• Communications of Mathematical Education
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• v.3
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• pp.207-228
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• 1997

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.75-105
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• 2005

This study explored a mathematical modeling flow and the effect of interactions among students and between a student and Excel on modeling in a small group modeling environment with Excel. This is a case study of three 8th graders' modeling activity using Excel during their extra lessons. The conclusions drawn from this study are as follows: First, small group modeling using Excel was formed by formulating 4∼10 modeling cycles in each task. Students mainly formed tables and graphs and refined and simplified these models. Second, students mainly formed tables, algebraic formulas and graphs and refined tables considering each variable in detail by obtaining new data with inserting rows. In tables, students mainly explored many expected cases by changing the values of the parameters. In Graphs, students mainly identified a solution or confirmed the solution founded in a table. Meanwhile, students sometimes constructed graphs without a purpose and explored the problem situations by graphs mainly as related with searching a solution, identifying solutions that are found in the tables. Thus, the teacher's intervention is needed to help students use diverse representations properly in problem situations and explore floatingly and interactively using multi-representations that are connected numerically, symbolically and graphically. Sometimes students also perform unnecessary activities in producing data by dragging, searching a solution by 'trial and error' and exploring 'what if' modeling. It is considered that these unnecessary activities were caused by over-reliance on the Excel environment. Thus, the teacher's intervention is needed to complement the Excel environment and the paper-and-pencil environment properly.

• 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.20 no.3
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• pp.221-239
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• 2010

Attention to Korean perspective mathematics education has been increasingly paid m international academic meetings or international comparative studies. Personal or intuitive, vague explanation has been given based on limited literature or observations. This increasing attention and Jack of studies warrant the necessity of systematic researches on it. This article aims at clarifying the research issues in searching for Korean perspective on mathematics education and finding the starting point through discussion on mathematical modeling by teacher on researchers and researchers. Firstly, hypothetical perspective will be described. Secondly, Fourteen teacher educators' and seven researchers' opinion on it will be discussed. Findings imply that strong responsibility for Korean mathematics teachers to reveal theoretical aspects of mathematical knowledge, i.e., structure or essence, as well as to pursue efficiency and effectiveness in mathematics teaching and learning is the main aspect of Korean perspective on mathematics education.

• The Mathematical Education
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• v.55 no.1
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• pp.41-71
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• 2016

The purpose of this study is to investigate elementary students' communication in process of applying mathematical modeling. For this study, 22 fifth graders in an elementary school were observed by applying mathematical modeling process (presentation of problem ${\rightarrow}$ model inducement activity ${\rightarrow}$ model exploration activity ${\rightarrow}$ model application activity). And the level of their communication with their activity sheets and outputs, observation records and interviews were also analyzed. Additionally, by analyzing the activity cases of and , this study researched that what is a positive influence on students' communication skills. Whereas showed significant advance in the level of communication, who communicated actively on speaking area but not on every areas showed insensible changes. To improve communication abilities, cognitive tension and debate situation are needed. This means, mathematical education should continuously provide students with mathematical communication learning, and a class which contains mathematical communication experiences (such as mathematical modeling) will be needed.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.627-629
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• 1998

본 논문에서는 파티클 시스템(Particel System)을 이용한 실시간 기체 모델링 알고리즘을 제시한다. 일반적으로 그래픽스 분야에서, 주요한 자연현상의 하나인 기체의 운동은 수학적으로 복잡한 모델을 사용하여 그 모델링이 매우 복잡하였다. 따라서 빠른 구현시간을 얻기 위해서는 고성능의 컴퓨터가 요구되어왔다. 이 알고리즘에서는 물리학에서 수학적으로 정의된, 기체의 움직임에 적용되는 요소 각각을 추계 모델(Stochastic Model)로 다시 재 정의하여 기체 입자각각에 적용시켜 계산과정을 간단히 하였다. 따라서 일반적으로 사용되는 연구용 컴퓨터시스템에서도 실시간 애니메이션의 구현이 가능하다.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.351-374
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• 2018

The purpose of this study is to support the understandings of teachers about the instructional strategies of collaborative problem solving and mathematical modeling as presented in the 2015 revised mathematics curriculum. For this, tasks of the Cubes unit from six grader's and lesson plans were developed. The specific problem solving processes of students and the practices of teachers which appeared in the classes were analyzed. In the course of solving a series of problems, students have formed a mathematical model of their own, modifying and complementing models in the process of sharing solutions. In particular, it was more effective when teachers explicitly taught students how to share and discuss problem-solving. Based on these results this study is expected to suggest implications on how to foster students' problem solving ability as mathematical subject competency in elementary classrooms.

• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.91-117
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• 2017

In this paper, we develop a logarithm units' teaching learning materials using genetic modeling which is designed for students to construct by themselves and figure out mathematical knowledge conceptually, and we analyze the process of students' comprehension of logarithm concepts through genetic modeling activities. For this purpose, we divide logarithm units into three subunits and develop teaching learning materials which include genetic original contexts and are framed by the four pedagogic phases of genetic modeling, application, extraction, comprehension, and construction so that students themselves are capable of construct the concepts of logarithm units. The developed teaching learning materials are applied into lessons for two intermediate-basic students and two intermediate-advanced students. Through this, we examine students' conceptual construction process about logarithms units with the four pedagogical stages of genetic modeling applied, and analyze the depth of their comprehension about the logarithm units based on the general phases of mathematics-learning introduced by van Hiele, and then we suggest several pedagogical implications.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.