A comparison Research of High School Mathematics Textbook between Korea and India
이송희 Song Hee Lee , 김선홍 Seon Hong Kim
25(2) 289308, 2011
이송희 Song Hee Lee , 김선홍 Seon Hong Kim
DOI: JANT Vol.25(No.2) 289308, 2011
The purpose of this research is to compare high school mathematics textbooks published by India with those published by Korea so that we apply merits of India`s high school mathematics education to our educational problems. We first study India`s educational systems, and analyze the mathematics textbooks from both countries by considering their external appearance, units, contents. Finally we give meaningful results and propose what we can do for our mathematics education based on our analysis performed in this paper.

Excel Grapher: Dynamical Graphing Tool
김경원 Kyung Won Kim , 이상구 Sang Gu Lee , 이재화 Jae Hwa Lee
25(2) 309321, 2011
김경원 Kyung Won Kim , 이상구 Sang Gu Lee , 이재화 Jae Hwa Lee
DOI: JANT Vol.25(No.2) 309321, 2011
In this paper, we introduce how we developed a dynamic Excel Grapher which can be used for mathematics education. Developed tools can be used in college mathematics as well as a secondary school mathematics education. It can be downloaded for your test or teaching. (http://matrix.skku.ac.kr/2010ExcelGrapher/index.htm)

A study on the Preservice teacher`s recognition and fallacy for a number with irrational exponent
이헌수 Heon Soo Lee , 박형빈 Hyung Bin Park , 배강수 Kang Soo Bea
25(2) 323339, 2011
이헌수 Heon Soo Lee , 박형빈 Hyung Bin Park , 배강수 Kang Soo Bea
DOI: JANT Vol.25(No.2) 323339, 2011
The expansion of exponential law as the law of calculation of integer numbers can be a good material for the students to experience an extended configuration which is based on an algebraic principle of the performance of equivalent forms. While current textbooks described that exponential law can be expanded from natural number to integer, rational number and real number, most teachers force students to accept intuitively that the exponential law is valid although exponent is expanded into real number. However most teachers overlook explaining the value of exponent of rational number or exponent of irrational number so most students have a lot of questions whether this value is a rational number or a irrational number. Related to students` questions, most teacher said that it is out of the current curriculum and students will learn it after going to college instead of detailed answers. In this paper, we will present several examples and the values about irrational exponents of a positive rational and irrational exponents of a positive irrational number, and study the recognition and fallacy of wouldbe teachers about the cases of irrational exponents of a positive rational and irrational exponents of a positive irrational number at the expansion of exponential law.

Botany: A Modern Natural Science Book Written by Mathematician SangSeol Lee
박영민 Young Min Park , 김채식 Chae Sik Kim , 이상구 Sang Gu Lee , 이재화 Jae Hwa Lee
25(2) 341360, 2011
박영민 Young Min Park , 김채식 Chae Sik Kim , 이상구 Sang Gu Lee , 이재화 Jae Hwa Lee
DOI: JANT Vol.25(No.2) 341360, 2011
This paper deals with contents that SangSeol Lee contributed to the natural science in the 19th century Korea. Prof. SungRae Park, the science historian, called SangSeol Lee Father of the Modern Mathematics education of Korea. SangSeol Lee wrote a manuscript Botany with a brush in late 19th century. Botany was transcribed from Science Primers: Botany (written by J. D. Hooker), which is translated into Chinese by Joseph Edkins in 1886. The existence of SangSeol Lee`s book Botany was not known to Korean scientists before. In this paper, we study the contents of Botany and its original text. Also we analyze people`s level of understanding Western sciences, especially botany at that time. In addition, we study authors of 16 Primers for Western Knowledge. We study the contribution of mathematician SangSeol Lee to science education in the 19th century Korea.

Investigation of the Effect of a Learning Program for University Engineering Mathematics
정수연 Su Youn Jeong , 송영무 Yeong Moo Song
25(2) 361379, 2011
정수연 Su Youn Jeong , 송영무 Yeong Moo Song
DOI: JANT Vol.25(No.2) 361379, 2011
The purposes of this research are to develop Engineering Mathematics materials using the relations between Engineering Mathematics contents and not only prestudy contents but also major contents and to find the effect of the mathematics study which is applying them for students majoring in electronics To accomplish the goals, I made list of Engineering Mathematics contents which is necessary to study electronics. Based on the list, I researched relations between Engineering Mathematics contents and not only prestudy contents but also major contents. After research, I selected some subjects which are related each other, developed study materials and examined responses to the materials. Then I analysed the effects on study attitude after used developed materials in my class. As a result, the major contents which was described in the introduction of the materials helped students to be motivated to study Engineering Mathematics and Prestudy contents described before Engineering Mathematics contents helped them to concentrate on studying Engineering Mathematics. Also it showed that developed study materials were effective in increasing selfconfidence which is one attitude in the subcategories for Mathematics study.

A Study on Various Transformations of Triangle`s Area formulas
조도흔 Do Heun Cho , 표명지 Myeung Ji Pyo , 장영수 Young Soo Jang , 이세찬 Se Chan Lee , 김기수 Gi Soo Kim , 한인기 In Ki Han
25(2) 381402, 2011
조도흔 Do Heun Cho , 표명지 Myeung Ji Pyo , 장영수 Young Soo Jang , 이세찬 Se Chan Lee , 김기수 Gi Soo Kim , 한인기 In Ki Han
DOI: JANT Vol.25(No.2) 381402, 2011
In this paper we study formulae of the triangle`s area. We solve problems related with making new formulae of the triangle`s area. These formulae is consisted of some elements of triangle, for example side, angle, median, perimeter, radius of circumcircle. We transform formulae S= 1/2 acsinB, S= abc/4R, s = (pa )(pb) (pc)(1/2), and make new formulae of the triangle`s area. Some formulas are received in the process of Research and Education program in the science high school. We expect that our results will be used in the Research and Education program in the science high school.

A Case Study on Students` Mathematical Concepts of Algebra, Connections and Attitudes toward Mathematics in a CAS Environment
박희정 Hui Jeong Park , 김경미 Kyung Mi Kim , 황우형 Woo Hyung Whang
25(2) 403430, 2011
박희정 Hui Jeong Park , 김경미 Kyung Mi Kim , 황우형 Woo Hyung Whang
DOI: JANT Vol.25(No.2) 403430, 2011
The purpose of the study was to investigate how the use of graphing calculators influence on forming students` mathematical concept of algebra, students` mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student`s learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the reallife problems. Third, we identified the change of six students` attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That`s because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages: formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

Analysis on the Effectiveness of Applying CRESST Formative Assessment Program to the 7th Grade LevelDifferentiated Math Classes
이봉주 Bong Ju Lee , 변희현 Hee Hyun Byun , 양명희 Myoung Hee Yang , 류현아 Hyun Ah Ryu
25(2) 431450, 2011
이봉주 Bong Ju Lee , 변희현 Hee Hyun Byun , 양명희 Myoung Hee Yang , 류현아 Hyun Ah Ryu
DOI: JANT Vol.25(No.2) 431450, 2011
Formative assessment is considered one of the effective strategies for teaching and learning mathematics. But it seems that there are few systematic researches which cover the process of practicing formative assessment in a class and providing feedback to the students. This study adopts CRESST Formative Assessment Program as a prototype. After some modifications of it to suit our educational system, this study analyzes the effectiveness of applying that program to the 7th grade leveldifferentiated math classes. Afterwards, this study tries to draw some significant educational discussions and implications for improving teaching and learning mathematics.

A Study on Problem Solving Related with Geometric Interpretation of Algebraic Expressions
유익승 Ik Seung Lyou , 한인기 In Ki Han
25(2) 451472, 2011
유익승 Ik Seung Lyou , 한인기 In Ki Han
DOI: JANT Vol.25(No.2) 451472, 2011
In this paper we studied problem solving related with geometric interpretation of algebraic expressions. We analyzed algebraic expressions, related these expressions with geometric interpretation. By using geometric interpretation we could find new approaches to solving mathematical problems. We suggested new problem solving methods related with geometric interpretation of algebraic expressions.

A study on teaching the system of numbers considering mathematical connections
정영우 Young Woo Chung , 김부윤 Boo Yoon Kim , 표성수 Sung Soo Pyo
25(2) 473494, 2011
정영우 Young Woo Chung , 김부윤 Boo Yoon Kim , 표성수 Sung Soo Pyo
DOI: JANT Vol.25(No.2) 473494, 2011
Across the secondary school, students deal with the algebraic conditions like as identity, inverse commutative law, associative law and distributive law. The algebraic structures, group, ring and field are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student`s natural mental activity I that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term ``algebraic structure`` with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.
