Inquiry of Quadratic Curves According to Definition on Taxicab Geometry
허남구 Heo Nam Gu
31(2) 103121, 2017
허남구 Heo Nam Gu
DOI: JANT Vol.31(No.2) 103121, 2017
Taxicab geometry was a typical nonEuclid geometry for mathematically gifted. Most educational material related quadratic curves on taxicab geometry for mathematically gifted served them to inquire the graph of the curves defined by focis and constant. In this study, we provide a shape of quadratic curves on taxicab geometry by applying three definitions(geometric algebraic definition, eccentricity definition, conic section definition).

An Exploration of the conditions of operating mathematics instruction in accordance with the national curriculum in Korea
최승현 Choe Seunghyun , 황혜정 Hwang Hye Jeang
31(2) 123138, 2017
최승현 Choe Seunghyun , 황혜정 Hwang Hye Jeang
DOI: JANT Vol.31(No.2) 123138, 2017
It is necessary to examine how operation and management of instruction in school field be affected by the curriculum. This study examines the actual conditions of instruction provided by teachers while expecting to be adjusted the curriculum with respect to the consideration given to individual student needs and regional specialization by focusing on the subject of mathematics. Ultimately, the purpose of this study is to assess and expect how well mathematics instruction would be being conducted in accordance with the goals of the curriculum. Furthermore, while reflecting the experimental result on teachers` opinions of the previous curriculum, this study suggests alternatives and supporting plans so that at the teacher level the curriculum might be successfully implemented.

Criticism and alternatives of calculus history described by secondary school mathematics textbooks  Focusing on the history of calculus until the 17th century 
김상훈 Kim Sang Hoon , 박제남 Park Jeanam
31(2) 139152, 2017
김상훈 Kim Sang Hoon , 박제남 Park Jeanam
DOI: JANT Vol.31(No.2) 139152, 2017
In this paper, we examine how secondary school mathematics textbooks on calculus introduce the history of calculus. In order to identify the problem, we consider the Babylonian integration by trapezoidal rule, which was made to calculate the location of Jupiter in 35050 B.C., and the integration by the method of the rotating plate of ibn alHaytham in Egypt, about 1000 years. In conclusion, our secondary school mathematics textbooks describe Newton and Leibniz as inventing calculus and place their roots in ancient Greece. The origin of the calculus is in Babylonia and the Fatimah Dynasty (9091171) (Egypt) and it is desirable that the calculus is developed in Europe after the development of the power series in India, and that the value of Asia Africa is introduced in the textbooks.

Teachers` Decision and Enactment of Their Content Knowledge Assessed Through Problem Posing  A U.S. Case
노지화 Noh Jihwa
31(2) 153166, 2017
노지화 Noh Jihwa
DOI: JANT Vol.31(No.2) 153166, 2017
164 preservice elementary teachers` decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

A analysis of the elementary school and the middle school mathematics education as a curriculum qualitymanagement
김선희 Kim Sun Hee , 이승미 Seungmi Lee
31(2) 167185, 2017
김선희 Kim Sun Hee , 이승미 Seungmi Lee
DOI: JANT Vol.31(No.2) 167185, 2017
The purpose of this study is to analyze the actual states of the elementary school and the middle school mathematics education as a curriculum qualitymanagement. To this end, this study surveyed the input, process and output phase in the school curriculum to the teachers, students and parents. The results are like these: First, the achievement standards contents in the elementary school and the middle schools are relevant in the input phase. Second, the teachers in the elementary school have more concern on the teaching & learning methods than those in the middle school in the process phase. Third, students and parents` satisfaction on the cognitive and affective domain in the elementary school is higher than that in the middle school in the output phase. This study suggests that these result has to be affected to make ways to apply the new curriculum, and the curriculum revision system has to be established to revise the curriculum as an important method of quality management

A Causal Model Analysis of NonCognitive Characteristics of Mathematics Learning
이환철 Lee Hwan Chul , 김형원 Kim Hyung Won , 백승근 Baeck Seunggeun , 고호경 Ko Ho Kyoung , 이현숙 Yi Hyun Sook
31(2) 187202, 2017
이환철 Lee Hwan Chul , 김형원 Kim Hyung Won , 백승근 Baeck Seunggeun , 고호경 Ko Ho Kyoung , 이현숙 Yi Hyun Sook
DOI: JANT Vol.31(No.2) 187202, 2017
The study in this paper, which is part of a bigger study investigating noncognitive characteristics of Korean students at the 412 grade levels, aims to identify the influential characteristics that explain students` decision to give up on mathematics learning. We consider seven noncognitive student characteristics: value, interest, attitudes, external motivation, internal motivation, learning conation and efficacy. Data were collected from 21,485 Korean students, and were analyzed with a logistic regression method using SPSS. The findings show that efficacy was the most significant indicator of students` decision to give up on mathematics learning in all three grade level bands: elementary (4th6th), middle (7th9th) and high (10th12th). In particular, the causal model analysis shows that students who highly value mathematics tend to have stronger internal and external motivation, which bring about stronger interest and learning conation, which in turn lead to positive attitudes and strong efficacy regarding the learning of mathematics. It was further found that while external motivation was a significant indicator of upper grade level students` decision to give up on mathematics learning, it was only a moderate indicator for lower grade level students. The findings of this study provide useful information about which noncognitive areas need to be focused on, in what grade levels, to help students stay on track and not fall behind in learning mathematics.

Suggestion and Application of Didactical Principles for Using Mathematical Teaching Aids
이경화 Lee Kyeong Hwa , 정혜윤 Jung Hye Yun , 강완 Kang Wan , 안병곤 Ahn Byoung Gon , 백도현 Baek Do Hyun
31(2) 203221, 2017
이경화 Lee Kyeong Hwa , 정혜윤 Jung Hye Yun , 강완 Kang Wan , 안병곤 Ahn Byoung Gon , 백도현 Baek Do Hyun
DOI: JANT Vol.31(No.2) 203221, 2017
The purpose of this study is to suggest didactical principles for using mathematical teaching aids and to applicate didactical principles in a relation with curriculum. First, we metaanalyzed related literature to suggest didactical principles for using mathematical teaching aids. And we suggested didactical principles as follows: principle of activities, principle of instruments, principle of learning. Using mathematical teaching aids with didactical principles in mind would help avoiding situations in which mathematical teaching aids are only used as interesting tools. Second, we concretized the meaning to applicate didactical principles and use mathematical teaching aids in a relation with curriculum. We considered domain, key concept, function, achievement standard, which were presented in the curriculum of mathematics, and suggested concrete activities. Third, we produced two designs for lessons on incenter and circumcenter of triangle and linear function`s graph using mathematical teaching aids.

A design of teaching units for experiencing mathematising of elementary gifted students: inquiry into the isoperimetric problem of triangle and quadrilateral
최근배 Keunbae Choi
31(2) 223239, 2017
최근배 Keunbae Choi
DOI: JANT Vol.31(No.2) 223239, 2017
In this paper, it is aimed to design the teaching units `Inquiry into the isoperimetric problem of triangle and quadrilateral` to give elementary gifted students experience of mathematization. For this purpose, the teacher and the class observer (researcher) made a discussion about the design of the teaching unit through the analysis of the class based on the thought processes appearing during the problem solving process of each group of students. The following is a summary of the discussions that can give educational implications. First, it is necessary to use mathematical materials to reduce students` cognitive gap. Second, it is necessary to deeply study the relationship between the concept of side, which is an attribute of the triangle, and the abstract concept of height, which is not an attribute of the triangle. Third, we need a lowlevel deductive logic to justify reasoning, starting from inductive reasoning. Finally, there is a need to examine conceptual images related to geometric figure.
