• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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

• 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.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.75-94
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• 2005

This study is intended to develop the criterion for evaluating the creative products that mathematically gifted students produce in their education program to enhance the development of creative productive ability. 1 distinguish the mathematical creativity with the creativity in the general domain, and make the production model of the creative mathematical product grounded on the mathematicians' work through the mathematical history. The model has the following components; the mathematical knowledge, the mathematical thinking and the mathematical inquiry skill, surrounding the resultive creative product. The students products are focused on one component of the model. Thus the criterion for the creative products is grounded on the each component of the model. According to it, teachers could evaluate the students'work, which got the validity and the reliability.

• 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.