The algebraic completion of the rational numbers based on ATD
김부윤 Boo Yoon Kim , 정경미 Gyeong Mee Chung
50(2) 135148, 2011
김부윤 Boo Yoon Kim , 정경미 Gyeong Mee Chung
DOI: JANT Vol.50(No.2) 135148, 2011
We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

A study of the elementary teachers` perception about the situationcontextual problem in mathematics education
김민경 Min Kyeong Kim , 민선희 Sun Hee Min , 김혜원 Hye Won Kim
50(2) 149164, 2011
김민경 Min Kyeong Kim , 민선희 Sun Hee Min , 김혜원 Hye Won Kim
DOI: JANT Vol.50(No.2) 149164, 2011
The purpose of this study was to analyze the perception of elementary school teachers about situationcontextual problem and to show efforts on order to enable students to improve their problem solving ability and thinking skills. In this research, two hundred elementary school teachers in Seoul were surveyed and three elementary school teachers were interviewed to determine their perception and the status about situationcontextual problem. As a result, most of teachers replied that situationcontextual problem would be useful and applicable to improve students` problem solving and creative thinking skill.

The Case Study for the Development of Conception of a Graph and the Formula with the absolute value through the Mathematical Modeling
신경희 Kyung Hee Shin , 김연지 Yeon Ji Kim
50(2) 165184, 2011
신경희 Kyung Hee Shin , 김연지 Yeon Ji Kim
DOI: JANT Vol.50(No.2) 165184, 2011
The purpose of this study is to detect the possibility of the development of conception of a graph and the formula with the absolute value through context questions, and also to investigate the effectiveness of the each step of the mathematical modeling activities in helping students to have the conception. The research was conducted to analyze the process of development of the mathematical conception by applying the mathematical modeling activities two times to subjects of two academic high school students in the first grade. The results of the study are as follows: Firstly, the subjects were able to comprehend the geometric conception of the absolute value and to make the graph and the formula with the sign of the absolute value by utilizing the condition of the question. Secondly, the researcher set five steps of the intentional mathematical model in order to arouse the effective mathematical notion and each step performed a role in guiding the subjects through the mathematical thinking process in consecutive order; consequently, it was efficacious in developing the conception.

Effects of Spreadsheetused Instruction on Statistical Thinking and Attitude
이종학 Jong Hak Lee , 김원경 Won Kyoung Kim
50(2) 185212, 2011
이종학 Jong Hak Lee , 김원경 Won Kyoung Kim
DOI: JANT Vol.50(No.2) 185212, 2011
The purpose of this study is to analyze whether spreadsheetused instruction can improve statistical thinking ability and attitude and also to identify what characteristics of statistical thinking is constructed. For this study, a subject of 2 classes were randomly selected among the 12 classes of the 11th grader in D high school and designated one class as the experimental group and the other class as the control group. Eight hours of the spread sheetused instruction and the traditional textbookoriented instruction had been carried out in each class. The research findings are as follows. First, the spread sheetused instruction is shown to be more effective in enhancing statistical thinking than the traditional textbookoriented instruction. Second, the spread sheetused instruction is shown to be more effective in improving statistical altitude than the traditional textbookoriented instruction. Third, students have shown the various characteristics of statistical thinking in the data descriptive process, data arrangesummary process, data representing process, and data analying process through the spread sheetused instructions. Hence, the spread sheetused instruction is recommended in teaching statistics.

Case Study on the 6th Graders` Understanding of Concepts of Variable
하수현 Su Hyun Ha , 이광호 Gwang Ho Lee
50(2) 213231, 2011
하수현 Su Hyun Ha , 이광호 Gwang Ho Lee
DOI: JANT Vol.50(No.2) 213231, 2011
The purpose of this study is to analyze the 6th graders` understanding of the concepts of variable on various aspects of school algebra. For this purpose, the test of concepts of variable targeting a sixthgrade class was conducted and then two students were selected for indepth interview. The level of mathematics achievement of the two students was not significant1y different but there were differences between them in terms of understanding about the concepts of variable. The results obtained in this study are as follows: First, the students had little basic understanding of the variables and they had many cognitive difficulties with respect to the variables. Second, the students were familiar with only the symbol ``□``, not the other letters nor symbols. Third, students comprehended the variable as generalizers imperfectly. Fourth, the students` skill of operations between letters was below expectations and there was the student who omitted the mathematical sign in letter expressions including the mathematical sign such as x+3. Fifth, the students lacked the ability to reason the patterns inductively and symbolize them using variables. Sixth, in connection with the variables in functional relationships, the students were more familiar with the potential and discrete variation than practical and continuous variation. On the basis of the results, this study gives several implications related to the early algebra education, especially the teaching methods of variables.

The Approximate Realization of Abu Sahl`s Geometric Construction about a Heptagon through GSP using Conic Sections
김향숙 Hyang Sook Kim , 박진석 Jin Suk Pak , 하형수 Hyoung Soo Ha
50(2) 233246, 2011
김향숙 Hyang Sook Kim , 박진석 Jin Suk Pak , 하형수 Hyoung Soo Ha
DOI: JANT Vol.50(No.2) 233246, 2011
The geometry field in the current high school curriculum deals mainly with analytic geometry and the reference to logic geometry leaves much to be desired. This study investigated the construction on a heptagon by using conic sections as one of measures for achieving harmony between analytic geometry and logic geometry in the high school curriculum with the Geometer`s Sketchpad(GSP), which is a specialized software prevalent in mathematics education field and is intended to draw an educational suggestion on it.

Development and verification of an affective inventory in Mathematical Learning
이종희 Chong Hee Lee , 김선희 Sun Hee Kim , 김수진 Soo Jin Kim , 김기연 Ki Yeon Kim , 김부미 Bu Mi Kim , 윤수철 Soo Cheol Yun , 김윤민 Yun Min Kim
50(2) 247261, 2011
이종희 Chong Hee Lee , 김선희 Sun Hee Kim , 김수진 Soo Jin Kim , 김기연 Ki Yeon Kim , 김부미 Bu Mi Kim , 윤수철 Soo Cheol Yun , 김윤민 Yun Min Kim
DOI: JANT Vol.50(No.2) 247261, 2011
In this study, the researchers developed an inventory which can measure the affective achievement in mathematical learning especially targeted to Korean students. By using EFA and CFA, the six affective factors of mathematical learning such as learning directivity, self control, anxiety, interest, cognizing value and confidence are distinguished. Also, the content validity of this inventory was examined by the experts groups, composed of mathematics education professors, high school mathematics teachers, and measurement experts. The reliability of the instrument was high enough to trust the results. Through a large scaled sampling, the reliability and validity of this inventory were verified. In addition, this inventory was developed not by a partial aspects of a certain theory but based on the recent theories. Due to these reasons, the results of this study can be respected that it plays a leading part in understanding the affective achievement of Korean students.
