• School Mathematics
• /
• v.6 no.3
• /
• pp.283-299
• /
• 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.

• Communications of Mathematical Education
• /
• v.10
• /
• pp.201-219
• /
• 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
• /
• v.35 no.3
• /
• pp.295-322
• /
• 2021

This study was conducted for one semester through one group pretest-posttest design with 49 first-year middle school students to explore the effects of mathematics-centered STEAM class experiences on students' mathematical modeling abilities. The main results of this study are as follows: First, the results of the pre and post-mathematical modeling ability tests showed that the average score of posttest was improved compared to the pretest, and that the experiences of mathematics-centered STEAM classes provided in this study had a positive effect on improving the mathematical modeling ability of first-year middle school students. Second, STEAM classes were more effective in solving mathematical modeling problems that require students' creative and divergent thinking. Third, the content analysis of student responses for each subquestion showed that STEAM classes were especially more helpful in activating students' mathematical model construction and validating steps.

• School Mathematics
• /
• v.9 no.4
• /
• pp.467-486
• /
• 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
• /
• v.27 no.2
• /
• pp.313-328
• /
• 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.

• Communications of Mathematical Education
• /
• v.24 no.4
• /
• pp.877-889
• /
• 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.

• Education of Primary School Mathematics
• /
• v.26 no.4
• /
• pp.317-332
• /
• 2023

Mathematical modeling activities hold the potential for diverse applications, involving the transformation of real-life situations into mathematical models to facilitate problem-solving. In order to assess the cognitive, affective, and social dimensions of students' engagement in mathematical modeling activities, this study conducted sessions with ten groups of fifth-grade elementary school students. The ensuing processes and outcomes were thoroughly analyzed. As a result, each group effectively applied mathematical concepts and principles in creating mathematical models and gathering essential information to address real-world tasks. This led to notable shifts in interest, enhanced mathematical proficiency, and altered attitudes towards mathematics, all while promoting increased collaboration and communication among group members. Based on these analytical findings, the study offers valuable pedagogical insights and practical guidance for effectively implementing mathematical modeling activities.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.1
• /
• pp.43-64
• /
• 2011

The purpose of this study was to analyze the progress of children's abstraction and to investigate how elementary students understand through mathematical modeling approach in the sixth grader's learning of surface area. Each small group showed their own level on abstraction in mathematical modeling progress. The participants showed improvements in understanding regarding to surface area context.

• Proceedings of the Korean Information Science Society Conference
• /
• 2004.10a
• /
• pp.733-735
• /
• 2004

생명 현상을 시스템적으로 이해하기 위해서는 현상에 대한 수학적 모델링이 필수적이다. 여러 가지 수학적 모델 가운데 상미분 방정식(ODE) 모델은 여러 가지 생화학 반응을 모델링 하는데 널리 사용되고 있다. 본 논문에서는 신호전달 경로에 B형 간염 바이러스가 미치는 영향을 ODE로 모델링하고, 이를 시뮬레이션 한 결과를 보인다. 또한, ODE모델을 설계하는데 있어 보다 유연하고 확장 가능한 새로운 표현 방식을 제안한다.

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