숙 Park Jung Sook , 박지현 Park Jee Hyun , 박수민 Park Soomin , 이경원 Lee Kyungwon , 박진희 Park Jin Hee
DOI: JANT Vol.61(No.1) 199220, 2022
This study aims to elicit the vision of the future human being and mathematical competencies that next generation should pursue to be nurtured through mathematics education as regarding the need for a national midterm to longterm mathematics education standard for nurturing learners that can accommodate changes in the future society is emerging. The research team established the criterion for domains of mathematical competencies through the analysis of prior research, and then, refined three dimensions of mathematical competencies and the domains of each dimension through expert advice (9 people in total, 3 times) and focus group interviews (10 people in total, 4 times). After conducting a largescale survey (295 people in total) which includes elementary and secondary teachers, professors, and researchers, etc., the vision of the future human being and mathematical competencies were elicited. In order to utilize the vision of the future human being and mathematical competencies, five stages of research on the development and utilization of mathematics education standards were proposed. Cooperating with related organizations, securing the research project period and expanding the scope of research team composition, and providing webbased documentation of mathematics education standards will be needed for the followup studies.
