• Title, Summary, Keyword: 수학적 모델

### The Role of Spreadsheet in Model Refinement in Mathematical Modeling Activity (수학적 모델링에서 스프레드시트 환경이 수학적 모델의 정교화 과정에 미치는 역할)

• Son, Hong-Chan;Lew, Hee-Chan
• School Mathematics
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• v.9 no.4
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• pp.467-486
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• 2007
• In mathematical modeling activity modeling process is usually an iterative process. When model can not be solved, the model needs to be simplified by treating some variables as constants, or by ignoring some variables. On the other hand, when the results from the model are not precise enough, the model needs to be refined by considering additional conditions. In this study we investigate the role of spreadsheet model in model refinement and modeling process. In detail, we observed that by using spreadsheet model students can solve model which can not be solved in paper-pencil environment. And so they need not go back to model simplification process but continue model refinement. By transforming mathematical model to spreadsheet model, the students can predict or explain the real word situations directly without passing the mathematical conclusions step in modeling process.

### A Study on a Modelling Process for Fitting Mathematical Modeling (수학적 모델링의 정교화 과정 연구)

• Kang, Ok-Ki
• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.73-84
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• 2010
• Mathematical modeling is an important part of mathematics education since it can be used or created to find mathematical models to understand real life various situations. Most of mathematical modeling tasks taught and learned currently in secondary school mathematics classes need simple mathematical modelling with one or two variables and produce fixed solutions to the real life problems. But many real life problems involve various and complex variables which can be used to get more proper solutions. Constructing mathematical models to get more appropriate solutions from the real problems having various and complex variables is not easy. In this paper the researcher suggested a model to fit mathematical models to get more appropriate solutions and showed three examples to apply the model in solving real life problems which can be treated in the secondary school mathematics classrooms.

### Development of Shelf-life Prediction Model of Tofu Using Mathematical Quantitative Assessment Model (수학적 정량평가 모델을 이용한 두부의 유통기한 예측 모델의 개발)

• Shin Il-Shik
• Food Industry And Nutrition
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• v.10 no.1
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• pp.11-16
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• 2005
• 식물성 단백질의 주요 공급원이며 우리나라 전통식품 중의 하나인 두부의 유통기한을 정량적으로 예측할 수 있는 수학적 모델을 개발하고자 온도와 초기균수에 따른 두부 부패세균의 성장 실험 결과를 데이터베이스화하여 이를 바탕으로 균의 성장을 정량적으로 평가할 수 있는 수학적 모델을 개발하였다. 근의 증식 지표인 최대증식속도상수(k), 유도기(LT), 세대시간(GT)은 온도에 지배적인 영향을 받았으며, 초기균수에 따른 유의 적 인 차이 는 없었다(p<0.05). 최대증식속도상수와 온도 및 초기균수의 상관관계를 나타내는 수학적 정량평가모델인 square root model을 이 용하여 두부 부패 세균의 성장을 정량적으로 예측할 수 있는 모델$({\surd}{\kappa}=0.016861(T+6.87095))$을 개발하였으며 실험치와 예측치의 상관계수는0.969이었다. 이 예측 정량평가모델로부터 예측한 최대증식속도상수와 두부의 관능적 부패시 점을 반영 한 Gompertz 변형 모델을 이용하여 두부의 유통기한을 예측할 수 있는 모델$(Spoilage-critrion(hr)=\frac{2{\times}Ln2+Ln[(Nmax/No)-1])}{k}$을 개발하였다

### Analysis on Types and Roles of Reasoning used in the Mathematical Modeling Process (수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석)

• 김선희;김기연
• School Mathematics
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• v.6 no.3
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• pp.283-299
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• 2004
• It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

### A study on mathematical models describing population changes of biological species (생물 종의 개체 수 변화를 기술하는 수학적 모델에 대한 고찰)

• Shim, Seong-A
• Journal for History of Mathematics
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• v.24 no.2
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• pp.47-59
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• 2011
• Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

### Social Transformation of Students' Conceptual Model in an RME-based Differential Equations Course: An Analysis of Students' Use of Conceptual Metaphor (RME 기반 수학 교실에서의 개념적 모델의 사회적 변환: 미분방정식에 대한 개념적 은유 사용 패턴 분석)

• 주미경;권오남
• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004
• This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

### A Study on the Factors of Mathematical Creativity and Teaching and Learning Models to Enhance Mathematical Creativity (수학적 창의성의 요소와 창의성 개발을 위한 수업 모델 탐색)

• Lee, Dae-Hyun
• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.39-61
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• 2012
• Mathematical creativity is essential in school mathematics and mathematics curriculum and ensures the growth of mathematical ability. Therefore mathematics educators try to develop students' creativity via mathematics education for a long time. In special, 2011 revised mathematics curriculum emphasizes mathematical creativity. Yet, it may seem like a vague characterization of mathematical creativity. Furthermore, it is needed to develop the methods for developing the mathematical creativity. So, the goal of this paper is to search for teaching and learning models for developing the mathematical creativity. For this, I discuss about issues of mathematical creativity and extract the factors of mathematical creativity. The factors of mathematical creativity are divided into cognitive factors, affective factors and attitude factors that become the factors of development of mathematical creativity in the mathematical instruction. And I develop 8-teaching and learning models for development of mathematical creativity based on the characters of mathematics and the most recent theories of mathematics education. These models make it crucial for students to develop the mathematical creativity and create the new mathematics in the future.

### A Study on the Manifestation Process Model Development of Group Creativity among Mathematically Gifted Students (수학영재의 집단창의성 발현 모델 개발)

• Sung, Jihyun;Lee, Chonghee
• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.557-580
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• 2017
• The purpose of this study is developing the manifestation process model of group creativity among mathematically gifted students. Therefore, I designed the manifestation process model of group creativity by researching the existing literatures on group creativity and mathematical creativity. The manifestation process model of group creativity was applied to mathematically gifted students' class. By analyzing students' response, the manifestation process model of group creativity was improved and concretized. In conclusion, the process of a combination of contributions was concretized and the major variables on group creativity such as a diversity, conflict, emotionally supportive environment and social comparison were verified. In addition, some reflective processes was discovered from a case study.

### Mathematical Modelling of the H1N1 Influenza (신종 인플루엔자의 수학적 모델링)

• Lee, Sang-Gu;Ko, Rae-Young;Lee, Jae-Hwa
• Communications of Mathematical Education
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• v.24 no.4
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• pp.877-889
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• 2010
• Mathematical modelling is a useful method for reinterpreting the real world and for solving real problems. In this paper, we introduced a theory on mathematical modelling. Further, we developed a mathematical model of the H1N1 influenza with Excel. Then, we analyzed the model which tells us what role it can play in an appropriate prediction of the future and in the decision of accompanied policies.

### Students' Conceptual Metaphor of Differential Equations: A Sociocultural Perspective on the Duality of the Students' Conceptual Model (학생들의 미분방정식 개념에 대한 수학적 은유의 분석: 개념적 모델의 이중성에 대한 사회문화적 관점)

• 주미경;권오남
• School Mathematics
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• v.5 no.1
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• pp.135-149
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• 2003
• We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.