Splitting operation for composite units and construction of fractions as multipliers
유진영 Yoo Jin Young , 신재홍 Shin Jaehong
62(1) 121, 2023
유진영 Yoo Jin Young , 신재홍 Shin Jaehong
DOI: JANT Vol.62(No.1) 121, 2023
The purpose of this study is to explore how the student, who interiorized three levels of units, constructed fractions as multipliers by analyzing her ways of conceiving improper fractions with three levels of units and coordinating two threelevelsofunits structures. Among the data collected from our teaching experiment with two 4th grade students meeting 13 times for three months, we focus on how Seyeon, one of the participating students, wrote numerical expressions in the form of “× fraction” for the given situations using her splitting operation for composite units. Given the importance of splitting operation for composite units for the construction of fractions as multipliers, implications for further research are discussed.

The analysis and algebraic consideration on the rationalizing denominators in school mathematics
최지훈 Choi Jihoon , 김인경 Kim Inkyung
62(1) 2334, 2023
최지훈 Choi Jihoon , 김인경 Kim Inkyung
DOI: JANT Vol.62(No.1) 2334, 2023
The rationalizing denominators presented in the mathematics textbooks is being used in various places of school mathematics curriculum. However, according to some previous research on the rationalizing denominators in school mathematics, it seems that there is no clear explanation as to why rationalizing denominators is necessary and why it should be used. In addition, a previous research insists that most students know how to rationalize denominators but do not understand why it is necessary and important. To confirm this, we examined the rationalizing denominators presented in the 2015 revised mathematics curriculum as school mathematics. Then we also examined the rationalizing denominators algebraically as academic mathematics. In detail, we conducted an analysis on the rationalizing denominators presented in randomly selected three mathematics textbooks and teacher guidebooks for middle school third grade. Then the algebraic meaning of the rationalizing denominators was examined from a proper algebraic structure analysis. Based on this, we present alternative definitions of the rationalizing denominators which is suitable for school mathematics and academic mathematics. Finally, we also present the mathematical contents (irrationals of the special form can be algebraically interpreted as numbers in the standard form) that teachers should know when they teach the rationalizing denominators in school mathematics.

Students’ cognition and a teacher’s questioning strategies in the errorfinding activity of the concept of irrational numbers
나윤성 Na Younsung , 최송희 Choi Song Hee , 김동중 Kim Dongjoong
62(1) 3555, 2023
나윤성 Na Younsung , 최송희 Choi Song Hee , 김동중 Kim Dongjoong
DOI: JANT Vol.62(No.1) 3555, 2023
The purpose of this study is to examine not only students' cognition in the mathematical errorfinding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, errorfinding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher’s questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

An analysis of students’ engagement in elementary mathematics lessons using openended tasks
남인혜 Nam Inhye , 신보미 Shin Bomi
62(1) 5778, 2023
남인혜 Nam Inhye , 신보미 Shin Bomi
DOI: JANT Vol.62(No.1) 5778, 2023
Students’ engagement in lessons not only determines the direction and result of the lessons, but also affects academic achievement and continuity of followup learning. In order to provide implications related to teaching strategies for encouraging students’ engagement in elementary mathematics lessons, this study implemented lessons for middlelow achieving fifth graders using openended tasks and analyzed characteristics of students’ engagement in the light of the framework descripors developed based on previous research. As a result of the analysis, the students showed behavioral engagement in voluntarily answering teacher's questions or enduring difficulties and performing tasks until the end, emotional engagement in actively expressing their pleasure by clapping, standing up and the feelings with regard to the topics of lessons and the tasks, cognitive engagement in using reallife examples or their prior knowledge to solve the tasks, and social engagement in helping friends, telling their ideas to others and asking for friends’ opinions to create collaborative ideas. This result suggested that lessons using openended tasks could encourage elementary students’ engagement. In addition, this research presented the potential significance of teacher’s support and positive feedback to students’ responses, teaching methods of group activities and discussions, strategies of presenting tasks such as the board game while implementing the lessons using openended tasks.

Elementary school students’ metaphors of angle concepts
김상미 Kim Sangmee
62(1) 7993, 2023
김상미 Kim Sangmee
DOI: JANT Vol.62(No.1) 7993, 2023
This study used metaphors as a analysis tool to investigate elementary school students’ formation and development of angle concepts. For this purpose, the students were asked to write words associated with angle, right angle, acute angle and obtuse angle and to explain why. In case of angle and right angle, responses of 268 students from 3rd to 6th graders were analyzed and for acute angle and obtuse angle, those of 192 students from 4th to 6th graders were examined. As the results of categorizing the metaphors, they can be classified into categories such as; (1) qualitative aspects: ‘things metaphor’, ‘personality metaphor’, ‘emotions metaphor’ etc., (2) quantitative aspects: ‘motions metaphor’, ‘changes metaphor’, ‘emotions metaphor’ etc., and (3) relational aspects: ‘shape relations metaphor.’ The metaphoric expressions were prominent in ‘qualitative aspects’ associated with shapes. As for the other aspects, ‘quantitative aspect’ the size of angles and the amount of spread and ‘relational aspects’  elements of angle and relationship with another shapes, the frequency increses were shown to as grade levels were up. In case of right angle and acute angle, ‘qualitative aspects’ associated with shapes were outstanding and the frequency of the metaphoric expressions of obtuse angle was distributed similarly in three aspects. As the figure strand and the measurement strand are integrated to an strand in the 2022 revised curriculum, we need more discussion of multifaced aspects of angle and the learning sequences in the ‘figure and measurement’ strand.

Challenges faced by elementary teachers in implementing the five practices for effective mathematical discussions
방정숙 Pang Jeongsuk , 김소현 Kim Sohyeon , 안효주 An Hyojoo , 정지수 Chung Jisu , 곽기우 Kwak Giwoo
62(1) 95115, 2023
방정숙 Pang Jeongsuk , 김소현 Kim Sohyeon , 안효주 An Hyojoo , 정지수 Chung Jisu , 곽기우 Kwak Giwoo
DOI: JANT Vol.62(No.1) 95115, 2023
Even the teachers who agree with the necessity of effective mathematical discussions find it difficult to orchestrate such discussions in the actual lessons. This study focused on analyzing the difficulties 15 elementary school teachers faced in applying "the five practices for orchestrating productive mathematics discussions" to their lessons. Specifically, this study analyzed the process of planning, implementing, and reflecting on the lessons to which three or four teachers as a teacher community applied the five practices. The results of this study showed that the teachers experienced difficulties in selecting and presenting tasks tailored to the student levels and class environment, monitoring all students' solutions, and identifying the core mathematical ideas in student solutions. In addition, this study revealed practical and specific difficulties that had not been described in the previous studies, such as writing a lesson plan for effective use, simultaneously performing multiple teacher roles, and visually sharing student presentations. This study is expected to provide practical tips for elementary school teachers who are eager to promote effective mathematical discussions and to provoke professional discourse for teacher educators through specific examples.

A case study on the design and application of metaverse class space in elementary mathematics: Focusing on the affective domain
박만구 Park Mangoo , 이윤경 Lee Yunkyung , 정보화 Jeong Bohwa , 정유진 Jung Yujin , 김지영 Kim Jiyoung
62(1) 117149, 2023
박만구 Park Mangoo , 이윤경 Lee Yunkyung , 정보화 Jeong Bohwa , 정유진 Jung Yujin , 김지영 Kim Jiyoung
DOI: JANT Vol.62(No.1) 117149, 2023
This study attempted to design a virtual space using ZEP, a metaverse platform, to enable mathematics classes in the metaverse space, to apply it to mathematics classes, and to find out changes in students' affective domain. As a result, students showed positive effects in terms of subject efficacy, subject interest, intrinsic motivation, class satisfaction and participation. In addition, we found the possibility of customized classes for each student level by performing different missions in classroom classes with limited time and space.

Exploring factors in terms of school and social environment that affect high school student’s affective attitude on mathematics according to the student’s academic level, grade, gender, and school location
정혜윤 Jung Hyeyun
62(1) 151173, 2023
정혜윤 Jung Hyeyun
DOI: JANT Vol.62(No.1) 151173, 2023
In this study, we explored factors that affect high school student’s affective attitude on mathematics with respect to the school mathematics instructoin, school mathematics assessment, mathematics textbook, private mathematics education, college entrance and career, and social atmosphere. Considering students’ grade, major, academic level, gender, and school location, 1,029 high school students participated in the survey. To analyze the survey results, descriptive statistics, ttest, ANOVA, and chisquare test were conducted using SPSS ver 29.0. Results are as follows. First, generally, college entrance and career and school mathematics instruction affected students’ affective attitude on mathematics. Second, according to student’s academic level and gender, there was a statistically significant difference in the factors affecting the affective attitude on mathematics. Third, according to students’ background, there was a statistically significant difference in students’ responses to subcategories of each factor. We suggested that to improve student’s affective attitude on mathematics, diversity of the school mathematics instruction, improvement of the mathematics textbook, student’s appropriate participation in the private mathematics education, improvement of student’s perception of the utilization of the mathematics in the future and the importance of the mathemaitcs in the society, and parents’ emotional support are needed.
