Development and application of the program for students with underachievement of math in high school  On the case of ADDIE model 
오택근 Oh Taekkeun
57(4) 329352, 2018
오택근 Oh Taekkeun
DOI: JANT Vol.57(No.4) 329352, 2018
This study analyzed each process of demand analysis(A), design(D), development(D), implementation(I) and evaluation(E) of the program to support mathematics learning of students with underachievement of math in high school. To analyze the demand, a survey was conducted on 235 high school math teachers and 334 high school students who were underachieved in mathematics. To design and develope the program, this study linked middle school math to high school math so that the students with poor math learning could easily participate in mathematics learning. The programs developed in this study were implemented in three high schools, where separate classes were organized and run for students with poor math learning. The evaluation of the programs developed in this study was done in two ways. One was a quantitative evaluation conducted by five experts, and the other was a qualitative evaluation conducted through interviews with teachers and students participating in the program. This study found that students with poor mathematics learning were more motivated to learn, started to do mathematics, and encouraged to be confident when using learning materials that included easy problems and detailed solutions that they could solve themselves. From these results, the following three implications can be derived in developing a program to support students who are experiencing poor mathematics learning in high school. First, we should develop learning materials that link middle school mathematics to high school mathematics so that students can supplement middle school mathematics related to high school mathematics. Second, we need to develop learning materials that include detailed solutions to basic examples and include homogeneous problems that can be solved while looking at the basic example’s solution process. Third, we should avoid the challenge of asking students who are underachieving to respond too openly.

A case study on student's thoughts and expressions on various types of geometric series tasks
이동근 Lee Dong Gun
57(4) 353369, 2018
이동근 Lee Dong Gun
DOI: JANT Vol.57(No.4) 353369, 2018
This study started with the following questions.
Suppose that students do not accept various forms of geometric series tasks as the same task. Also, let's say that the approach was different for each task. Then, when they realize that they are the same task, how will students connect the different approaches?
This study is a process of proactively confirming whether or not such a question can be made. For this purpose, three students in the second grade of high school participated in the teaching experiment. The results of this study are as follows. It also confirmed how the students think about the various types of tasks in the geometric series. For example, students have stated that the value is 1 in a series type of task. However, in the case of the 0.999... type of task, the value is expressed as less than 1. At this time, we examined only mathematical expressions of students approaching each task. The problem of reachability was not encountered because the task represented by the series symbol approaches the problem solved by procedural calculation. However, in the 0.999... type of task, a variety of expressions were observed that revealed problems with reachability.
The analysis of students' expressions related to geometric series can provide important information for infinite concepts and limit conceptual research. The problems of this study may be discussed through related studies. Perhaps more advanced research may be based on the results of this study. Through these discussions, I expect that the contents of infinity in the school field will not be forced unilaterally because there is no mathematical error, but it will be an opportunity for students to think about the learning method in a natural way.

Manifestation examples of group creativity in mathematical modeling
정혜윤 Jung Hye Yun , 이경화 Lee Kyeong Hwa
57(4) 371391, 2018
정혜윤 Jung Hye Yun , 이경화 Lee Kyeong Hwa
DOI: JANT Vol.57(No.4) 371391, 2018
The purpose of this study is to analyze manifestation examples and effects of group creativity in mathematical modeling and to discuss teaching and learning methods for group creativity. The following two points were examined from the theoretical background. First, we examined the possibility of group activity in mathematical modeling. Second, we examined the meaning and characteristics of group creativity. Six students in the second grade of high school participated in this study in two groups of three each. Mathematical modeling task was “What are your own strategies to prevent or cope with blackouts?”. Unit of analysis was the observed types of interaction at each stage of mathematical modeling. Especially, it was confirmed that group creativity can be developed through repetitive occurrences of mutually complementary, conflictbased, metacognitive interactions. The conclusion is as follows. First, examples of mutually complementary interaction, conflictbased interaction, and metacognitive interaction were observed in the realworld inquiry and the factorfinding stage, the simplification stage, and the mathematical model derivation stage, respectively. And the positive effect of group creativity on mathematical modeling were confirmed. Second, example of non interaction was observed, and it was confirmed that there were limitations on students' interaction object and interaction participation, and teacher's failure on appropriate intervention. Third, as teaching learning methods for group creativity, we proposed students' role play and teachers' questioning in the direction of promoting interaction.

The impacts of teacher education on students’ academic achievement and satisfaction in mathematics lessons
Suh Heejoo , Bae Yunhee , Lee Ji Su , Han Sunyoung
57(4) 393412, 2018
Suh Heejoo , Bae Yunhee , Lee Ji Su , Han Sunyoung
DOI: JANT Vol.57(No.4) 393412, 2018
Teacher quality is a key factor that determines quality of education. Being aware of this, the Korean government and teachers have been striving to improve teachers’ professionalism. Research about the impacts of efforts to enhance teacher professionalism on students’ academic achievement and course satisfaction, however, is extremely limited. This study sought to advance our understanding of the relationship between these factors by analyzing what teacher characteristics impact students’ achievement and satisfaction. To this end, the study drew on the middle and high school data from 3rd to 6th year survey of the Seoul Educational Longitudinal Study. Structural equational modeling were used as the main approach. Latent profile analysis, a kind of mixture modeling analysis, were used as needed. This study found that teachers’ participation in instruction enhancement activity and professional development impact students’ attitude toward mathematics lessons and their perception on class atmosphere, and ultimately impact their academic achievement as well as their overall satisfaction in the course. In addition, teachers’ use of EBS textbooks and videos impact 3rd grade high schoolers’ academic achievement. These findings suggest that effort to improve teacher professionalism positively impact students’ academic achievement and course satisfaction, although there is a difference according to the year grade. This study provides implications for education policy makers and teacher educators.

An application and development of an activity lesson guessing a population ratio by sampling with replacement in 'Closed box'
이기돈 Lee Gi Don
57(4) 413431, 2018
이기돈 Lee Gi Don
DOI: JANT Vol.57(No.4) 413431, 2018
In this study, I developed an activity oriented lesson to support the understanding of probabilistic and quantitative estimating population ratios according to the standard statistical principles and discussed its implications in didactical respects. The developed activity lesson, as an efficient physical simulation activity by sampling with replacement, simulates unknown populations and real problem situations through completely closed 'Closed Box' in which we can not see nor take out the inside balls, and provides teaching and learning devices which highlight the representativeness of sample ratios and the sampling variability. I applied this activity lesson to the gifted students who did not learn estimating population ratios and collected the research data such as the activity sheets and recording and transcribing data of students' presenting, and analyzed them by Qualitative Content Analysis. As a result of an application, this activity lesson was effective in recognizing and reflecting on the representativeness of sample ratios and recognizing the random sampling variability. On the other hand, in order to show the sampling variability clearer, I discussed appropriately increasing the total number of the inside balls put in 'Closed Box' and the active involvement of the teachers to make students pay attention to controlling possible selection bias in sampling processes.

Reconstruction and application of an analytic framework for discursive approach to interpretations of graphThe case of a Korean textbook and CMP
김원 Kim Won , 최상호 Choi Sangho , 김동중 Kim Dongjoong
57(4) 433452, 2018
김원 Kim Won , 최상호 Choi Sangho , 김동중 Kim Dongjoong
DOI: JANT Vol.57(No.4) 433452, 2018
The purpose of this study is to provide implications for improvement of mathematics textbook based on discursive approach to textbook analysis that complementarily combines a communicational approach to cognition and social semiotics. For this purpose, we reconstructed an analytic framework for discursive approach to written discourses of Korean textbook and CMP, and applied it to our analysis. Results show that several characteristics in meanings were developed by the use of words and visual mediators. First, in the case of ideational meaning, there were qualitative and quantitative differences between vocabularies used and between information addressed by visual mediators. Second, in the case of structural meaning, an offer and application of procedure was emphasized in a Korean textbook, whereas expectation and selection experiences of diverse possibilities for problem solving was underlined in CMP. In the case interpersonal meaning of studentauthor, imperative instructions were paid attentions in a Korean textbook. In contrast, students’ interdependence and active participation were stressed in CMP. Therefore, this study addressed ideas about how to analyze mathematics textbooks based on integrated meanings developed by the use of words and visual mediators. In addition, it distributes implications for improvements of Korean mathematics textbooks through the analytic framework of both mathematical meanings and interpersonal meanings of studentauthor.

Examining how elementary students understand fractions and operations
박현재 Park Hyunjae , 김구연 Kim Gooyeon
57(4) 453475, 2018
박현재 Park Hyunjae , 김구연 Kim Gooyeon
DOI: JANT Vol.57(No.4) 453475, 2018
This study examines how elementary students understand fractions with operations conceptually and how they perform procedures in the division of fractions. We attempted to look into students’ understanding about fractions with divisions in regard to mathematical proficiency suggested by National Research Council (2001). Mathematical proficiency is identified as an intertwined and interconnected composition of 5 strands conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. We developed an instrument to identify students’ understanding of fractions with multiplication and division and conducted the survey in which 149 6thgraders participated. The findings from the data analysis suggested that overall, the 6thgraders seemed not to understand fractions conceptually; in particular, their understanding is limited to a particular model of partwhole fraction. The students showed a tendency to use memorized procedureinvert and multiply in a given problem without connecting the procedure to the concept of the division of fractions. The findings also proposed that on a given problemsolving task that suggested a pathway in order for the students to apply or follow the procedures in a new situation, they performed the computation very fluently when dividing two fractions by multiplying by a reciprocal. In doing so, however, they appeared to unable to connect the procedures with the concepts of fractions with division.

A study of the inservice teachers’ and preservice teachers’ recognition the domain in the problem of the continuity of a function
이세형 Lee Se Hyung , 장현석 Chang Hyun Suk , 이동원 Lee Dong Won
57(4) 477491, 2018
이세형 Lee Se Hyung , 장현석 Chang Hyun Suk , 이동원 Lee Dong Won
DOI: JANT Vol.57(No.4) 477491, 2018
In this paper we study inservice teachers’ and preservice teachers’ recognition the domain in the problem concerning the continuity of a function. By a questionnaire survey we find out that most of inservice teachers and preservice teachers are understanding the continuity of a function as explained in high school mathematics textbook, in which the continuity was defined by and focused on comparing the limit with the value of the function. We also notice that this kind of definition for the continuity of a function makes them trouble to figure out whether a function is continuous at an isolated point, and to determine that a given function is continuous on a region by not considering its domain explicitly. Based on these results we made several suggestions to improve for inservice teachers and preservice teachers to understand the continuity of a function more exactly, including an introduction of a more formal words usage such as ‘continuous on a region’ in high school classroom.
