• Title/Summary/Keyword: mathematical modeling

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A Comparative Study on High School Students' Mathematical Modeling Cognitive Features

  • Li, Mingzhen;Hu, Yuting;Yu, Ping;Cai, Zhong
    • Research in Mathematical Education
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    • v.16 no.2
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    • pp.137-154
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    • 2012
  • Comparative studies on mathematical modeling cognition feature were carried out between 15 excellent high school third-grade science students (excellent students for short) and 15 normal ones (normal students for short) in China by utilizing protocol analysis and expert-novice comparison methods and our conclusions have been drawn as below. 1. In the style, span and method of mathematical modeling problem representation, both excellent and normal students adopted symbolic and methodological representation style. However, excellent students use mechanical representation style more often. Excellent students tend to utilize multiple-representation while normal students tend to utilize simplicity representation. Excellent students incline to make use of circular representation while normal students incline to make use of one-way representation. 2. In mathematical modeling strategy use, excellent students tend to tend to use equilibrium assumption strategy while normal students tend to use accurate assumption strategy. Excellent students tend to use sample analog construction strategy while normal students tend to use real-time generation construction strategy. Excellent students tend to use immediate self-monitoring strategy while normal students tend to use review-monitoring strategy. Excellent students tend to use theoretical deduction and intuitive judgment testing strategy while normal students tend to use data testing strategy. Excellent students tend to use assumption adjustment and modeling adjustment strategy while normal students tend to use model solving adjustment strategy. 3. In the thinking, result and efficiency of mathematical modeling, excellent students give brief oral presentations of mathematical modeling, express themselves more logically, analyze problems deeply and thoroughly, have multiple, quick and flexible thinking and the utilization of mathematical modeling method is shown by inspiring inquiry, more correct results and high thinking efficiency while normal students give complicated protocol material, express themselves illogically, analyze problems superficially and obscurely, have simple, slow and rigid thinking and the utilization of mathematical modeling method is shown by blind inquiry, more fixed and inaccurate thinking and low thinking efficiency.

A study on the communication in process of applying mathematical modeling to children in elementary mathematics classroom (초등학생의 수학적 모델링 적용과정에서 나타나는 의사소통에 관한 연구: 5학년 수와 연산을 중심으로)

  • Lee, Ji Young;Kim, Min Kyeong
    • 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.

Prospective Teachers' Perception of Mathematical Modeling in Elementary Class (수학적 모델링 수업에 대한 초등 교사의 인식)

  • Choi, Jisun
    • Journal of Educational Research in Mathematics
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    • v.27 no.2
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    • pp.313-328
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    • 2017
  • This study aims to identify prospective elementary school teachers' perception of mathematical modeling in elementary class. Forty elementary school teachers participated in this study. Each teacher analysed the previous case studies about mathematical modeling in elementary class, developed a hypothetical learning trajectory, applied the hypothetical learning trajectory to his/her class, reflected students' learning and his/her teaching, and made reflective journals. These journals contained teachers' perception of mathematical modeling and the difficulties that teachers experienced in teaching mathematics as mathematical modeling. These journals were analyzed to identify teachers' perception of mathematical modeling in elementary class. This study shows that teachers have common features of mathematical modeling but their perspectives are little bit different, are classified into four kinds. And the difficulties that teachers experienced in teaching mathematics as mathematical modeling are classified into 5 categories; Task, Students' cognitive demand, Teacher' monitering, All students' participation, and Classroom culture. At last, suggestions for mathematical modeling in elementary class are done according to the result of this study.

Reconstruction and application of reforming textbook problems for mathematical modeling process (수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용)

  • Park, SunYoung;Han, SunYoung
    • The Mathematical Education
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    • v.57 no.3
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    • pp.289-309
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    • 2018
  • There has been a gradually increasing focus on adopting mathematical modeling techniques into school curricula and classrooms as a method to promote students' mathematical problem solving abilities. However, this approach is not commonly realized in today's classrooms due to the difficulty in developing appropriate mathematical modeling problems. This research focuses on developing reformulation strategies for those problems with regard to mathematical modeling. As the result of analyzing existing textbooks across three grade levels, the majority of problems related to the real-world focused on the Operating and Interpreting stage of the mathematical modeling process, while no real-world problem dealt with the Identifying variables stage. These results imply that the textbook problems cannot provide students with any chance to decide which variables are relevant and most important to know in the problem situation. Following from these results, reformulation strategies and reformulated problem examples were developed that would include the Identifying variables stage. These reformulated problem examples were then applied to a 7th grade classroom as a case study. From this case study, it is shown that: (1) the reformulated problems that included authentic events and questions would encourage students to better engage in understanding the situation and solving the problem, (2) the reformulated problems that included the Identifying variables stage would better foster the students' understanding of the situation and their ability to solve the problem, and (3) the reformulated problems that included the mathematical modeling process could be applied to lessons where new mathematical concepts are introduced, and the cooperative learning environment is required. This research can contribute to school classroom's incorporation of the mathematical modeling process with specific reformulating strategies and examples.

A Study of Modeling Applied Mathematical Problems in the High School Textbook -Focused on the High School Mathematics Textbookin the First Year- (모델링을 활용한 문제의 연구 - 일반수학을 중심으로 -)

  • 김동현
    • Journal of the Korean School Mathematics Society
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    • v.1 no.1
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    • pp.131-138
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    • 1998
  • The aims of mathematical education are to improve uniformity and rigidity, and to apply to an information age which our society demands. One of the educational aims in the 6th educational curriculum emphasizes on the expansion of mathematical thought and utility, But, The change of contents in the text appears little. This means that mathematical teachers must actively develop the new types of problems. That the interests and concerns about mathematics lose the popularity and students recognize mathematics burdensome is the problems of not only teaching method, unrealistically given problems but abstractiveness and conceptions. Mathematical Modeling is classified exact model, almost exact theory based model and impressive model in accordance with the realistic situation and its equivalent degree of mathematical modeling. Mathematical Modeling is divided into normative model and descriptive model according to contributed roles of mathematics. The Modeling Applied Problems in the present text are exact model and stereotyped problems. That the expansion of mathematical thought in mathematics teaching fell into insignificance appears well in the result of evaluating students. For example, regardless of easy or hard problems, students tend to dislike the new types of mathematical problems which students can solve with simple thought and calculation. The ratings of the right answer tend to remarkably go down. If mathematical teachers entirely treat present situation, and social and scientific situation, students can expand the systematic thought and use the knowledge which is taught in the class. Through these abilities of solving problems, students can cultivate their general thought and systematic thought. So it is absolutely necessary for students to learn the Modeling Applied Problems.

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A study on literature review of mathematical modeling in mathematical competencies perspective (수학 교과 역량 관점에서의 수학적 모델링에 관한 선행 연구 탐색)

  • Choi, Kyounga
    • Journal of the Korean School Mathematics Society
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    • v.20 no.2
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    • pp.187-210
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    • 2017
  • The animated discussion about mathematical modeling that had studied consistently in Korea since 1990s has flourished, because mathematical modeling was involved in the teaching-learning method to improve problem solving competency on 2015 reformed mathematics curriculum. In an attempt to re-examine the educational value and necessity of application to school education field, this study was to review the literature of mathematical modeling in mathematical competencies perspective. As a result, mathematical modeling could not only be involved the components of problem solving competency, but also support other competencies; reasoning, creativity-amalgamation, data-processing, communication, and attitude -practice. In this regard, This paper suggested the necessity of the discussion about the position of mathematical modeling in mathematical competencies and the active use of mathematical modeling tasks in mathematics textbook or school classes.

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Secondary Teachers' Perspectives on Mathematical Modeling and Modeling Mathematics: Discovery, Appreciation, and Conflict

  • Ahmad M. Alhammouri;Joseph DiNapoli
    • Research in Mathematical Education
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    • v.26 no.3
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    • pp.203-233
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    • 2023
  • Recent international reform movements call for attention on modeling in mathematics classrooms. However, definitions and enactment principles are unclear in policy documents. In this case study, we investigated United States high-school mathematics teachers' experiences in a professional development program focused on modeling and its enactment in schools. Our findings share teachers' experiences around their discovery of different conceptualizations, appreciations, and conflicts as they envisioned incorporating modeling into classrooms. These experiences show how professional development can be designed to engage teachers with forms of modeling, and that those experiences can inspire them to consider modeling as an imperative feature of a mathematics program.

ON THE STOCHASTIC OPTIMIZATION PROBLEMS OF PLASTIC METAL WORKING PROCESSES UNDER STOCHASTIC INITIAL CONDITIONS

  • Gitman, Michael B.;Trusov, Peter V.;Redoseev, Sergei A.
    • Journal of applied mathematics & informatics
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    • v.6 no.1
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    • pp.111-126
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    • 1999
  • The article is devoted to mathematical modeling of prob-lems of stochastic optimization of the plastic metal working. Classifi-cation and mathematical statements of such problems are proposed. Several calculation techniques of the single goal function are pre-sented. The probability theory and the Fuzzy numbers were applied for solution of the problems of stochastic optimization.

Instructional Alignment Observation Protocol (IAOP) for Implementing the CCSSM: Focus on the Practice Standard, "Model with Mathematics"

  • Hwang, Jihyun
    • Research in Mathematical Education
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    • v.23 no.3
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    • pp.149-164
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    • 2020
  • This study aimed to establish an observation protocol for mathematical modeling as an alternative way to examine instructional alignment to the Common Core State Standards for Mathematics. The instructional alignment observation protocol (IAOP) for mathematical modeling was established through careful reviews on the fidelity of implementation (FOI) framework and prior studies on mathematical modeling. I shared the initial version of the IAOP including 15 items across the structural and instructional critical components as the FOI framework suggested. Thus, the IAOP covers what teachers should do and know for practices of mathematical modeling in classrooms and what teachers and students are expected to do. Based on the findings in this study, validity and reliability of the IAOP should be evaluated in follow-up studies.

A Study on Development of Problem Contexts for an Application to Mathematical Modeling (수학적 모델링 적용을 위한 문제상황 개발 및 적용)

  • Kim, Min-Kyeong;Hong, Jee-Yun;Kim, Hye-Won
    • The Mathematical Education
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    • v.49 no.3
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    • pp.313-328
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    • 2010
  • Mathematical modeling has been observed in the way of a possibility to contribute in improving students' problem solving abilities. One of the important views of real life problem context could be described such as a useful ways to interpret the real life leading to children's abstraction process. The problem contexts for the grade 6 with mathematical modeling perspectives were developed by reviewing the current 7th National Mathematics Curriculum of Korea. Those include the 5 content areas such as number & operation, geometry, measurement, probability & statistics, and pattern & problem solving. One of problem contexts, "Space", specially designed for pattern & problem solving area, was applied to the grade 6 students and analyzed in detail to understand student's mathematical modeling progress.