• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.93-117
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• 2019

Considering precedent studies in which research subjects are mainly confined to secondary school students or higher grade students of elementary schools, we can notice that there has been implicit agreement that instruction of mathematical modeling is quite difficult to lower grade students of elementary schools. Compared to this tendency, this study aims to examine the possibility of instruction of mathematical modeling for all of school ages, and more specifically, the applicability of mathematical modeling tasks to lower graders. To do this, we developed a mathematical modeling task proper to cognitive characteristics of lower graders and applied this task to the second graders. Based on the research results by lesson observation and the teacher's reflection, some didactical suggestions were induced for teaching the lower grade elementary school students mathematical modeling.

• East Asian mathematical journal
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• v.34 no.3
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• pp.317-330
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• 2018

We develop a mathematical model for the obesity dynamics to investigate the long term obesity trend with the consideration of psychological and social factors due to the increasing prevalence of obesity around the world. Many mathematical models for obesity dynamics adopted the modeling idea of infectious disease and treated overweight and obese people infectious and spreading obesity to normal weight. However, this modeling idea is not proper in obesity modeling because obesity is not an infectious disease. In fact, weight gain and loss are related to social interactions among different weight groups not only in the direction from overweight/obese to normal weight but also the other way around. Thus, we consider these aspects in our model and implement personal weight gain feature, a psychological factor such as body image dissatisfaction, and social interactions such as positive support on weight loss and negative criticism on weight status from various weight groups. We show that the equilibrium point with no normal weight population will be unstable and that an equilibrium point with positive normal weight population should have all other components positive. We conduct computer simulations on Korean demography data with our model and demonstrate the long term obesity trend of Korean male as an example of the use of our model.

• Research in Mathematical Education
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• v.25 no.2
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• pp.99-115
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• 2022

This study examined difficulties middle school students have in learning mathematics and proposed a flipped classroom consisting of Khan Academy activities, small-group problem solving, and mathematical modeling to help improve their learning. A mixed-method approach was used to identify difficulties students have in learning mathematics, explore how the flipped classroom helped them reduce the learning difficulties identified, and examine if there were differences in students' mathematics achievement and their affective characteristics after participating in the flipped classroom. Qualitative analyses showed that students had difficulties in understanding mathematical concepts and finding effective ways to learn as well as negative views towards learning mathematics. This study also found that each activity of the flipped classroom had a different impact on student learning. Before class, the Khan Academy activities were most likely to help students understand mathematical concepts. In class, small-group problem solving activities were most helpful for students who had trouble finding effective learning methods and environments. Mathematical modeling activities were most likely effective in changing students' negative views towards mathematics. A quantitative analysis showed that the flipped classroom not only significantly improved the students' mathematics achievement, but also positively affected their confidence and motivation and how much they valued learning mathematics.

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

• Journal of the Korean School Mathematics Society
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• v.24 no.3
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• pp.283-308
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• 2021

This study aims to analyze statistical tasks in Korean and Singaporean textbooks with the mathematical modeling perspective and compare the learning contents and experiences of students from both countries. I analyzed mathematical modeling tasks in the textbooks based on five aspects: (1) the mathematical modeling process, (2) the data type, (3) the expression type, (4) the context, and (5) the mathematical activity. The results of this study show that Korean and Singaporean textbooks provide the highest percentage of the "working-with-mathematics" task, the highest percentage of the "matching task," and the highest percentage of the "picture" task. The real-world context and mathematical activities used in Korean and Singaporean textbooks differed in percentage. This study provides implications for the development of textbook tasks to support future mathematical modeling activities. This includes providing a balanced experience in mathematical modeling processes and presenting tasks in various forms of expression to raise students' cognitive level and expand the opportunity to experience meaningful mathematizing. In addition, it is necessary to present a contextually realistic task for students' interest in mathematical modeling activities or motivation for learning.

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

• East Asian mathematical journal
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• v.40 no.3
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• pp.341-353
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• 2024

This paper aims to provide a general review of Opinion Dynamics (OD) and its related models, along with application examples for special agents. We will discuss special classes of social actors, such as informed actors, opponents, and extremists, in the context of opinion dynamics. Our main objective is to determine the extent to which opinion dynamics, as a mathematical sociology, relates to social reality. To achieve this, we present key elements of mathematical sociology in Opinion Dynamics, which we then apply to real socioeconomic phenomena using modeling assumptions and mathematical formulations.

• School Mathematics
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• v.9 no.4
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• pp.467-486
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• 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
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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.