• Journal of the Korean School Mathematics Society
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• v.23 no.3
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• pp.323-349
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• 2020

In this study, we conducted eight reciprocal peer tutoring classes where each student took either role of a tutor or a tutee to study covariational reasoning in ninth graders. Students were given the opportunity to teach their peers with their covariational reasoning as tutors, and at the same time to learn covariational reasoning as tutees. A heterogeneous group was formed so that scaffolding could be provided in the teaching and learning process. A total of eight reciprocal peer tutoring worksheets were collected: four quantitative graph type questions and four questions of the qualitative graph to the group. The results of the analysis are as follows. In reciprocal peer tutoring, students who experienced a higher level of covariational reasoning than their covariational reasoning level showed an improvement in covariational reasoning levels. In addition, students enhanced the completeness of reasoning by modifying or supplementing their own covariational reasoning. Minimal teacher intervention or high-level peer mediation seems to be needed for providing feedback on problem-solving results.

• The Mathematical Education
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• v.46 no.1 s.116
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• pp.33-52
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• 2007

This study is based on the grade 3 National Diagnostic Assessment of Basic Competency(NDABC) in 2005. The purpose of this study is to analyze the results of NDABC by students' gender. It was 19,257 grade 3 students that participated in this study. The average scores are 89.41 and 88.34 for each male and female. The percentage of Below-Basic level for male students is 4.6% and for female 5.6%. The percentage of female students at Below-Basic level is increasing for 3 years. In particular, the percentage of females at Below-Basic level is higher than that of males in the content of measurement, the cognitive domain of reasoning and problem solving, and the situation of real life. The item difficulty for males is lower in fraction, polygon, and right triangle than for females. But female students need to improve the space sense and the problem solving ability in real life. As for the background of students, males think that mathematics is exciting and not difficult in comparison with what females think. And parents of mates are more concerned about children's learning than those of females.

• Journal of the Korean Institute of Gas
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• v.8 no.2 s.23
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• pp.28-34
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• 2004

Enhanced methodologies for process diagnosis and abnormal situation management have been developed for the last two decades. However, there is no single method that always shows better performance over all kinds of diagnostic problems. In this paper, a framework of message-passing, cooperative, intelligent diagnostic agents is presented for improved on-line fault diagnosis through cooperative problem solving of different expertise. A group of diagnostic agents in charge of different process functional perform local diagnoses in parallel; exchange related information with other diagnostic agents; and cooperatively solve the global diagnostic problem of the whole process plant or business units just like human experts would do. For their better understanding, sharing and exchanging of process knowledge and information, we also suggest a way of remodeling processes and protocols, taking into account semantic abstracts of process information and data. The benefits of the suggested multi-agents-based approach are demonstrated by the implementations for solving the diagnostic problems of various chemical processes.

• Human Ecology Research
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• v.59 no.4
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• pp.433-448
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• 2021

The purpose of this study was to analyze two subject competencies (practical problem-solving capability and independent life capability) reflected in the activity tasks included in the 'home life and safety' area of 12 middle school technology-home economics textbooks in accordance with the 2015 revised curriculum. The analysis criteria were sub-elements of two subject competencies. Seven sub-elements were derived from each competency. Frequency analysis was performed to determine how often the sub-elements were reflected in the activity tasks. The results were as follows. First, with regard to the sub-elements of 'practical problem-solving capability', 'value judgment' was reflected most frequently in the activity tasks followed by 'exemplification of solution', 'logical thinking', 'critical thinking', 'decision-making', 'practical reasoning', and 'evaluation of solutions'. Secondly, the sub-elements of 'independent life capability' were unevenly distributed in the activity tasks. The 'capability to perform conscious living' was reflected most frequently followed by 'development and self-identity', 'time, money, and leisure management', and 'reasonable consumption and resource utilization'. For teachers wanting to teach activity-oriented classes and student participatory classes, the results pinpoint the materials necessary to develop learners' subject competencies by using textbooks from different publishing companies.

• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• Journal of Korean Physical Therapy Science
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• v.9 no.4
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• pp.141-153
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• 2002

Problem based learning(PBL) is one of the learning strategies from the constructivism. It is a learning centered students. The tutors are facillitators as activators, helpers and cooperators not organizer in the classrooms. PBL makes that students learn creativity, independence, reasoning skits, communication and collaboration for problem solving. As the PBL process, students get the problems that are in real situation, discussed with others for brain storming, self directed study and revisited to the situation. They think critically and apply to the real situation. When students are to be physical therapists, they are easy to adopt their job and efficient to manage well. But inspite of a lot of advantages to them, there are much conflict to use as the learning strategies. Students perceived one of best learning method that they have experienced, but there are stress, burden, anxiety, timeless to prepare, lack of information and so on. PBL is effective to learning health oriented subjects, problem solving, even a lot preparation and processing for learning. It is reduced the differences between theories in colleges and practices in the fields. In processing of PBL, students get more many skills than the conventional learning. As trying many times to the classrooms, we can fixed to PBL with mistakes and conflict for better the development of the teaching and learning.

• Communications of Mathematical Education
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• v.26 no.2
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• pp.221-249
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• 2012

The purpose of this study is to investigate students decision-making progress through ill-structured problem solving process. For this study, 25 fifth graders in an elementary school were observed by applying ABCDE model (Analyze - Browse - Create - Decision making - Evaluate), and analyzed their decision-making progress analyzing framework which follows 3 steps - making their own decision, discussing/revising with peers, and lastly decision making/solving problem. Upper two groups with better performance in ill-structured problem solving model among 6 groups showed active discussion in group and decision making process with 3 steps (making their own decision, discussing/revising with peers). Even though their decisions are not good-fit to mathematical reasoning result, development and application of ill-structured problems would bring better ability of high level thinking and problem solving to students.

• Research in Mathematical Education
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• v.14 no.3
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• pp.211-218
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• 2010

It is a truism that mathematics is about relations (cf. [Halford, G. S. (1999). The properties of representations used in higher cognitive processes: Developmental implications. In: Sigel, I. E. (Ed.), The Development of Mental Representation: Theories and Applications (pp. 147-168). Mahwah, New Jersey: Erlbaum]). In this article we are considering few problems related to the Viviani's and Routh's Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student's problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani's Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.