• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.95-116
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• 2013

Though the term "mathematical modeling" has no single definition or perspective, it is pursued commonly by groups from various perspectives who emphasize the activities of understanding and representing real phenomenon mathematically, building models to solve problems, and reinterpreting real phenomenon to make an attempt to understand the real world and related mathematical models more deeply. The purpose of this study is to identify how mathematization arises and find difficulties of mathematization in mathematical modeling process that share common features with the mathematical modeling activities as presented here. As a result of this research, we confirmed that the students mathematized real phenomena by building various representations, and interpreting them with regard to relationships and contexts inherent real phenomena. The students' communication fostered interplay between iconic representations and indexical representations. We also identified difficulties of mathematization in mathematical modeling process.

• Communications of Mathematical Education
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• v.10
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• pp.201-219
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• 2000

학생들이 실세계와 수학적 세계사이를 연관시켜 사고하고 해석하는 방법 및 실제 문제를 해결하는 일반적인 전략의 방법론의 하나가 수학적 모델링(Mathematical modelling)이라고 볼 수 있다. 한편, 수학 교수 ${\cdot}$ 학습 과정에서 구체적인 조작 활동을 통하여 학생 스스로가 지식을 ‘구성(construction)’ 할 수 있도록 해 주어야 한다는 구성주의적 사조가 대두되고 있는데, 본 논문에서는 구성주의적 관점에서 수학적 모델링을 통한 수학 교수 ${\cdot}$ 지도를 위한 활용 방안을 한 예시를 통해서 고찰해 보고자 한다.

• 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.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.253-269
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• 2005

수학시간에 많은 학생들이 흥미를 갖고 능동적인 학습활동을 할 수 있도록, 실세계 상황의 과제가 제시된 소집단 협력학습, 토론활동 위주의 문제중심학습(PBL:Problem-Based Learning)을 고등학교의 수학교실에 적용한다. 이를 위하여 본고에서는 학습여건의 조성, 적합한 학습과제의 특성, 교사의 역할 등을 중심으로 살펴보고, 발전적인 PBL학습모형을 개발하여 교실 실제에 적용함으로써 고등학교 학생들의 정의적 영역의 태도 변화에 미치는 영향을 살펴보고자 한다.

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.1-19
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• 2005

There have been raised the question that students have been of no interst in mathematcs and incompetent for solving real world problem because students have been recognized mathematcs as abstract knowldege. We research whether students' modeles developed in modeling activity can mediate between concrete and abstract. The analysis of our case study revealed that students' modeles aren't decontextualized abstraction but is located in situated abstraction that is a network connecting between concrete and abstract. Thus, these modeles are a tool mediating between concrete and abstract. Also, students' modeling activities can provide students with the opportunity of being competent for solving real world problem.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.103-122
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• 2016

The purpose of this study was to analyze the sentences related with mathematical modeling in the third and fourth grade mathematics textbooks in accordance with changing of Korean mathematics curricula. In the preliminary analysis, the researchers used the criteria that Kim(2010) had analyzed Mathematics in Context[MiC], and analyzed South Korean textbooks from the perspective of mathematical modeling. The researchers revised them for the analysis criteria among South Korean elementary mathematics textbooks and employed them as the analysis framework of the present study. From the mathematical modeling perspective, the study reached the following conclusions in accordance with the change of textbooks from the 7th curriculum to the 2009 revised curriculum. The contexts of real-world situations presented in the textbooks are increased in all areas except Probability and Statistics areas, the methods of expression of mathematical model are diversified in all areas except Patterns area, and the communication types are also diversified and frequencies increased in all areas except Patterns area. Based on this research, several suggestions were made for the development of future textbooks.

• The Mathematical Education
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• v.62 no.3
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• pp.381-400
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• 2023

As the era of solving various and complex problems in the real world using artificial intelligence and big data appears, problem-solving competencies that can solve realistic problems through a mathematical approach are required. In fact, the 2015 revised mathematics curriculum and the 2022 revised mathematics curriculum emphasize mathematical modeling as an activity and competency to solve real-world problems. However, the real-world problems presented in domestic and international textbooks have a high proportion of artificial problems that rarely occur in real-world. Accordingly, domestic and international countries are paying attention to the reality of mathematical modeling tasks and suggesting the need for authentic tasks that reflect students' daily lives. However, not only did previous studies focus on theoretical proposals for reality, but studies analyzing teachers' perceptions of reality and their competency to reflect reality in the task are insufficient. Accordingly, this study aims to analyze in-service mathematics teachers' perception of reality among the characteristics of tasks for mathematical modeling and the in-service mathematics teachers' competency for designing the mathematical modeling tasks. First of all, five criteria for satisfying the reality were established by analyzing literatures. Afterward, teacher training was conducted under the theme of mathematical modeling. Pre- and post-surveys for 41 in-service mathematics teachers who participated in the teacher training was conducted to confirm changes in perception of reality. The pre- and post- surveys provided a task that did not reflect reality, and in-service mathematics teachers determined whether the task given in surveys reflected reality and selected one reason for the judgment among five criteria for reality. Afterwards, frequency analysis was conducted by coding the results of the survey answered by in-service mathematics teachers in the pre- and post- survey, and frequencies were compared to confirm in-service mathematics teachers' perception changes on reality. In addition, the mathematical modeling tasks designed by in-service teachers were evaluated with the criteria for reality to confirm the teachers' competency for designing mathematical modeling tasks reflecting the reality. As a result, it was shown that in-service mathematics teachers changed from insufficient perception that only considers fragmentary criterion for reality to perceptions that consider all the five criteria of reality. In particular, as a result of analyzing the basis for judgment among in-service mathematics teachers whose judgment on reality was reversed in the pre- and post-survey, changes in the perception of in-service mathematics teachers was confirmed, who did not consider certain criteria as a criterion for reality in the pre-survey, but considered them as a criterion for reality in the post-survey. In addition, as a result of evaluating the tasks designed by in-service mathematics teachers for mathematical modeling, in-service mathematics teachers showed the competency to reflect reality in their tasks. However, among the five criteria for reality, the criterion for "situations that can occur in students' daily lives," "need to solve the task," and "require conclusions in a real-world situation" were relatively less reflected. In addition, it was found that the proportion of teachers with low task development competencies was higher in the teacher group who could not make the right judgment than in the teacher group who could make the right judgment on the reality of the task. Based on the results of these studies, this study provides implications for teacher education to enable mathematics teachers to apply mathematical modeling lesson in their classes.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.267-281
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• 2004

Many students feel the word problems are very difficult. This study analyzes the linguistic and cognitive factors that affect word problem solving so that we help students bring through the difficulty. There are a text base, a situation model, and a real world in the linguistic aspects. Students have a difficulty at the transition from text base to situation model(equation), and make lots of errors at the situation model. In the cognitive aspects, I investigated problem solving schemes, strategies, and complexity level. Students are likely to choose strategy by the contents which teacher instructed, but not by low complexity level, and mix up the amount of sugar and sugar water, and concentration. We can recognize how complex the types of word problems are to solve, which strategies students choose largely, and what errors that students make in the problem solving are.

• The KIPS Transactions:PartB
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• v.9B no.3
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• pp.277-286
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• 2002

Genetic programming (GP) has been combined with quantum mechanical perturbation theory to make a new algorithm to construct mathematical models and perform predictions for chaotic time series from real world. Procedural similarities between time series modeling and perturbation theory to solve quantum mechanical wave equations are discussed, and the exemplary GP approach for implementing them is proposed. The approach is based on multiple populations and uses orthogonal functions for GP function set. GP is applied to original time series to get the first mathematical model. Numerical values of the model are subtracted from the original time series data to form a residual time series which is again subject to GP modeling procedure. The process is repeated until predetermined terminating conditions are met. The algorithm has been successfully applied to construct highly effective mathematical models for many real world chaotic time series. Comparisons with other methodologies and topics for further study are also introduced.

• Journal of the Korean School Mathematics Society
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• v.25 no.2
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• pp.125-148
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• 2022

This study aimed to compare and analyze the number and characteristics of modeling problems in chapters related to function contents in International Baccalaureate Diploma Program (IBDP) mathematics textbooks and Korean high school mathematics textbooks. This study implies how the textbooks contributed to the improvement of students' modeling competency. In this study, three textbooks from IBDP and all nine textbooks from the Korean 2015 revised curriculum were selected. All the problems in textbooks were classified into real-world problems and non-real-world problems. Problems classified as real-world problems were once again divided into word problems and modeling problems according to the need to set up mathematical models. Modeling problems were further categorized into standard applications and good modeling problems depending on whether all the necessary information was included in the problem-solving process. Among the 12 textbooks, the textbook with the most modeling problems was the IBDP textbook, 'Math: Applications and Interpretation', which accounted for 50.41% of modeling problems to the total number of problems. This textbook provided learners with significantly higher modeling opportunities than other IBDP and Korean textbooks, which had 2% and 9% modeling problem ratios. In all 12 textbooks, all problems classified as modeling problems appeared as standard applications, and there were no proper modeling problems. Among the six sub-competencies of mathematical modeling, 'mathematical analysis' and 'interpretation and evaluation of results' sub-competencies appeared the most with very similar number of modeling problems, followed by the 'mathematization'. It is expected that the results of this study will help compare the number and ratio of modeling problems in each textbook and provide a better understanding of which modeling sub-competencies appear to what extent in the modeling problems.