홍석강 Suk Kang Hong

DOI: JANT Vol.37(No.1) 1-13, 1998

---

In this paper, we have represented the efficient way how to enumerate the optimal number-right scores to adjust the item difficulty and to improve item discrimination. To estimate the optimal number-right scores in two equivalent math-tests by linear score equating a measurement error model was applied to the true scores observed from a pair of equivalent math-tests assumed to measure same trait. The model specification for true scores which is represented by the bivariate model is a simple regression model to inference the optimal number-right scores and we assume again that the two simple regression lines of raw scores and true scores are independent each other in their error models. We enumerated the difference between mean value of x^* and μ_x and the difference between the mean value of y^* and a+bμ_x by making an inference the estimates from 2 error variable regression model. Furthermore, so as to distinguish from the original score points, the estimated number-right scores y`^(*) as the estimated regression values of true scores with the same coordinate were moved to center points that were composed of such difference values with result of such parallel score moving procedure as above mentioned. We got the asymptotically normal distribution in Figure 5 that was represented as the optimal distribution of the optimal number-right scores so that we could decide the optimal proportion of number-right score in each item. Also by assumption that equivalence of two tests is closely connected to unidimensionality of a student`s ability. we introduce new definition of trait score to evaluate such ability in each item. In this study there are much limitations in getting the real true scores and in analyzing data of the bivariate error model. However, even with these limitations we believe that this study indicates that the estimation of optimal number right scores by using this enumeration procedure could be easily achieved.

나지영 , 정순영

DOI: JANT Vol.37(No.1) 15-33, 1998

---

The purpose of this paper is to investigate a characteristic of the assessment of high school math and to introduce an algorithm for school teachers to perform the achievement tests for math in classrooms. Moreover, we introduce a system of objectives which will be appropriate for math in the situation of Korea and illustrate our approach via `96 High School Achievement Test held by Korea National Board of Educational Evaluation.

최택영 , 김인연 Taeg Young Choi , In Young Kim

DOI: JANT Vol.37(No.1) 35-54, 1998

---

Half century has passed since Korean peninsula was divided into South and North Korea. Now a days, there are many differences of politics, economy, culture and education between South and North Korea. Especially mathematics education in which I am interested has a lot of changes and differences. This is proved true by defects` proof. For those reasons, I compared South Korea`s education ideology, goal and system, and goals of mathematics education with North Korea`s. I compared geometric(1-4 years, published by Pyong-yang Educational Book Publication Co. 1991) of mathematics texts(1-6 years) which are used in the secondary school with mathematics text of South Korea in contents and organization of them. As a result of this comparison, education ideology and goal are distinctly different from those of South Korea because of the difference of pursuing humanity. In North Korea, the curriculum is very strict without autonomy. There are 1283 mathematics classes which are occupied 19% for six years during the secondary school. The contents are very similar, but there is a little difference in the definition of a term. The problems which praise Kim Il-sung and his son and reveal loyalty to them were found, and there were a lot of problems in order to promote hostile feeling against U.S.A and South Korea, too. In conclusion, mathematics education of Korean peninsula should be reunified in the fields of the terms and contents at first.

김흥기 Heung Ki Kim

DOI: JANT Vol.37(No.1) 55-72, 1998

---

We prove many statements in middle and high school mathematics, so it is necessary to have some method for understanding the modes of proof. But it is hard to discuss about the modes of proof without knowing logics. Venn-diagrams can be used in a great variety of situations, and it is useful to the students unfamiliar with logical procedure. Since knowing a mode of proof that could be used may still not guarantee success of proof, it is also necessary to illustrate many cases of proof strategies. To achieve the above requirements, (1) Even though intuition, the modes of proof used in middle school mathematics should be understood by using venn-diagrams and the students can use the right proof in the right statement. (2) We must illustrate many kinds of proof so that the students can get the proof stratigies from these illustrations. (3) If possible, logic should be treated in middle school mathematics for students to understand the system of proof correctly.

류성림 Sung Rim Ryu

DOI: JANT Vol.37(No.1) 73-85, 1998

---

The purpose of this study is to investigate the understanding of middle school students on the meaning of proof and to suggest a teaching method to improve their understanding based on three levels identified by Kunimune as follows: Level I to think that experimental method is enough for justifying proof, Level II to think that deductive method is necessary for justifying proof, Level III to understand the meaning of deductive system. The conclusions of this study are as follows: First, only 13% of 8th graders and 22% of 9th graders are on level II. Second, although about 50% students understand the meaning of hypothesis, conclusion, and proof, they can`t understand the necessity of deductive proof. This conclusion implies that the necessity of deductive proof needs to be taught to the middle school students. One of the teaching methods on the necessity of proof is to compare the nature of experimental method and deductive proof method by providing their weak and strong points respectively.

송순희 , 김윤영 Soon Hi Song , Yoon Young Kim

DOI: JANT Vol.37(No.1) 87-99, 1998

---

Mathematics education is very important in future because mathematics is the basis of every study, for example, natural and social science, etc. Our nation wide curriculum has been revised six times since 1948. In 1992, the sixth revision was enforced and we are using the revised textbook now. This study aims at helping of continuous investigation for educational curriculum and textbook, and aims at efficient teaching by preventing unnecessary repetition and excessive gap in real field by analyzing the articulation of Analytics part in school textbook from elementary to high school. This thesis consists of the followings. 1. Investigation of the principles and natures of articulation along with curriculum course and notice the articulation based on the analysing tools. 2. Importance of learning functions. 3. To get the propriety, formation of 8 judging group and classification of content materials in function chapters by the judges based on the analyzing tools. 4. Analysis of presentation method and terminologies in the first concepts, suggestion teaching method to reduce gap and help of understanding on first concepts in the study of function. As a result, `development` consists of 55.8% of the total and it is higher than `duplication` and `gap`. To be specific in periods, between elementary school and middle school `development` takes 64.5% and this shows an acceptable articulation in the period. While 39.4% of `gap` in articulation between middle school and high school looks high compared with `gap` between the previous periods. The item suggested with the `gap` is the `definition of function`, `value of function`, `parallel translation`, `exponential and logarithmic function`. It is observed that these materials is suddenly appeared in high school.

좌창보 , 김철수 Chang Bo Joa , Chul Soo Kim

DOI: JANT Vol.37(No.1) 101-114, 1998

---

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

최정숙 , 신인선 Jung Suk Choi , In Sun Shin

DOI: JANT Vol.37(No.1) 115-138, 1998

---

We seek the possibility of introduction of Fractals to the high school math. curriculum through identifying Fractals teaching programs appropriate for the scopes and sequences in math. education for the high school students. We presented the contents of Fractal theory suitable for the high school students. The following subjects were chosen to be introduced; self-similarity, Fractal dimension, Cantor set, Sierpinsky triangle, Sierpinsky carpet, Koch curve, Koch island, perimeter estimate of rugged profiles drawn on paper, and chaos game. We developed the working papers and the criteria for appraisal. Each working paper focuses on the activities in which students can solve the given problems, understanding the characteristics and ideas of Fractals. The working papers were given to the second year students who take science course, and the degree of achievements were analyzed based on the appraisal criteria. The results show that it is possible to introduce Fractals to the high school students