• Education of Primary School Mathematics
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• v.6 no.1
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• pp.41-54
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• 2002

The purpose of this study is to find out what mathematical situation means, how to pose a meaningful situation and how situation-centered teaching could be done. The obtained informations will help learners to improve their math abilities. A survey was done to investigate teachers' perception on teaching-learning in mathematics by elementary teachers. The result showed that students had to find solutions of the textbook problems accurately in the math classes, calculated many problems for the class time and disliked mathematics. We define mathematical situation. It is artificially scene that emphasize the process of learners doing mathematizing from physical world to identical world. When teacher poses and expresses mathematical situation, learners know mathematical concepts through the process of mathematizing in the mathematical situation. Mathematical situation contains many concepts and happens in real life. Learners act with real things or models in the mathematical situation. Mathematical situation can be posed by 5 steps(learners' environment investigation step, mathematical knowledge investigation step, mathematical situation development step, adaption step and reflection step). Situation-centered teaching enhances mathematical connections, arises learners' interest and develops the ability of doing mathematics. Therefore teachers have to reform textbook based on connections of mathematics, other subject and real life, math curriculum, learners' level, learners' experience, learners' interest and so on.

• School Mathematics
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• v.11 no.4
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• pp.665-683
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• 2009

The purpose of this study is to improve forward mathematics study by analyzing the effects of the teaching and learning process applied situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes. For this purpose, the research questions were established as follows: 1. How the situation-based mathematical problem posing activity(WQA activity) changes the problem solving ability of students? 2. How the situation-based mathematical problem posing activity(WQA activity) changes the mathematical attitudes of students? The results of the study were as follows: (1) There was significant difference between experimental group and comparative group in problem solving ability. This means that situation-based mathematical problem posing activity was generally more effective in improving problem solving ability than general classroom-based instruction. (2) There was not significant difference between experimental group and comparative group in mathematical attitudes. But the experimental group's average scores of mathematical attitudes except mathematical confidence was higher than comparative group's ones. And there was significant difference in the mathematical adaptability. The results obtained in this study suggest that the situation-based mathematical problem posing activity can be used to improve the students' problem solving ability and mathematical attitudes

• Communications of Mathematical Education
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• v.23 no.2
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• pp.429-459
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• 2009

The purpose of this study was to help the students deepen their mathematical understanding and practitioner improve her mathematics lessons. The teacher-researcher developed mathematical situation based problem solving instruction model which was modified from PBL(Problem Based Learning instruction model). Three lessons were performed in the cycle of reflection, plan, and action. As a result of performance, reflective knowledges were noted as followed points; students' mathematical understanding, mathematical situation based problem solving instruction model, improvement of mathematics teachers.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.561-582
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• 2013

Meanwhile, the meaning has been emphasized in mathematics. But the meaning of meaning had not been clearly defined and the meaning classification had not been reported. In this respect, the meaning was classified as expressive and cognitive. Furthermore, it was reclassified as mathematical situation and real situation. Based on this classification, we investigated how student recognizes the meaning when solving mathematical modeling problem. As a result, we found that the understanding of cognitive meaning in real situation is more difficult than that of the other meaning. And we knew that understanding the meaning in solving of equation, has more difficulty than in expression of equation. Thus, to help students understanding the meaning in the whole process of mathematical modeling, we have to connect real situation with mathematical situation. And this teaching method through unit and measurement, will be an alternative method for connecting real situation and mathematical situation.

• 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.

• The Mathematical Education
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• v.51 no.1
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• pp.77-88
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• 2012

This qualitative research provides a situation model, which is designed for promoting learning of eigenvalue and eigenvector. This study also demonstrates the usefulness of the model through a small groups discussion. Particularly, participants of the discussion were asked to decide the numbers of milk cows in order to make constant amounts of cheese production. Through such discussions, subjects understood the notion of eigenvalue and eigenvector. This study has following implications. First of all, the present research finds significance of situation model. A situation model is useful to promote learning of mathematical notions. Subjects learn the notion of eigenvalue and eigenvector through the situation model without difficulty. In addition, this research demonstrates potentials of small groups discussion. Learners participate in discussion more actively under small group debates. Such active interaction is necessary for situation model. Moreover, this study emphasizes the role of teachers by showing that patience and encouragement of teachers promote students' feeling of achievement. The role of teachers are also important in conveying a meaning of eigenvalue and eigenvector. Therefore, this study concludes that experience of learning the notion of eigenvalue and eigenvector thorough situation model is important for teachers in future.

• East Asian mathematical journal
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• v.36 no.2
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• pp.173-201
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• 2020

Mathematical modeling has been emphasized because it offers important opportunities for students to both apply their learning of mathematics to a situation and to explore the mathematics involved in the context of the situation. However, unlike its importance, mathematical modeling has not been grounded in typical mathematics classes because teachers do not have enough understanding of mathematical modeling and they are skeptical to implement it in their lessons. The current study analyzed the data, such as video recordings, slides, and surveys for teachers, collected in four lessons of teacher education in terms of mathematical modeling. The study reported different kinds of tasks that are authentic with regards to mathematical modeling. Furthermore, in teacher education, teachers' identities have separated a mode as learners and a mode as teachers and conflicts and intentional transition were observed. Analysis of the surveys shows what teachers think about mathematical modeling with their understanding of it. In teacher education, teachers achieved different kinds of modeling tasks and experience them which are helpful to enact mathematical modeling in their lessons. However, teacher education also needs to specifically offer what to do and how to do it for their lessons.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• IE interfaces
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• v.22 no.4
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• pp.359-367
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• 2009

The vehicle travel time between the demand points in downtown area is greatly influenced by complex road condition and traffic situation that change real time to various external environments. Most of research in the vehicle routing problems compose vehicle routes only considering travel distance and average vehicle speed between the demand points, however did not consider dynamic external environments such as traffic situation by service time zones. A realistic vehicle routing problem which considers traffic situation of smooth, delaying, and stagnating by three service time zones such as going to work, afternoon, and going home was suggested in this study. A mathematical programming model was suggested and it gives an optimal solution when using ILOG CPLEX. A hybrid genetic algorithm was also suggested to chooses a vehicle route considering traffic situation to minimize the total travel time. By comparing the result considering the traffic situation, the suggested algorithm gives better solution than existing algorithms.

• 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.