Examining Pre and Inservice Mathematics Teachers’ Proficiencies in Reasoning and ProofProduction
유은수 Yoo Eunsoo , 김구연 Kim Gooyeon
58(2) 161185, 2019
유은수 Yoo Eunsoo , 김구연 Kim Gooyeon
DOI: JANT Vol.58(No.2) 161185, 2019
This study aims to examine pre and inservice mathematics teachers’ reasoning and how they justify their reasoning. For this purpose, we developed a set of mathematical tasks that are based on mathematical contents for middle grade students and conducted the survey to pre and inservice teachers in Korea. Twentyfive preservice teachers and 8 inservice teachers participated in the survey. The findings from the data analysis suggested as follows: a) the pre and inservice mathematics teachers seemed to be very dependent of the manipulation of algebraic expressions so that they attempt to justify only by means of procedures such as known algorithms, rules, facts, etc., rather than trying to find out a mathematical structure in the first instance, b) the proof that teachers produced did not satisfy the generality when they attempted to justify using by other ways than the algebraic manipulation, c) the teachers appeared to rely on using formulas for finding patters and justifying their reasoning, d) a considerable number of the teachers seemed to stay at level 2 in terms of the proof production level, and e) more than 3/4 of the participating teachers appeared to have difficulty in mathematical reasoning and proof production particularly when faced completely new mathematical tasks.

A comparative study on the external & internal structure of mathematics curriculum between Korea and Japan : Focusing on the aspects of recent revisions
권오남 Kwon Oh Nam , 이경원 Lee Kyungwon , 이아란 Lee Ahran , 한채린 Han Chaereen
58(2) 187223, 2019
권오남 Kwon Oh Nam , 이경원 Lee Kyungwon , 이아란 Lee Ahran , 한채린 Han Chaereen
DOI: JANT Vol.58(No.2) 187223, 2019
This study aims to investigate the aspects of revision in the external and internal structure of curriculum and documentation in Korea and Japan and to propose the direction and task to enhance the current framework of the national curriculum. Japan has been selected for comparison in that it explicitly prepared social changes such as the dramatic evolution of artificial intelligence and population aging in its new curriculum. Therefore, various aspects of revision were analyzed the 2009 & 2015 revised mathematics curriculum of Korea and the 2008 & 2017 mathematics curriculum of Japan respectively in the elementary, middle, and high school grade bands. Then, the differences between the two countries were identified through comparison. First, the structure of the mathematics curriculum in Japan was connected with the general guidelines more tightly than Korea, and the external structure of the mathematics curriculum stayed consistently after the revision. Second, contrary to Korea, which pursued the appropriateness and reduction of mathematical content, Japanese mathematics curriculum has been pursuing detailed contents both quantitatively and qualitatively. Lastly, Japan emphasized statistical problemsolving ability. Based on this, we suggested considering of consistency in the structure curriculum documentation, detailing contents of the curriculum, and strengthening of statistical education.

The connection between illustrations and contents in elementary mathematics textbooks
홍갑주 Hong Gap Ju
58(2) 225237, 2019
홍갑주 Hong Gap Ju
DOI: JANT Vol.58(No.2) 225237, 2019
The picture of the mathematics curriculum should carry the complex role of relieving the difficulties of mathematics while conveying the core of the mathematics contents well. This study examined the precedence of picture and text harmony and the importance of emotional expression. The discussion of children's picture books became an important reference in this process. The understanding of the child's psychology and cognitive characteristics in the long history of picture books and the insight into the relationship between text and pictures will be important guidelines for elementary school textbooks. Based on these previous studies, this study found some impressive examples of Chinese, Japanese, Indian, and American textbooks on the two complementary relationships between paintings and texts and emotional expressions of paintings. If necessary, we compared these textbooks with Korean textbooks. Through this analysis, this study draws some implications for Korean textbook drawing and textbook production process. That is, the process of reading the picture and interpreting its meaning should be treated as part of the study of mathematics. The mathematical concepts to be dealt with or the sentence description of the problem should be concurrent with the design of the picture. The monotonous expressions and dialogues of characters in textbooks should be avoided, and the personality and emotions of characters should be more abundant and freely expressive.

A study on the student's question about the existence of the inverse function for the task that connects the two correspondence relations
이동근 Lee Dong Gun
58(2) 239262, 2019
이동근 Lee Dong Gun
DOI: JANT Vol.58(No.2) 239262, 2019
This study deals with the anxieties that originated from specific student questions. Through the analysis of the textbooks, we confirmed that the question was a sufficiently plausible question. Third interviews were also held with three high school students. Through the interviews, we analyzed students' expressions about the new correspondence relationship that the two correspondence relations are linked. In the determination of the composite function and the determination of the inverse function existence,
We have observed a case of how the worries about domain are being reconstructed from students into meaningful mathematical knowledge. Through this, we confirmed that the question will be confusing to students in the field. In this study, we observed the transfer of domain in relation to student domain in composite function. In particular, a present study revealed that the students involved in the interview were influenced by this domain transfer phenomenon in determining whether the task given in the interview was a function. This was the same in determining the existence of a inverse function. The examples presented in this study are limited to specific cases in limited circumstances. Therefore, it can not be applied directly to teaching and learning situations.
However, it is expected that this study will provide other researchers with insight into function learning related research.

Analysis of the issues derived from the implementation of the 2015 revised mathematics curriculum in 1^{st} and 2^{nd} grade
김성경 Kim Seongkyeong , 오택근 Oh Taekkeun
58(2) 263282, 2019
김성경 Kim Seongkyeong , 오택근 Oh Taekkeun
DOI: JANT Vol.58(No.2) 263282, 2019
The purpose of this study is to analyze the implementation of 2015 revised mathematics curriculum. This study focused on issues raised from the implementation. The teachinglearning methods for enhancing mathematical competencies, the amount and difficulty of mathematics in the 1st and 2nd grade, the level of vocabulary and sentence for students in the textbooks, and the support for successful implementation of the curriculum were collected and analyzed through questionnaires and interviews. As a result of the research, most of the teachers tried to improve the teaching and learning method considering mathematical competencies, but had difficulty in connecting contents and competencies. They also recognized that the amount and difficulty in the 1st and 2nd grade math, and the level of vocabulary and sentences presented in math textbooks were generally appropriate. However, they pointed out that the textbooks were overemphasized in various ways out of basic calculation methods, and that the long sentences, which are not easy to read and understand by students who are not familiar with reading Korean, are included in the < Soohak Ikhim >. They recognised that there is a large difference in level of reading Korean and understanding math among students. So we suggest that more active support is needed for the students who are learning slowly and the students who are having difficulty in reading Korean.

A study on the performance of sixthgrade elementary school students about the perimeter and area of plane figure and the surface area and volume of solid figure
임영빈 Yim Youngbin , 임예은 Yim Yeeun , 김수미 Km Soo Mi
58(2) 283298, 2019
임영빈 Yim Youngbin , 임예은 Yim Yeeun , 김수미 Km Soo Mi
DOI: JANT Vol.58(No.2) 283298, 2019
Among the measurement attributes included in the elementary school mathematics curriculum, perimeter, area, volume and surface area are intensively covered in fifth and sixth graders. However, not much is known about the level of student performance and difficulties in this area. The purpose of this study is to examine the understanding and performance of sixthgrade elementary school students on some ideas of measurement and ultimately to give some suggestions for teaching measurement and the development of mathematics textbooks. For this, diagnosis questions were developed in relation to the following parts: measurement of perimeter and area of plane figure, measurement of surface area and volume of solid figure, and the relationships between perimeter and area, and the relationships between surface area and volume. The performances of 95 sixth graders were analyzed for this study. The results showed children's low performance in the measurement area, especially measurement of perimeter and surface area, and relationship of the measurement concepts. Finally, we proposed the introduction order of the measurement concepts and what should be put more emphasis on teaching measurement. Specifically, it suggested that we consider placing a less demanding concept first, such as the area and volume, and dealing more heavily with burdensome tasks such as the perimeter and surface area.

Change of teacher knowledge through task design in the teacherresearcher community : Focused on knowledge of students in the area of derivatives application
이경화 Lee Kyeonghwa , 송창근 Song Changgeun , 정혜윤 Jung Hyeyun
58(2) 299317, 2019
이경화 Lee Kyeonghwa , 송창근 Song Changgeun , 정혜윤 Jung Hyeyun
DOI: JANT Vol.58(No.2) 299317, 2019
In this study, we analyzed the change of teacher knowledge through task design in the teacherresearcher community focused on knowledge of students in the area of derivatives application. The following subjects were studied. First, we have analyzed the focus of the discussion related to teacher knowledge of students within the teacherresearcher community. Second, we have analyzed the change of teacher knowledge of students according to the focus. The results of this study are as follows. First, community member’ different knowledge of students led the discussion on the task solving paths. The main focus of the discussion was the possibility in inducing responses and motivation. Second, the process of reviewing and evaluating task solving paths and reaching consensus led the improvement of teacher knowledge. Teachers and researchers led changes of teacher knowledge by sharing the knowledge based on previous research and experience, respectively. This ultimately shows the necessity of colearning between teachers and researchers in teacher education.

An analysis of the algorithm efficiency of conceptual thinking in the divisibility unit of elementary school
최근배 Choi Keunbae
58(2) 319335, 2019
최근배 Choi Keunbae
DOI: JANT Vol.58(No.2) 319335, 2019
In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.
