• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.243-260
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• 2009

Many students have difficulty studying mathematics because of its unique characteristics and the numbers of underachievers in mathematics are increasing, not decreasing, even though great teaching-learning methods have been provided. The purpose of this research is to examine if instruction using mind-map in mathematical studies has positive effects on achievement and attitudes of underachievers in mathematics. For this, mathematics learning ability test before instruction, survey of attitudes toward mathematics before and after instruction and mathematics learning ability test before and after instruction were performed for 32 underachievers in two classes of first grade in C high school in South Chung cheong Province. The positive effects of instruction using mind-map in mathematical studies on academic achievements and attitudes of underachievers were expected, but results indicate that there is no significant effect. However, results indicate that the use of mind-map in mathematics instruction has positive effects partially on the changes of learning attitudes. Therefore, the characteristics of underachievers in mathematics should be understood first, mind-map according to them should be applied and students should have time to properly perceive and draw mind-map skillfully. In teachers' professional knowledge of mind-map and consideration for students, when follow-up researches and systematic instruction proceed together for a long period time, the desired results can be realized.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.407-423
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• 2006

The reason why creativity becomes the important subject in 21th century is that it does an important role which solves many problems surrounding our whole life in this internationalization, globalization, knowledge-information age. But scholars who formerly researched the creativity-field explain the necessity of creativity with the internal and fundamental reasons. That is, scholars say that creative activities produce originative products and originality itself. And it is the root of which will be able to discover meaning of life and it -creativity - is successive activities that is demanded when individual life want to obtain important value by expressing one's inner world to the outside using creative resource. Recently, with the trends of present age and the educational needs, research about creativity is actively carried out and it draws out the results that creativity can be developed and enhanced through education and training. So, now many researches have focused on how to develop the creativity. Investigating those researches, we found that the recent issues of researches on creativity were changing and now they focused on creative instruction methods and behavioral factors. Especially, they were selected as the subject related to the creative education - creative instructional method and program, atmosphere in classroom, and factors of teacher. It means that the past researches which were a little bit conceptive have been changing to material ones which will be able to enhance creativity and its effect. So, in this research, we have developed the program for CPS(Creativity Problem Solving) and verified its effect.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.199-216
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• 1998

One of the main features of the 7th revised national curriculum is the implementation of a 'Differentiated Curriculum'. Differentiated Curriculum is often interpreted as meaning the same as 'tracking' or 'ability grouping' in western countries. In the 7th revised curriculum, mathematics is organized and implemented by 'Level-Based Differentiated Curriculum'. To develop mathematics textbooks and teaching-and-learning materials for Differentiated Curriculum, the ideas of 'Enriched and Supplemental Differentiated Curriculum'need to be applied, that is, to provide advanced contents for fast learners, and plain contents for slow learners. Level Based Differentiated Curriculum could be implemented by ability grouping either between classes or within classes. According to these two exemplary models, the implementation models for supplemental course and enriched course are determined. The contents for supplemental course are comprised of minimal essential elements selected from the standard course at a decreased level of complexity and abstraction. The contents of enriched courses are focused on various applications of mathematical knowledge in the real world. Special remedy course will be offered to extremely underachieved students, The principles of developing teaching-and-learning material for special remedy course were obtained from the histo-genetic principle, progressive mathematizing principle, and constructivism.

• Journal of KIISE:Software and Applications
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• v.31 no.3
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• pp.276-292
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• 2004

In this paper. we present methods that extract lung regions from chest EBT(electron beam tomography) images then segment the extracted lung region into lung lobes. We use histogram based thresholding and mathematical morphology for extracting lung regions. For detecting pulmonary fissures, we use edge detector and knowledge-based search method. We suggest this edge detector, which uses adaptive filter scale, to work very well for real edge and insensitive for edge by noise. Our experiments showed about 95% accuracy or higher in extracting lung regions and about 5 pixel distance error in detecting pulmonary fissures.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Journal of Wellbeing Management and Applied Psychology
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• v.3 no.2
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• pp.21-26
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• 2020

The purpose of this article is to capture this situation within the changes that take place due to it, inside the Greek society where there is a great need for professional social workers who are able to work targeted and effectively with foreigners, both children and adults, who have or develop mental health problems for the very first time. Over the recent decades the increasing number of migration flows has exerted and continues to exert great pressure on the health system and on the welfare structures of Greece. The bases for the development of a rudimentary reception and integration system that still is in progress have been delayed, while there has been no happy medium, between the enormous pressure that foreigner users of this system put on, and the humanitarian obligation of a well-governed state towards all residents of the country. Straight through everyday clinical practice in the field of intercultural work, social work has the knowledge and techniques for a total management of emerging problems and at the same time provides a value system with an ethical background which approaches refugees and migrants in order to provide quality services, mostly to users of mental health services.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.187-200
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• 1998

This paper presents an original approach for solving short-term power scheduling in extended power system with two fuels in a unit and a limited fuel using Lagrangian relaxations. The underlying model incorporates the full set of costs and constraints including setup, production, ramping, and operational status, and takes the form of a mixed integer nonlinear control problem. Moreover, the mathematical model developed includes two fuels in a unit and a limited fuel, regulation reserve requirements of prespecified group of units. Lagrangian relaxation is used to disaggregate the model by generator into separate subproblems which are then solved with a nested dynamic program including empirical knowledges. The strength of the methodology lies partially in its ability to construct good feasible solutions from information provided by the dual. Thus, the need for branch-and-bound is eliminated. In addition, the inclusion of two fuels in a unit and a limited fuel provides new insight into the limitations of current techniques. Computational experience with the proposed algorithm indicates that Problems containing up to 23 units including 8 unit used two fuels and 24 time periods can be readily solved in reasonable times. Duality gaps of less than 4％ were achieved.