• Communications of Mathematical Education
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• v.37 no.2
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• pp.257-276
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• 2023

Mathematical modeling can be described as a series of processes in which real-world problem situations are understood, interpreted using mathematical methods, and solved based on mathematical models. The effectiveness of mathematics instruction using mathematical modeling has been demonstrated through prior research. This study aims to explore insights for mathematical modeling instruction by analyzing the metacognitive characteristics shown in the mathematical modeling cycle, according to the mathematical thinking styles of elementary math gifted students. To achieve this, a mathematical thinking style assessment was conducted with 39 elementary math gifted students from University-affiliated Science Gifted Education Center, and based on the assessment results, they were classified into visual, analytical, and mixed groups. The metacognition manifested during the process of mathematical modeling for each group was analyzed. The analysis results revealed that metacognitive elements varied depending on the phases of modeling cycle and their mathematical thinking styles. Based on these findings, didactical implications for mathematical modeling instruction were derived.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.507-516
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• 2000

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• 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.

• Design & Manufacturing
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• v.13 no.2
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• pp.6-11
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• 2019

In this study, we constructed the mathematical model to evaluate the roundness for plastic injection mold parts with complicated 3D curvatures. Mathematically we started off from the equation of circle and successfully derived an analytical solution so as to minimize the area of the residuals. On the other hand, we employed the numerical method the similar optimization process for the comparison. To verify the mathematical models, we manufactured and used a ball valve type plastic parts to apply the derived model. The plastic parts was fabricated under the process conditions of 220-ton injection mold machine with a raw material of polyester. we experimentally measured (x, y) position using 3D contact automated system and applied two mathematical methods to evaluated the accuracy of the mathematical models. We found that the analytical solution gives better accuracy of 0.4036 compared to 0.4872 of the numerical solution. The numerical method however may give adaptiveness and versatility for optional simulations such as a fixed center.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• 한국생물공학회:학술대회논문집
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• 2000.04a
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• pp.177-180
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• 2000

An algorithm for modeling of yeast fermentation process using genetic-fuzzy algorithm is presented in this work. The algorithm involves developing the fuzzy modeling of the process and model update capability against the system change. The membership functions of state variables and specific rates and the decision table were generated using genetic algorithm. This algorithm could replace the complex mathematical model to simple fuzzy model and cope with the change of process characteristics well.

• KSBB Journal
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• v.14 no.5
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• pp.550-560
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• 1999

There have been many research efforts on biofilter modeling including Ottengraf et al. who derived a model equation for the concentration profile of pollutants(e.g., VOCs) in the biolayer and solved their outlet concentration of the waste gas stream through biofilter. However, for most of research works done so far, the effects to explain the effect of adsorption of organic particles to medium(i.e., adsorbent) have been ignored. In this work biofilter modeling accompanying process lumping has been proposed and the theoretical effect of adsorption property of the medium, on the biofilter performance of eliminating organic components in waste gas stream, is intensively discussed.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.157-177
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• 2001

Modern society's technological and economical changes require high-level education that involve critical thinking, problem solving, and communication with others. Thus, today's perspective of mathematics and mathematics learning recognizes a potential symbolic relationship between concrete and abstract mathematics. If the problems engage students' interests and aspiration, mathematical problems can serve as a source of their motivation. In addition, if the problems stimulate students'thinking, mathematical problems can also serve as a source of meaning and understanding. From these perspectives, the purpose of my study is to prove that mathematical modeling tasks can provide opportunities for students to attach meanings to mathematical calculations and procedures, and to manipulate symbols so that they may draw out the meanings out of the conclusion to which the symbolic manipulations lead. The review of related literature regarding mathematical modeling and model are performed as a theoretical study. I especially concentrated on the study results of Freudenthal, Fischbein, Lesh, Disessea, Blum, and Niss's model systems. We also investigate the emphasis of mathematising, the classified method of mathematical modeling, and the cognitive nature of mathematical model. And We investigate the purposes of model construction and the instructive meaning of mathematical modeling. In conclusion, we have presented the methods that promote students' effective model construction ability. First, the teaching and the learning begins with problems that reflect reality. Second, if students face problems that have too much or not enough information, they will construct useful models in the process of justifying important conjecture by attempting diverse models. Lastly, the teachers must understand the modeling cycle of the students and evaluate the effectiveness of the models that the students have constructed from their classroom observations, case study, and interaction between the learner and the teacher.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.