• 한국수학교육학회지시리즈A:수학교육
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• 제30권1호
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• pp.1-19
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• 1991

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 curriculm. 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 invovles mathematical concepts, methods, results, topics, we shall speak of the process of applying mathemtaics 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 mathemtaical 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 objcets, . 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 mathemtaics 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 19608 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. Applicaton 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, and what are less-important topics of application-oriented curriculum should be studied and selected. 5. For any mathematics teacher, application and modelling should form part of pre- and in-service education.

• 디지털콘텐츠학회 논문지
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• 제11권4호
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• pp.463-471
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• 2010

하수 처리장은 화학적, 물리적, 생물학적 처리가 복합적으로 연계된 공정으로 구성 되는데, 각각의 단위공정과 전체시스템의 처리 성능 및 운영 상태의 정도를 파악 하려면 처리공정의 수학적 모델을 빠르게 연산 할 수 있는 컴퓨터 시뮬레이터를 이용하면 편리하다. 주어진 물리적 환경에서 처리공정의 오염물질, 화학물질, 생물학적 매체의 질량 수지를 계산하는 컴퓨터 시뮬레이터는 데이터의 입출력 과정과 수학모델의 연산과정을 효율적으로 수행하는 응용 소프트웨어로써 처리조 내부에서 일어나는 반응의 상태를 정량적으로 추산하는 도구이다. 이러한 시뮬레이션 소프트웨어는 처리시설의 성능 및 효율을 예측하여 운용자에게 최적 관리를 위한 의사결정의 타당성을 제공하게 되는데, 시뮬레이션 소프트웨어를 처리시설에 적합하도록 시나리오를 설정하고 데이터 수집 시스템에 연결하면 실시간으로 처리시설의 분석이 가능한 자동화 운영 시스템의 역할을 수행한다. 본 논문에서는 통합전산망에서 수집되는 데이터를 시뮬레이션 소프트웨어에서 운용, 실제 운영 상태와 시뮬레이션 결과를 실시간 비교, 분석하여 최적의 운전인자를 도출할 수 있는 시나리오 운영 소프트웨어 "WEC-Sim"의 설계 및 구현에 대하여 논한다.

• Journal of Microbiology and Biotechnology
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• 제17권1호
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• pp.146-153
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• 2007

A mathematical competition model between normal flora and an invading pathogen was devised to allow analysis of bacterial infections in a host. The normal flora includes the various microorganisms that live on or within the host and act as a primary human immune system. Despite the important role of the normal flora, no mathematical study has been undertaken on models of the interaction between it and invading pathogens against a background of antibiotic treatment. To quantify key elements of bacterial behavior in a host, pairs of nonlinear differential equations were used to describe three categories of human health conditions, namely, healthy, latent infection, and active infection. In addition, a cutoff value was proposed to represent the minimum population level required for survival. The recovery of normal flora after antibiotic treatment was also included in the simulation because of its relation to human health recovery. The significance of each simulation parameter for the bacterial growth model was investigated. The devised simulation showed that bacterial proliferation rate, carrying capacity, initial population levels, and competition intensity have a significant effect on bacterial behavior. Consequently, a model was established to describe competition between normal flora and an infiltrating pathogen. Unlike other population models, the recovery process described by the devised model can describe the human health recovery mechanism.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권2호
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• pp.283-300
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• 2010

고등학생들이 부정형의 한 형태인 $0^0$을 올바로 이해하는데 어려움을 느낀다는 것은 오래전부터 알려져 왔으며, 비교적 최근까지도 $0^0$의 처리 방법에 대하여 수학자들 사이에 약간의 논란이 있었다. 고등학교 교육과정에는 $0^0$에 대한 명확한 처리방법이 명시되지 않고 있으므로 어떤 학생들은 그것의 값이 무엇인지 질문을 하기도 한다. 본 연구에서는 $0^0$과 관련된 자료들을 토대로 역사적 수학적 분석을 통하여 $0^0$은 부정형임을 명확히 하고, 현직 교사와 최근에 고등학교를 졸업한 학생들을 대상으로 실시한 간단한 설문조사를 통하여 고등학교 교육현장의 $0^0$에 대한 교수 실태를 파악한다. 그리고 교사와 예비교사를 위하여 $0^0$에 대한 효과적인 지도 방안에 대하여 논의한다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제34권2호
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• pp.161-177
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• 2020

본 연구는 고등학생을 대상으로 실험집단과 비교집단을 구성하고, 일대다(一對多) 튜토링 협동학습을 실시하였다. 집단 간 점수 차이와 집단별 사전·사후 점수 차이에 대한 유의성 검증은 비모수 통계기법을 사용하였으며, 학생들의 정의적 영역을 살펴보기 위하여 개방형 설문조사 2회와 개별 면담하였다. 실험집단과 비교집단 간 점수 차이는 통계적으로 유의하지 않았지만, 세 집단의 사전·사후 수학 점수 차이 검증 결과는 실험집단만 통계적으로 유의한 차이가 있었다. 그리고 학생교사는 일반학생을 가르치는 동안 자신을 성찰하고 자기효능감이 향상되었으며, 일반학생은 학생교사에게 도움을 받음으로써 수업에 대한 재미와 관심을 더 두게 되고 자신감이 향상되었다. 수학 교과 역량 측면은 의사소통, 문제해결, 추론, 태도 및 실천 역량이 향상되었음을 알 수 있었다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제22권4호
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• pp.281-294
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• 2019

본 연구의 목적은 초등학교 3학년 2학기의 곱셈 학습에서 반성적 활동을 적용함으로써 학업성취도의 수학 학습과정 중에 나타나는 오류 및 처치 행동을 분석하는 데 있다. 연구참여하는 학생들에게 곱셈단원에 대하여 반성적 활동을 적용하여 수업을 재구성하여 진행하였다. 이들의 수학 학업성취도의 변화를 알아보기 위하여 사전 사후 검사를 실시하였고, 반성적 활동에서의 학습자의 오류 처치양상을 분석하기 위해 포커스 그룹의 수학적인 의사소통을 녹음하여 분석하였다. 그리고 오류 유형 및 오류 처치를 위하여 학생들의 활동지와 녹음된 대화를 분석하였다. 연구 결과, 반성적 활동을 적용한 경우 학습자의 수학학업성취도가 상승하였다. 두 자리 수의 곱셈을 학습할 때 오류 유형은 다양하게 나타났다. 그리고 반성적 활동은 학습자가 곱셈 알고리즘에 대해 반성하고 오류가 있는 계산을 분석하여 자신의 오류를 반성적으로 되돌아보고 처치하도록 돕게 됨을 확인하였다.

• 제어로봇시스템학회논문지
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• 제3권2호
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• pp.204-213
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• 1997

In this paper, an application of fuzzy-neuron reasoning to the control of an activated sludge plant is presented. The activated sludge process is widely used in modern wastewater treatment plants. The operation control of the activated sludge process, however, is difficult due to the following reasons : 1)The complexity of the wastewater components, 2)the change of the wastewater influent, and 3)the adjustment errors in the control process. Because of these reasons, it is difficult to obtain mathematical model that really reflect the relationship between the variables and parameters in the process of wastewater treatment correctively and effectively. In this paper, the activated sludge process(A.S.P.) is modeled by a new fuzzy-neuron network representing nonlinear characteristics. These fuzzy-neurons have fuzzy rules with complementary membership function. Based on the constructed model, graphic simulator on X-window system as a graphic integrated environment is implemented. The efficacy of the proposed control scheme was evaluated and demonstrated by means of the field test.

• 상하수도학회지
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• 제31권1호
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• pp.73-81
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• 2017

The UV/chlorine process is a UV-based advanced oxidation process for removing various organic pollutants in water. The process is becoming increasingly popular because of its effectiveness in practice. It is important to the safe and efficient operation of a UV/chlorine process that the optimal operating conditions for both target removal objective and saving energy are determined. Treatment efficiency of target compounds in UV/chlorine process was mainly affected by pH and scavenging factor. In this study, kinetic based mathematical model considering water characteristics and electrical energy dose calculations model was developed to predict of treatment efficiency and optimal operating conditions. The model equation was validated for the UV/chlorine process at the laboratory scale and in pilot tests at water treatment plants.

• 상하수도학회지
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• 제22권4호
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• pp.437-444
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• 2008

Many other countries have investigated the new backwash water treatment process to save the existing water resource. There are various methods for reusing backwash water, but the membrane system has received the most interest for its efficiency. The objective of this study was to certify the application of membrane filtration system for the backwash water treatment. The experiment equipment was composed of Lab scale tubular membrane filtration system. Generally, cross-flow operation mode is used in the tubular membrane system but cross-flow operation mode demands high electric cost mainly for the pump energy. So to cut off electric cost, dead-end operation mode was used in this experiment. Filtration and bleed operation cycle was used in this membrane system. Backwash water was concentrated during the filtration process and when backwash water reached our target suspended solid concentration, it was discharged from this system. For efficient operation of filtration and bleed, mathematical matrix was drawn up and with this matrix we could simulate various sets of filtration and bleed time.

• 한국양식학회지
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• 제6권4호
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• pp.311-321
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• 1993

Ammonia accumulation is regarded as the limiting factor of the first priority in water qualities of aquatic culture systems. Nitrification efficiency and characteristics in seawater were evaluated using Rotating Biological Contactor (RBC) process as a part of the recycling water treatment facilities for marine fish culture system. Ammonia removal efficiency regarded 99.7 to $83.7\%$ at the ammonia surface loading rates of 48 to $393 mg/m^2$ -day. RBC process was able to withstand to the fluctuation of influent ammonia concentrations and loading and produced the stable effluent. The mathematical model on the fixed-film biological reactor developed by Kornegay seemed to be suitable to RBC process kinetic evaluation for the recycling water treatment of the marine fish culture system. Area capacity constant (P) and half-velocity constant (Ks) in the model were 0.188g/m^2$-day and 1.25mg/l, respectively.