An analysis of solution methods by fifth grade students about ‘reverse fraction problems’
방정숙 Pang Jeongsuk , 조선미 Cho Seonmi
58(1) 120, 2019
방정숙 Pang Jeongsuk , 조선미 Cho Seonmi
DOI: JANT Vol.58(No.1) 120, 2019
As the importance of algebraic thinking in elementary school has been emphasized, the links between fraction knowledge and algebraic thinking have been highlighted. In this study, we analyzed the solution methods and characteristics of thinking by fifth graders who have not yet learned fraction division when they solved ‘reverse fraction problems’ (Pearn & Stephens, 2018). In doing so, the contexts of problems were extended from the prior study to include the following cases: (a) the partial quantity with a natural number is discrete or continuous; (b) the partial quantity is a natural number or a fraction; (c) the equivalent fraction of partial quantity is a proper fraction or an improper fraction; and (d) the diagram is presented or not. The analytic framework was elaborated to look closely at students’ solution methods according to the different contexts of problems. The most prevalent method students used was a multiplicative method by which students divided the partial quantity by the numerator of the given fraction and then multiplied it by the denominator. Some students were able to use a multiplicative method regardless of the given problem contexts. The results of this study showed that students were able to understand equivalence, transform using equivalence, and use generalizable methods. This study is expected to highlight the close connection between fraction and algebraic thinking, and to suggest implications for developing algebraic thinking when to deal with fraction operations.

Longitudinal mediation effect of mathematics class factors between goal perception and mathematics academic achievement on middle school students
정희선 Jung Hee Sun
58(1) 2139, 2019
정희선 Jung Hee Sun
DOI: JANT Vol.58(No.1) 2139, 2019
This study examines the longitudinal effect of goal perception, mathematics class factors(perceptions about mathematics teachers (PMT), mathematics classroom attitude), and mathematics academic achievement. This study consists of three research models. First, we examined the longitudinal change of goal perception, perceptions about mathematics teachers (PMT), mathematics classroom attitude, and mathematics academic achievement using latent growth curve modeling. Secondly, the slope of PMT is a critical mediator between the slope of goal perception and the slope of mathematics academic achievement. Finally, the slope of mathematics classroom attitude is a critical mediator between the slope of goal perception and the slope of mathematics academic achievement.
Data were extracted from Seoul Education Longitudinal Study from 2010 to 2012 (in three waves), and the analysis used by middle school students, measured by 4163 students of the threewave surveys. Latent growth modeling was applied to verify the research problems. The results of the research are as follows. First, the slope of goal perception had positive and significant effects on the slope of PMT and mathematics classroom attitude, respectively. Second, the slope of PMT and mathematics classroom attitude had positively significant effects on the slope of mathematics academic achievement. Finally, it was confirmed that the slopes of PMT and mathematics classroom attitude are critical mediators between the slope of goal perception and the slope of mathematics academic achievement.

The effects of career identity on learning persistence and academic achievement: Mediating effect of utility value
우연경 Woo Yeonkyoung , 김성경 Kim Seongkyeong , 최영인 Choi Youngin
58(1) 4154, 2019
우연경 Woo Yeonkyoung , 김성경 Kim Seongkyeong , 최영인 Choi Youngin
DOI: JANT Vol.58(No.1) 4154, 2019
The purpose of this study was to examine the effects of career identity on learning persistence and academic achievement, and mediating effect of utility value. To examine the effect of mediating role of utility value, we divided utility value into two types, utility value of daily matters and utility value of career. This study was conducted on 228 senior students in high school, to investigate relations among career identity, utility value, learning persistence and academic achievement in mathematics, by using the structural equation model. The results are as follows. First, career identity positively predicted learning persistence in mathematics. Second, career identity positively predicted the utility value of daily matters and career. Third, both type of utility value in mathematics positively predicted learning persistence in mathematics. Fourth, the utility value of daily matters and career, in mathematics subjects, showed differential predictability toward learning persistence and academic achievement. Both type of utility value in mathematics positively predicted learning persistence, but showed differential predictability toward learning academic achievement. Specifically, the utility value of daily matters in the near future did not predict the academic achievement, but the utility value of career in the distant future positively predicted the academic achievement. Fifth, the utility value was found to play a mediating role in the relationship between career identity and learning persistence. Based on the results of this study, implications for mathematics education were discussed.

Analysis on the relationship between core competencies and mathematical competencies and the tasks for mathematical competencies : A case of high school ‘Mathematics’ textbooks according to 2015 revised mathematics curriculum
윤상준 Yoon Sangjoon , 이아란 Lee Ahran , 권오남 Kwon Oh Nam
58(1) 5577, 2019
윤상준 Yoon Sangjoon , 이아란 Lee Ahran , 권오남 Kwon Oh Nam
DOI: JANT Vol.58(No.1) 5577, 2019
Textbooks play a very important role as a medium for implementing curriculum in the school. This study aims to analyze tasks for mathematical competencies in the high school ‘mathematics’ textbooks based on the 2015 revised mathematics curriculum emphasizing competencies. And our study is based on the following two research question.
1. What is the relationship between core competencies and mathematical competencies?
2. What is the distribution of competencies of tasks for mathematical competencies presented in the textbooks?
3. How does the tasks for mathematical competencies reflect the meaning of the mathematical competencies?
For this study, the tasks, marked mathematical competencies, were analyzed by elements of each mathematical competencies based on those concept proposed by basic research for the development of the latest mathematics curriculum.
The implications of the study are as follows. First, it is necessary to make efforts to strengthen the connection with core competencies while making the most of characteristics of subject(mathematics). Second, it needs to refine the textbook authorization standards, and it should be utilized as an opportunity to improve the textbook. Third, in order to realize competenciescentered education in the school, there should be development of teaching and learning materials that can be used directly.

A case study on students' expressions in solving the limitations of functions problems
이동근 Lee Dong Gun
58(1) 7999, 2019
이동근 Lee Dong Gun
DOI: JANT Vol.58(No.1) 7999, 2019
This study is a study to collect information about ‘Limitations of functions’ related learning. Especially, this study was conducted on three students who can find answers by algebraic procedure in the process of extreme problem solving. Students have had the experience of converting from their algebraic procedures to graphical expressions. This shows how they reflect on their algebraic procedures. This study is a study that observes these parts. To accomplish this, twelfth were teaching experiment in three high school students. And we analyzed the contents related to the research topic of this study. Through this, students showed the difference of expressions in the method of finding limits by using algebraic interpretation methods and graphs. In addition, we examined the connectivity of the limitations of functions problem solving process of functions using algebraic procedures and graphs in the process of converting algebraic expressions to graph expressions.
This study is a study of how students construct limit concepts. As in this study, it is meaningful to accumulate practical information about students' limit conceptual composition. We hope that this study will help students to study limit concept development process for students who have no limit learning experience in the future.

Exploring Changes in Multiethnic Students’ Mathematics Achievement Motivation : A Longitudinal Study using ExpectancyValue Theory
조은혜 Eunhye Cho , 황성환 Sunghwan Hwang
58(1) 101120, 2019
조은혜 Eunhye Cho , 황성환 Sunghwan Hwang
DOI: JANT Vol.58(No.1) 101120, 2019
The goal of this study was to apply an expectancyvalue model(Wigfield & Eccles, 2000) to explain changes in six multiethnic students’ achievement motivation in mathematics during sixth (2012) to eighth (2014) grades. In order to achieve this goal, we used narrative research methods. Although individual students’ achievement motivation and mathematics related life experiences differed, there are some common factors influencing their motivation development, especially (a) roles played by parents and teachers; (b) assessment of peers’ competencies; (c) past learning experiences related to mathematics curriculum; (d) perception of the relationship between mathematics competency and other subjects; (e) home backgrounds; and (f) perceived task values. In this study, we achieved some insight into why some multiethnic students are willing to study hard to get good scores while others are uninterested in mathematics, and why some multiethnic students are likely to pursue new mathematical tasks and persist despite challenges, while others easily give up studying mathematics in the face of adversity. We argue that in order to increase and sustain multiethnic students’ achievement motivation, educators and parents should recognize that motivation is contextually formulated in the intersection of current people, time, and space, not a personal entity formed in an individual’s mind. The findings of this study shed light on the development of achievement motivation and can inform efforts to develop multiethnic students’ positive motivation, which might influence their mathematics achievement and success in school.

Domestic research trends of mathematics teacher education: Focused on the journals published since 2000 by the Korean Society of Mathematics Education
선우진 Sunwoo Jin , 방정숙 Pang Jeongsuk
58(1) 121138, 2019
선우진 Sunwoo Jin , 방정숙 Pang Jeongsuk
DOI: JANT Vol.58(No.1) 121138, 2019
The purpose of this study was to analyze the trends of domestic research on mathematics teacher education in terms of the period, topics, methods, subjects, and mathematics content strands. For this purpose, a total of 220 research articles dealing with mathematics teacher education were analyzed, which have been published since 2000 by the Korean Society of Mathematics Education in the three journals: (a) The Mathematical Education; (b) Education of Primary School Mathematics; and (c) Communications of Mathematical Education. Regarding the period when the research was conducted, the number of articles on mathematics teacher education has been rapidly increased since the late 2000s. Regarding the topics, research on teacher orientation has been the most frequent topic and the studies dealing with professional development for teachers, teaching practices, or teacher knowledge tend to be popular. Regarding methods, survey and case study have been most frequently employed in studying mathematics teacher education. Regarding subjects, the main participants were inservice teachers, preservice teachers, elementary school teachers, and secondary school teachers, respectively, who were in charge of a regular class. Finally, regarding mathematics content strands, previous studies on mathematics teacher education were not specific to mathematics content strands. Given these results, this paper closes with important implications for future research directions on mathematics teacher education in Korea.

How middleschool mathematics textbooks of Korea and the US support to develop students’ statistical reasoning
이선정 Lee Sunjung , 김구연 Kim Gooyeon
58(1) 139160, 2019
이선정 Lee Sunjung , 김구연 Kim Gooyeon
DOI: JANT Vol.58(No.1) 139160, 2019
This study attempts to examine statistical tasks in the middleschool mathematics textbooks of Korea and Connected Mathematics 3 [CMP] of the US in terms of an opportunitytolearn for statistical reasoning. We utilized an analytical framework consisting of types of context, statistical reasoning level, cognitive demand of the tasks, and types of student response. The findings from the task analysis suggested that Korean textbooks focused on finding answers by applying previously learned algorithms or formulas and thus provided students with very limited opportunities to experience statistical reasoning. Also, the results proposed that the mathematical tasks in statistics unit of CMP3 offer more essential and complex tasks that promote students’ conceptual understanding of various statistical ideas and statistical reasoning in a meaningful way.
