노선숙Sun Sook Noh,김민경Min Kyeong Kim,유현주Hyun Joo Yu,차인숙In Sook Cha

DOI: JANT Vol.40(No.2) 161-177, 2001

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This study is to investigate what students want to learn and what mathematics teachers should teach in their classrooms. 1314 students and 527 mathematics teachers were randomly selected to administer the questionnaire. The result shows that their is a considerable mismatch between students` learning desires and teachers` teaching practices in classrooms. What students want to learn is creative knowledge; however, what they learn in the classroom is `imitative` knowledge. This study suggests that the overall educational goal of mathematics education in Korea should emphasize (1) learning to communicate mathematically, (2) learning to reason mathematically, (3) becoming confident in pupils` own ability, (4) learning to value mathematics, and (5) becoming mathematical problem solvers.

최택영Taeg Young Choi,함석돈Seok Don Ham

DOI: JANT Vol.40(No.2) 179-194, 2001

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The seventh curriculum put into operation gradually from first-year student in 2000 academic years of elementary school is subject to form and apply a step-wise level curriculum. Mathematics(correspond to junior high school course from 7th school year to 9th school year) should apply a step-wise level curriculum from 7th school year in 2001 academic years. Accordingly, mathematics teachers must diagnose actual conditions of educations, distribution tables of test results, step-wise teaching-studying programs etc. They also make proper plans suitable for actual situations of each school, prepare appropriate teaching materials and aids. I investigated preceding studies planned for preparation of putting into operation of a step-wise level curriculum. It showed that most of the studies were conducted at schools of medium or large scale and studies conducted at schools of small scale was rare. There were 113 small scale middle schools out of total 297 middle schools in Kyongsangbuk-do area in 2000. In this situation, I felt necessities of modeling of a step-wise level curriculum suitable for small scale schools. In this study, I modeled a step-wise level curriculum suitable for small scale middle schools, applied this model to 44 students in M middle school. I modeled two types of curriculum. One is a step-wise level curriculum that execute special supplementation process to students who do not complete 7-가 step successfully. The other is a step-wise level curriculum which is a regular model for a step-wise level of 7-나 step. I carried out an academic achievement test and intimacy test about mathematics before and after the application of the model. In this study, I found out that this model was very effective in academic achievement of students and helpful to declined students in scholarship. In the intimacy test, It was found out that most of the students gained confidence in mathematics, felt less anxiety, formed positive self consciousness. Therefore, I think that this model will be helpful to the application of the seventh step-wise level curriculum.

이영하Young Ha Lee,박희연Hui Youn Park

DOI: JANT Vol.40(No.2) 195-215, 2001

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The purpose of this paper is to present a specific set of home teaching methods in hopes to prevent slow learner of the elementary mathematics. This paper deals with the number and operations, one of five topics in the elementary mathematics. A survey of two hundred elementary school teachers was made to see the teacher`s opinions of the role of home studying and to concretize the contents of the research topics. There were asked which is the most essential contents for the concrete learning and which is the most difficult monad that might cause slow learner. And those were found to be; counting, and arithmetic operations(addition and subtraction) of one or two-digit numbers and multiplication and their concepts representations and operations(addition and subtraction) of fractions. The home teaching methods are based on the situated learning about problem solving in real life situations and on the active learning which induces children`s participation in the process of teaching and learning. Those activities in teaching each contents are designed to deal with real objects and situations. Most teaching methods are presented in the order of school curriculum. To teach the concepts of numbers and the place value, useful activities using manipulative materials (Base ten blocks, Unifix, etc.) or real objects are also proposed. Natural number`s operations such as addition, subtraction and multiplication are subdivided into small steps depending upon current curriculum, then for understanding of operational meaning and generalization, games and activities related to the calculation of changes are suggested. For fractions, this paper suggest 10 learning steps, say equivalent partition, fractional pattern, fractional size, relationship between the mixed fractions and the improper fraction, identifying fractions on the number line, 1 as a unit, discrete view point of fractions, comparison of fractional sizes, addition and subtraction, quantitative concepts. This research basically centers on the informal activities of kids under the real-life situation because such experiences are believed to be useful to prevent slow learner. All activities and learnings in this paper assume children`s active participation and we believe that such active and informal learning would be more effective for learning transfer and generalization.

김영국Young Kuk Kim,박기양Ki Yang Park,박규홍Kyoo Hong Park,박혜숙Hye Sook Park,박윤범Yun Beon Park,유현주Hyun Ju Yu,권오한Oh Han Kwon,이선아Sun A . Lee

DOI: JANT Vol.40(No.2) 217-239, 2001

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To lessen the ratio of under achievers is one of the most urgent task which recent school mathematics education is confronted with. To cope with this problem efficiently, math. teachers should know more specifically and concretely the causes that make the students dislike mathematics. But actually, there are too many reasons for these situations. So, in this paper, we tried to devise a tool to analyze and measure each student`s math. disliking status. We proceeded this research via the following procedures. 1. Grasping the causes which make the students dislike mathematics as specifically as possible. To obtain this, we asked more than 300 of secondary school students to write down their thoughts about school mathematics. 2. Analyzing the responses, we abstracted 74 numbers of items which were supposed to be the causes for secondary school students` mathematics disliking. 3. With these items we made a test to measure students` aptitude for each item. 4. With this test paper, we tested over 800 of secondary school students. Though factor analysis and theoretical argument, we categorized the 74 items into 11 groups whose names were defined as factors of mathematics disliking. 5. For each of these 11 factors, we developed a norm which could serve as standard of comparison in measuring each student`s mathematics disliking status. Using this tool teachers were able to describe each student`s traits of mathematics disliking more specifically.

한길준Gil Jun Han,우호식Ho Sik Woo

DOI: JANT Vol.40(No.2) 241-252, 2001

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Many high school students are having difficulties for studying advanced mathematics concepts. It is more complicated than in junior high school and they are losing interest and confidence. In this paper, advanced mathematics concepts are not just basic concepts such as natural numbers, fractions or figures that can be learned through life experience but concepts that are including variables, functions, sets, tangents and limits are more abstract and formal. For the students to understand these ideas is too heavy a burden and so many of the students concentrate their efforts on just memorizing and not understanding. It is necessary to search for a meaningful method of teaching for advanced mathematics that covers deductive methods and symbols. High school teachers are always asking themselves the following question, "How do we help the students to understand the concept clearly and instruct it in a meaningful way?" As a solution we propose the followings : I. To ensure they have the right understanding of concept image involved in the concept definition. II. Put emphasis on the process of making mental representations and the role of intuition. III. To instruct students and understand them as having many chance of the instructional conversation. In conclusion, we studied the meaningful method of teaching with the theory of Ausubel related to the above proposed methods. To understand advanced mathematics concepts correctly, the mutual understanding of both teachers and students is necessary.

황혜정Hye Jeang Hwang

DOI: JANT Vol.40(No.2) 253-263, 2001

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Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing students` self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students` acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student`s degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

노선숙Sun Sook Noh,김민경Min Kyeong Kim

DOI: JANT Vol.40(No.2) 265-289, 2001

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The elementary and middle school curriculum in Korea has been modified periodically to reach today`s 7th national curriculum. Although the intent of each new curriculum was to improve education, lack of proper preparation for teachers and students has not made the new curriculums as effective as it could be. Goodlad et al.(1979) suggested that curriculum should encompass all practices including not only knowledge but all the elements of the curriculum and experiences of the student and teachers. The purpose of this paper is to investigate the actual practices of the current curriculum with focus on the use of instructional media in mathematics teaching and learning. A nationwide curriculum survey was carried out with the Goodlad`s curriculum inquiry model as the framework. The result shows that elementary and secondary mathematics teachers used textbook manual (for teachers) and practice books most frequently for their class preparation. In addition to these, mathematics teachers also used manipulatives, visual aids, computers, internet, and calculators in a decreasing order. In general, many mathematics teachers did not use much instructional media in their classes and said that there are not enough effective instructional media to use. However, the teachers have positive attitude toward the educational media that they have used. In this study, we analyzed the survey data regarding educational tools, their use and effects to support the development of a new curriculum model in mathematics for a knowledge-based society.

김흥기Heung Ki Kim

DOI: JANT Vol.40(No.2) 291-315, 2001

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There are some problems in the introduction of proof in middle school mathematics. Among the problems, one is the use of postulates and the another is the methods of proof how to connect a statement with others. The first case has been heated mainly in this note. Since proof means to state the reason logically why the statement is true on the basis of others which have already been known as true and basic properties, in order to prove logically, it is necessary to take the basic properties and the statement known already as true. But the students don`t know well what are the basic properties and the statement known already as true for proving. No use of the term postulation(or axiom) cause the confusion to distinguish postulation and theorem. So they don`t know which statements are accepted without proof or not accepted without proof. To solve this problems, it is necessary to use the term postulate in middle school mathematics. In middle school mathematics, we present some model of the introduction of proof which are used the postulates needed for the proof.

김향숙Hyang Sook Kim

DOI: JANT Vol.40(No.2) 317-333, 2001

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The equations of figures given by rectangular coordinates are used to look into the properties of them, which are very restricted in examining them in the school mathematics. Therefore, it is quite natural to consider the figures in terms of parameters without restriction to coordinates and also, it is possible for the students to analyze them. Thus, the visualization of figures is important for students in mathematics education. In particular, the teaching-learning methods using computers make loose the difficulties of geometry education, and from the viewpoint that various abstract figures can be visualized and that can be obtained by means of this visualization the learning of figures can be accomplished through the direct experience or control. This study is intended to present concretely the aim and its utility to visualize figures represented as parameters with Mathematica. In this paper, we introduce a new teaching-learning method of figures represented by parameters using Mathematica so that the learners establish themselves their knowledge obtained through their search, investigation, supposition and they accomplish the positive transition to advanced learning. So the learners extend their ability of sensuous intuition to their ability of logical reasoning through their logical intuition. Consequently they can develop the ability of thinking mathematically, so many natural phenomena and physical ones.

박임숙Im Sook Park

DOI: JANT Vol.40(No.2) 335-343, 2001

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Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra.. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

김웅환Yung Hwan Kim

DOI: JANT Vol.40(No.2) 345-349, 2001

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This study suggested a teaching method to improve intuitive understanding of the statistical basic concepts about the central limit theorem with experiment. It is very hard to understand about the concept of the central limit theorem in the school mathematics class. The result of this study experiment for the class of statistics education shows that the students and mathematics teachers were interesting at this experiment. They corrected their misunderstanding about the central limit theorem by discussion for the result of experiment with team members. I think that this study can help teachers to teach the students using the experiment method.