응용과 모델 구성을 중시하는 수학과 교육 과정 개발 방안 탐색 = Application and Modelling in Mathematical Curriculum

다국어 초록 (Multilingual Abstract)

This study intends to provide some desirable suggestions for the development of application oriented mathematics curriculum. More specific objects of this study is : 1. To identify the meaning of application and modelling in mathematics curriculum. 2. To illuminate the historical background of and trends in application and modelling in the mathematics curricula. 3. To consider the reasons for including application and modelling in the mathematics curriculum. 4. To find out some implication for developing application oriented mathematics curriculum. The meaning of application and modelling is clarified as follows: If an arbitrary area of extra-mathematical reality is submitted to any kind of treatment which involves mathematical concepts, methods, results, topics, we shall speak of the process of applying mathematics to that area. For the result of the process we shall use the term an application of mathematics. Certain objects, relations between them, and structures belonging to the area under consideration are selected and translated into mathematical objects, relation and structures, which are said to represent the original ones. Now, the concept of mathematical model is defined as the collection of mathematical objects, relations, structures, and so on, irrespective of what area is being represented by the model and how. And the full process of constructing a mathematical model of a given area is called as modelling, or model-building. During the last few decades an enormous extension of the use of mathematics in other disciplines has occurred. Nowadays the concept of a mathematical model is often used and interest has turned to the dynamic interaction between the real world and mathematics, to the process translating a real situation into a mathematical model and vice versa. The continued growing importance of mathematics in everyday practice has not been reflected to the same extent in the teaching and learning of mathematics in school. In particular the world-wide New Maths Movement of the 1960s actually caused a reduction of the importance of application and modelling in mathematics teaching. Eventually, in the 1970s, there was a reaction to the excessive formallism of New Maths, and a return in many countries to the importance of application and connections to the reality in mathematics teaching. However, the main emphasis was put on mathematical models. Application and modelling should be part of the mathematics curriculum in order to : 1. Convince students, who lacks visible relevance to their present and future lives, that mathematical activities are worthwhile, and motivate their studies. 2. Assist the acqusition and understanding of mathematical ideas, concepts, methods, theories and provide illustrations and interpretations of them. 3. Prepare students for being able to practice application and modelling as private individuals or as citizens, at present or in the future. 4. Foster in students the ability to utilise mathematics in complex situations. Of these four reasons the first is rather defensive, serving to protect or strengthen the position of mathematics, whereas the last three imply a positive interest in application and modelling for their own sake or for their capacity to improve mathematics teaching. Suggestions, recomendations and implications for developing application oriented mathematics curriculum were made as follows: 1. Many applications and modelling case studies suitable for various levels should be investigated and published for the teacher. 2. Mathematics education both for general and vocational students should encompass application and modelling activities, of a constructive as well as analytical. and critical nature. 3. Application and modelling activities should be introduced in mathematics curriculum through the interdisciplinary integrated approach. 4. What are the central ideas of, arid what are less-important topics of application-oriented curriculum should be s