The Fourth Industrial Revolution and College Mathematics Education6)  Case study of Linear Algebra approach 
이상구 Lee Sanggu , 이재화 Lee Jae Hwa , 김영록 Kim Young Rock , 함윤미 Ham Yoonmee
32(3) 245255, 2018
이상구 Lee Sanggu , 이재화 Lee Jae Hwa , 김영록 Kim Young Rock , 함윤미 Ham Yoonmee
DOI: JANT Vol.32(No.3) 245255, 2018
In this paper, we discuss efforts that has been made by mathematics departments in Korea to meet the need of the 4th industrial revolution era. First of all, we introduce various industrial mathematics programs that some universities in Korea started to provide in order to nurture math/math education graduate to be prepared for the demand of the society. We also introduced a mathematics for Big Data course that we did offer recently which can be shared.

On the Isoperimetric Problem of Polygons: the mathematical reasoning and proof with the Geometer’s Sketchpad
최근배 Choi Keunbae
32(3) 257273, 2018
최근배 Choi Keunbae
DOI: JANT Vol.32(No.3) 257273, 2018
In this paper, we deal with the isoprimetric problem of polygons from the point of view of learning materials for elementary gifted students. The isoperimetric problem of the polygon of odd degree can be solved by Etransformation(see Figure III1) and Mtransformation(see Figure III3). But in the case of even degree’s polygon, it is quite difficult to solve the problem because of the connected components of diagonals (here we consider the diagonals forming triangle with two adjacent sides of polygon). The primary purpose of this paper is to give an idea to solve the isoperimetric problem of polygons of even degree using the properties of ellipse. This idea is derived from the programs of the Institute of Science Education for Gifted Students in the Jeju National University.

Application of Eye Tracker for Study on the Effect of Analytic Proof Learning of Gifted Students
정경우 Jung Kyungwoo , 윤종국 Yun Jonggug , 이광호 Lee Kwang Ho
32(3) 275296, 2018
정경우 Jung Kyungwoo , 윤종국 Yun Jonggug , 이광호 Lee Kwang Ho
DOI: JANT Vol.32(No.3) 275296, 2018
The purpose of this study is to investigate the change of gaze and the change of the proof learning achievement after learning the analytic method for proof to mathematical gifted students using eye tracking technique. In order to complete the purpose of this study, a mixed method research was used, that is a combination of quantitative and qualitative research methods. Quantitative analysis was conducted based on the data obtained through the eye tracker, and qualitative analysis was also done using post interview data to make up for the quantitative analysis. The subjects of this study were 8 mathematical gifted 3rd grade middle school students in the gifted education center. The conclusions of this study are as follows.
First, the learning of analysis leads to a change of gaze in the proof learning of students. The students, after learning the analysis, moved their gaze from the bottom to the top when solving the proof problem, and the occupancy rate of the gaze to the bottom of the proof was higher than the higher part.
Second, the change of gaze caused by the learning of the analysis have a correlation with the achievement of the proof learning and it can be seen that the method learning improves the achievement of the proof learning of the students.

Interpretation of Preservice Teachers’ Knowledge by ShulmanFischbein Framework : For Students’ Errors in Plane Figures
김지선 Kim Ji Sun
32(3) 297314, 2018
김지선 Kim Ji Sun
DOI: JANT Vol.32(No.3) 297314, 2018
This article aims at providing implication for teacher preparation program through interpreting preservice teachers’ knowledge by using ShulmanFischbein framework. ShulmanFischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers’ knowledge (mathematical algorithmic, formal, intuitive SMK and mathematical algorithmic, formal, intuitive PCK). To accomplish the purpose, five preservice teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students’ misconception in the area of geometry. The analysis revealed that preservice teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students’ misconception, preservice teachers did not deeply consider the levels of students’ thinking in that they asked 46 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students’ misconception, preservice teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that preservice teachers need to be provided with opportunity to investigate students’ conception and misconception.

The effect of the academic achievement and mathematics happiness index through a good teaching program in mathematics
안종수 An Jong Su
32(3) 315340, 2018
안종수 An Jong Su
DOI: JANT Vol.32(No.3) 315340, 2018
The purpose of this study was to increase having a happy school life, by applying a good teaching program in mathematics to create achieving happiness education which raised the students' dreams and talents. For this purpose, first, what was the effects on academic achievement through a good teaching program in mathematics. Second, what was the effect on the happiness index in mathematics learning through a good teaching program in mathematics. Third, what could raise the students' dreams and talents, when realized, to ensure that the students have happiness education. First, specific research issues for the realization of the objectives of this study were considering how to apply a good teaching program in mathematics. Second, what was the effect on students' academic achievement and mathematics happiness index through a good teaching program in mathematics? As a result of applying good teaching program in mathematics, there was a difference in academic achievement and could improve mathematical happiness index.

Development and Application of STEAM Education Model centered on Mathematics Subject using Reallife Context
반은섭 Ban Eunseob
32(3) 341362, 2018
반은섭 Ban Eunseob
DOI: JANT Vol.32(No.3) 341362, 2018
The purpose of this study is to develop a STEAM education model on the basis of mathematics curriculum using real life context, and to analyze the effect of the class based on developed model to make applicable pedagogical discussion. For this purpose, STEAM class materials that can be used in terms of recognition, connection, extension, and application of mathematical concepts, principles and laws are considered, taking into consideration the ways in which real life contexts and mathematical learning could be harmonized. As a results of using these materials, it was empirically confirmed that students' cognitive thinking and affective aspects abilities were improved. The STEAM instruction centered on the mathematics curriculum and the mathematics class based on the data developed in this study have a unique identity compared to the conventional general mathematics teaching methods using the textbooks. And it is pursuing the future class model which could present desirable creativity and personality education. The result of this study would provide preliminary data and meaningful implications to the researchers for next curriculum and concomitant instructional materials as well as the mathematics teachers.

A Study on the Development of Instruction Model on Project inquiry and Materials for the New Subject of 'Mathematical Task Inquiry' in the curriculum revised in 20155)
황혜정 Hwang Hye Jeang , 김주미 Kim Ju Mi
32(3) 363383, 2018
황혜정 Hwang Hye Jeang , 김주미 Kim Ju Mi
DOI: JANT Vol.32(No.3) 363383, 2018
The subject of 'Mathematical Task Inquiry' was introduced newly in the curriculum revised in 2015. The subject is dealt with after completing the subject of‘mathematics’to be dealt with in the tenth grade. Its main content is comprised of the understanding and learning of the purpose and procedure of inquiry task and of study ethics, and its educational goal is to enforce the prior mathematical knowledge and to obtain the ability to select interesting topics that combine mathematics with other subjects. However the textbook of the subject does not exist, and teachers should handle with the subject with responsibility for their own ways. Because of this reason, this study is to develop an instruction model on project(task) inquiry model and materials. Namely, according to the model, students is guided to select and decide the subject of the task, and develop the task for themselves, solve it with peers in cooperation, and announce the solution and their feelings. During those students’exploration and activities, the role of teachers is to guide students to complete their work. By the way, in order to develop more creative tasks that is appropriate to their academic and cognitive level, this study conducted the experimentation for the subject of 9 students (6 girls and 3 boys), who are scheduled to advance to the 11 grade of J high school located in G domestic. The experimentation was consisted of three class and after the third class, the semistructured interview was conducted immediately for the students.

The Effects of Mathematical Problem Posing Activities on 10th Grade Students’ Mathematics Achievement and Affective Characteristic of Mathematics
이재영 Lee Jaeyoung , 한혜숙 Han Hyesook
32(3) 385406, 2018
이재영 Lee Jaeyoung , 한혜숙 Han Hyesook
DOI: JANT Vol.32(No.3) 385406, 2018
The purpose of this study is to investigate the effect of mathematics classes focused on mathematical problem posing activities on 10th grade students’ mathematics achievement and affective characteristics of mathematics. This study was conducted in a total of 45 regular mathematics classrooms with 81 students from two classes through a nonequivalent control group design. The results of the study showed that the teaching method based on mathematical problem posing activities had a more positive effect on students' mathematics achievement and the affective characteristics of mathematics than the teaching method that focuses on problem solving. The teaching method based on problem posing activities proposed in this study could induce students' selfreflective learning motivation, which in turn gave them a more solid understanding of the mathematical concepts they had learned. In addition, it was found that students' problem solving ability, mathematical communication ability, and mathematical thinking ability were positively influenced by problem posing activities. Regarding the affective characteristics of mathematics, the mathematical problemposing activity suggested in this study turned out to be a very effective strategy for improving students' interest in mathematics.

A discursive approach to analysis of definition of graph in first year middle school textbooks1
김원 Kim Won , 최상호 Choi Sangho , 김동중 Kim Dongjoong
32(3) 407433, 2018
김원 Kim Won , 최상호 Choi Sangho , 김동중 Kim Dongjoong
DOI: JANT Vol.32(No.3) 407433, 2018
In order to analyze textbooks from a discursive approach, the purpose of this study is to structuralize an analytic framework based on previous literature review and apply it to analyzing the meanings and their syntheses developed by words and visual mediators appeared in the definition of graph in firstyear middle school textbooks. The discursive approach consists of the communicational approach developed by Sfard(2008) and the systemic functional linguistics developed by Halliday(1985/2004). In this study, ideational metafunctions for ideational meanings and interpersonal metafunctions for interpersonal meanings were employed to analyze the meanings produced by words and visual mediators in textbooks, whereas textual metafunctions for textual meanings were used for analyzing the synthesized relationships between words and visual mediators. Results show that first, density in mathematical discourse was very high and subjects in mathematical activities were ambiguous in the ideational meanings of words, and behavior aspect was more emphasized than thinking aspect in the interpersonal meanings of words which request student participations. In the case of ideational meanings of visual mediators, there was a lack of narrative diagrams, whereas there were qualitative differences in the case of offer. Second, there was a need for promoting a wide range of diverse synthetic relationships between words and visual mediators for developing enriched mathematical meanings through the varying uses like specification, explanation, similarity, and complement. These results are so important that they provide a new analytic framework from a discursive approach to textbook analysis because not only words, but also visual mediators are analyzed as tools for producing meanings in mathematics textbooks and their synthetic relationships are also examined.

The Characteristic Analysis of Content Areas and Behavioral Areas Based on the Deviation of NAEA Achievement LevelBased CorrectAnswer Rate
허난 Huh Nan , 양성현 Yang Seong Hyun
32(3) 435453, 2018
허난 Huh Nan , 양성현 Yang Seong Hyun
DOI: JANT Vol.32(No.3) 435453, 2018
The results analysis of National Assessment of Educational Achievement(NAEA) can provide various implications for teaching and learning in the school field. In this study we analyzed the deviation of NAEA achievement levelbased correctanswer rate and the distribution of the responses percentages for three years from 2015 to 2017 focused on multiplechoice items. First we calculated the deviation of correctanswer rate between advanced level and proficient level and between proficient level and basic level, and then we selected the items whose deviation of correctanswer rate is more than the third quartile. We explored what the content areas, behavior areas and achievement standards of each item are and what the achievement standards and characteristics of these questions are. Based on the results of the analysis, we intended to derive implications for appropriate teachinglearning methods at each achievementlevel.
