An analysis of fractional division instruction emphasizing algebraic thinking
조선미 Cho¸ Seonmi , 방정숙 Pang¸ Jeongsuk
60(4) 409429, 2021
조선미 Cho¸ Seonmi , 방정숙 Pang¸ Jeongsuk
DOI: JANT Vol.60(No.4) 409429, 2021
This study investigated instructional methods for fractional division emphasizing algebraic thinking with sixth graders. Specifically, instructional elements for fractional division emphasizing algebraic thinking were derived from literature reviews, and the fractional division instruction was reorganized on the basis of key elements. The instructional elements were as follows: (a) exploring the relationship between a dividend and a divisor; (b) generalizing and representing solution methods; and (c) justifying solution methods. The instruction was analyzed in terms of how the key elements were implemented in the classroom. This paper focused on the fractional division instruction with problem contexts to calculate the quantity of a dividend corresponding to the divisor 1. The students in the study could explore the relationship between the two quantities that make the divisor 1 with different problem contexts: partitive division, determination of a unit rate, and inverse of multiplication. They also could generalize, represent, and justify the solution methods of dividing the dividend by the numerator of the divisor and multiplying it by the denominator. However, some students who did not explore the relationship between the two quantities and used only the algorithm of fraction division had difficulties in generalizing, representing, and justifying the solution methods. This study would provide detailed and substantive understandings in implementing the fractional division instruction emphasizing algebraic thinking and help promote the followup studies related to the instruction of fractional operations emphasizing algebraic thinking.

Analysis of problem solving competency and types of tasks in elementary mathematics textbooks: Challenging/Thinking and inquiry mathematics in the domain of number and operation
여승현 Yeo¸ Sheunghyun , 서희주 Suh¸ Heejoo , 한선영 Han¸ Sunyoung , 김진호 Kim¸ Jinho
60(4) 431449, 2021
여승현 Yeo¸ Sheunghyun , 서희주 Suh¸ Heejoo , 한선영 Han¸ Sunyoung , 김진호 Kim¸ Jinho
DOI: JANT Vol.60(No.4) 431449, 2021
Elementary mathematics textbooks present contents for enhancing problem solving competency. Still, teachers find teaching problem solving to be challenging. To understand the supports textbooks are suggesting, this study examined tasks from the challenging/thinking and inquiry mathematics. We analyzed 288 mathematical activities based on an analytic framework from the 2015 revised mathematics curriculum. Then, we employed latent class analysis to classify 83 mathematical tasks as a new approach to categorize tasks. As a result, execution of the problem solving process was emphasized across grade levels but understanding of problems was varied by grade levels. In addition, higher grade levels had more opportunities to be engaged in collaborative problem solving and problem posing. We identified three task profiles: ‘execution focus’, ‘collaborativesolution focus’, ‘multifacetedsolution focus’. In Grade 3, about 80% of tasks were categorized as the execution profile. The multifacetedsolution was about 40% in the thinking/challenging mathematics and the execution profile was about 70% in Inquiry mathematics. The implications for developing mathematics textbooks and designing mathematical tasks are discussed.

Effects on equity in mathematics education: Multilevel analysis via the PISA 2015
황지현 Jihyun Hwang , 신동훈 Dong Hoon Shin
60(4) 451466, 2021
황지현 Jihyun Hwang , 신동훈 Dong Hoon Shin
DOI: JANT Vol.60(No.4) 451466, 2021
The interaction between student and school levels should be considered to understand and examine equity in education. For this reason, we included the socioeconomic composition of schools to scrutinize the equity related to students’ socioeconomic status and mathematical literacy in Korea. We applied the hierarchical linear modeling approach to the Programme for International Student Assessment (PISA) 2015 data for binational comparison between Korea (5,548 students from 168 schools) and the U.S. (5,217 students from 161 schools). The findings show that schoollevel achievement and the socioeconomic composition of schools cannot be ignored to understand Korean students’ achievement gap between high and low socioeconomic status. In addition, U.S. students from low socioeconomic status were likely to have similar mathematics literacy scores. These findings indicated that inequity in Korean mathematics education could be intertwined with the characteristics of Korean students like high demands for supplementary private education and school characteristics like curriculum selection. This research also reminds mathematics educators that people should not simply mimic other education systems to resolve education issues in their own system.

A study on coding mathematics curriculum and teaching methods that converges school mathematics and school informatics
강하람 Kang¸ Ha Ram , 임채령 Lim¸ Chae Lyeong , 조한혁 Cho¸ Han Hyuk
60(4) 467491, 2021
강하람 Kang¸ Ha Ram , 임채령 Lim¸ Chae Lyeong , 조한혁 Cho¸ Han Hyuk
DOI: JANT Vol.60(No.4) 467491, 2021
This study is a study on the coding mathematics curriculum that converges elementary and middle school mathematics and information subjects and a minimum coding gamebased education method for this. For the past 3 years, the coding mathematics curriculum and educational methods to effectively operate the curriculum were studied by applying them to 6th graders of elementary school and 1st graders of middle school. As a result of the first year of research, the coding mathematics curriculum was modified to a coding environment including the mathematical concept of a threedimensional coordinate space, and the threedimensional object was improved to be output as a real 3D print. As a result of the 2nd year study, it was improved so that even lowlevel students can build buildings by introducing different level commands for each component of the building so that selfdirected learning is possible. As a result of the 3rd year study, a teachinglearning strategy based on a minimal coding game was designed to induce an increase in the level of computational thinking, and evaluation and feedback for diagnosing computational thinking were developed. Educational methods to promote selfdirected learning and computing thinking ability, and researched coding mathematics curriculum are meaningful for the research and practice of the convergence education of school mathematics and informatics.

Effects of learnercentered mathematical instruction perceived by middle school students on math selfefficacy and class engagement: Multigroup analysis based on achievement level
송효섭 Song¸ Hyo Seob , 정희선 Jung¸ Hee Sun
60(4) 493508, 2021
송효섭 Song¸ Hyo Seob , 정희선 Jung¸ Hee Sun
DOI: JANT Vol.60(No.4) 493508, 2021
This study aims to examine the effects of learnercentered mathematical instruction perceived by middle school students such as discussion learning, selfdirected learning, and cooperative learning on their math selfefficacy and engagement in mathematics class. Moreover, it attempts to verify if there are differences in the mean of latent variables and effect among groups divided based on achievement level. Research results are as follows. First, discussion learning did not have a direct effect on students’ engagement in mathematics class, but still created an indirect effect on it through math selfefficacy. Selfdirected learning and cooperative learning created a direct effect on engagement in mathematics class as well as an indirect effect through selfefficacy on mathematics. Second, highachievement group had a higher perception of discussion learning, selfdirected learning, and cooperative learning than a lowachievement group, and showed a higher level of math selfefficacy and engagement in mathematics class. Third, there were significant differences among groups, in the effect of discussion learning on selfefficacy in mathematics, effect of selfdirected learning on selfefficacy in mathematics, and effect of math selfefficacy on engagement in mathematics class. Thus, this study offers meaningful implications for the role of math teachers as assistants in learning for learnercentered math classes.

Preservice teachers’ conceptions about considering the realistic contexts in the word problems
이지현 Lee¸ Jihyun , 이규희 Yi¸ Gyuhee
60(4) 509527, 2021
이지현 Lee¸ Jihyun , 이규희 Yi¸ Gyuhee
DOI: JANT Vol.60(No.4) 509527, 2021
We investigated whether and how preservice teachers took the realistic contexts seriously in the course of solving word problems; additionally, we investigated how preservice teachers evaluated students’ realistic and nonrealistic answers to word problems. Many preservice teachers, similar to students, solved some of the realistic problems unrealistically without taking the realistic contexts seriously. Besides, they evaluated students’ nonrealistic answers higher than the realistic answers. Whether the preservice teachers could solve problems realistically or not, they did not appreciate students’ realistic considerations for the reasons that those were not fitted to the intentions of the word problems, or those were evidence of the flaws of the problem. Furthermore, the analysis of premises implied in the preservice teachers’ evaluation comments showed the implicit didactic contracts about realistic word problem solving that they accepted and also anticipated students to follow. Our analysis of the preservice teachers’ conceptions of realistic word problems can help teacher educators design the teacher program to challenge and revise preservice teachers’ folk pedagogy.

An analysis of characteristics of the perception for mathematics learning of Korean language learners in 6th grade of elementary school
도주원 Do¸ Joowon
60(4) 529542, 2021
도주원 Do¸ Joowon
DOI: JANT Vol.60(No.4) 529542, 2021
The purpose of this research is to compare the mathematical beliefs that directly or indirectly affect the mathematics learning of Korean languge learners with those of nonKorean languge learners and identify the characteristics. To this end, an analytical comparative research was conducted through a questionnaire survey on perceptions of mathematics learning for 6th grade students of elementary school with different cultural and linguistic backgrounds in the same mathematics classroom. As a result of the analysis, Korean languge learners and nonKorean languge learners gave different meanings to learning mathematics, and they recognized various meanings of success in mathematics. In addition, the math learning ability of nonKorean learners was evaluated higher than that of Korean learners. Based on their positive beliefs, they decided how to resolve conflict situations with different problemsolving results. It will be necessary to prepare a teaching/learning plan that can fully implement multicultural mathematics education in the mathematics classroom where Korean language learners with different cultural and linguistic backgrounds belong. The results of this research can contribute to raising awareness of the need for followup researches to find ways to reduce the learning gap between Korean languge learners and nonKorean languge learners. It is expected that this research will contribute to understanding the perceptive characteristics of Korean language learners about learning mathematics and to prepare a plan to utilize them in mathematics lessons.

A study on the use of continuous spectrum in problem solving in a dynamic geometry environment
허남구 Heo¸ Nam Gu
60(4) 543554, 2021
허남구 Heo¸ Nam Gu
DOI: JANT Vol.60(No.4) 543554, 2021
The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method.
In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students.
The continuous spectrum can be used in the ‘Understand the problem’ of Polya(1957)’s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the ‘Devise a plan’ stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis.
The continuous spectrum can be used in the ‘Review/Extend’ stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem.
Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students’ geometric learning.

Exploring the factors of situational interest in learning mathematics
박주현 Park¸ Joo Hyun , 한선영 Han¸ Sunyoung
60(4) 555580, 2021
박주현 Park¸ Joo Hyun , 한선영 Han¸ Sunyoung
DOI: JANT Vol.60(No.4) 555580, 2021
The purpose of this study is to explore the factors of situational interest in math learning, and based on the results, to reveal the factors of situational interest included in teaching and learning methods, teaching and learning activities in mathematics class, and extracurricular activities outside of class. As a result of conducting a questionnaire to high school students, the factors of situational interest in learning mathematics were divided into 10 detaildomain(Enjoy, Curiosity, Competence / Real life, Other subjects, Career / Prior knowledge, Accumulation knowledge / Transformation, Analysis), 4 generaldomain(Emotion, Attitude / Knowledge, Understanding), 2 higherdomain(Affective / Cognitive) were extracted. In addition, it was revealed that various factors of situational interest were included teaching and learning methods, teaching and learning activities and extracurricular activities. When examining the meaning of 10 situational interest factors, it can be expected that the factors for developing individual interest are included, so it can be expected to serve as a basis for expanding the study on the development of individual interest in mathematics learning. In addition, in order to maintain individual interest continuously, it is necessary to maintain situational interest by seeking continuous changes in teaching and learning methods in the school field. Therefore, it can be seen that the process of exploring the contextual interest factors included in teachercentered teaching and learning methods and studentcentered teaching and learning activities and extracurricular activities is meaningful.
