• 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 the Korea Academia-Industrial cooperation Society
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• v.18 no.2
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• pp.704-710
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• 2017

Our research team is developing a 6-DOF manipulator that is adequate for the narrow workspace of press forming processes. This paper addresses the task sequence optimization methods for the manipulator to minimize the task-finishing time. First, a kinematic model of the manipulator is presented, and the anticipated times for moving among the task locations are computed. Then, a mathematical model of the task sequence optimization problem is presented, followed by a comparison of three meta-heuristic methods to solve the optimization problem: an ant colony system, simulated annealing, and a genetic algorithm. The simulation shows that the genetic algorithm is robust to the parameter settings and has the best performance in both minimizing the task-finishing time and the computing time compared to the other methods. Finally, the algorithms were implemented and validated through a simulation using Mathworks' Matlab and Coppelia Robotics' V-REP (virtual robot experimentation platform).

• Communications of Mathematical Education
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• v.37 no.2
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• pp.257-276
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• 2023

Mathematical modeling can be described as a series of processes in which real-world problem situations are understood, interpreted using mathematical methods, and solved based on mathematical models. The effectiveness of mathematics instruction using mathematical modeling has been demonstrated through prior research. This study aims to explore insights for mathematical modeling instruction by analyzing the metacognitive characteristics shown in the mathematical modeling cycle, according to the mathematical thinking styles of elementary math gifted students. To achieve this, a mathematical thinking style assessment was conducted with 39 elementary math gifted students from University-affiliated Science Gifted Education Center, and based on the assessment results, they were classified into visual, analytical, and mixed groups. The metacognition manifested during the process of mathematical modeling for each group was analyzed. The analysis results revealed that metacognitive elements varied depending on the phases of modeling cycle and their mathematical thinking styles. Based on these findings, didactical implications for mathematical modeling instruction were derived.

• School Mathematics
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• v.5 no.1
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• pp.1-25
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• 2003

This study develops a performance assessment system to improve grade 4-9 students' creativity. First, this study discusses its educational meaning, its task types, scoring methods and practical application methods. Then, this study provides the typical examples of performance assessment task classified by each of the types and its scoring rubrics. Finally, this study analyzes students' achievement levels for each task. Each task includes item informations such as content area, evaluation goal, evaluation procedure, preparatory material, characteristics, considering points, scoring rubric etc. for grade 4-9 teachers to use them in their evaluation processes directly without difficulties.

• School Mathematics
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• v.3 no.2
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• pp.295-324
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• 2001

Until now, There have been few studies to investigate a degree of abilities or interesting about mathematical problem-posing of first and second grades in elementary school. This is due to the fact that this students(1st and 2nd grades) have a limited amount of study time and their minds are not fully developed, and are lacking in their representation of ability to use the national language. This being the case, it is difficult to investigate their Mathematical problem-posing in a practical manner. However, our 7th elementary school Mathematics curriculum emphasizes the teaching and learning of Mathematical problem-posing from a basic level of first and second grade with emphasis on activity in teaming Mathematics. Through this study, having analysed the problems those children posed, I have found out they improved in numbers and correctness of their posed problems. And I too could found out showing to their much interesting and confidence to mathematical problem-posing and could confirmed for the children to admit themselves its merits through analyzing some questions to ask their opinions to it. I expect that this study can help to develop the teaching and learning materials for mathematical problem-posing and also to improve its methods of elementary school mathematics. The next study task is, I think, that it is necessary to accumulate the studies to investigate and analyse the practical learning activities of children for problem-posing contents of mathematics text books.

• Research in Mathematical Education
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• v.11 no.1
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• pp.33-51
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• 2007

The present study explores mathematics teachers' understanding of division by zero and their approaches to explaining the impossibility of division by zero. This study analyzes Chinese and Korean middle school mathematics teachers' responses to the teaching task of explaining the impossibility of dividing 7 by zero, and examples of teachers' reasoned explanations for their answers are presented. The findings from this study suggest that most Korean teachers offer multiple types of mathematical explanations for justifying the impossibility of division by zero, while Chinese teachers' explanations were more uniform and based less on mathematical ideas than those of their Korean counterparts. Another finding from this study is that teachers' particular conceptions of zero were strongly associated with their justifications for the impossibility of division by zero, and the influence of the teachers' conceptions of zero was revealed as a barrier in composing a well-reasoned explanation for the impossibility of division by zero. One of the practical implications of this study is those teachers' basic attitudes toward always attempting to give explanations for mathematical facts or mathematical concepts do not seem to be derived solely from their sufficient knowledge of the facts or concepts of mathematics.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.333-350
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• 1999

The purpose of this study is to define performance assessment of mathematics, to make a model of performance task of mathematics for the first grade middle school students in higher group, to examine validity and reliability of performance task and to investigate the effects on the students' achievement and attitude. It first defines performance assessment and exanmines its main features and scoring methods. Based on these, nine performance assessment tasks and scoring criteria were designed for the first grade middle school students in higher group. The validity of performance tasks were examined by experts. The loaming achievement and mathematical attitude test between two groups were performed as pre and post test. The thinking of students about performance assessment was investigated by attitude survey. The results of this study are as follows: First, the validity of the performance tasks is very high. Second, The control group. Forth, there is a difference in student's attitude about mathematics between scorer reliability was high due to the scorer training. Third, there is little difference in teaming achievement between experimental and experimental and control group in 5% meaningful levels. That is, student's of both groups attitude about mathematics comes negatives, but the width of change of negative attitude in experimental group is less than control group. In the trend of negative attitude of mathematics as grade comes higher, this results showed that performance assessment of mathematics had positive influence on attitude of mathematics. The result of survey about mathematical performance assessment experience showed that students have positive attitude to performance assessment and recognized effectiveness of the performance assessment of mathematics.

• The Mathematical Education
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• v.53 no.2
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• pp.275-290
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• 2014

This study investigated the types of the 3D geometric thinking and spatial reasoning through the observation of the 2D representing activities for representing the 3D geometrical objects with preservice secondary mathematics teachers. For this purpose, the 43 sophomoric students in college of education were divided into 10 groups and observed their group task performance on the basis of the representation they used. Observed processes were all recorded and the participants were interviewed based on the task. As a result, the role of physical object that becoming the object of geometric thinking and spatial reasoning, and diverse strategies and phenomena of the process that representing the 3D geometric figures in 2D were discovered. Furthermore, these processes of representing were assumed to be influenced by experience and study practice of students, and various forms of representing process were also discovered in the process of small group activities.

• School Mathematics
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• v.16 no.1
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• pp.1-17
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• 2014

Mathematical creativity in school mathematics is connected with problem solving. The purpose of this study was to analyse elementary students' the mathematical creativity using multiple solution tasks which required to solve a mathematical problem in different ways. For this research, I examined and analyzed the response to four multiple solution tasks according to the evaluation system of mathematical creativity which consisted of the factors of creativity(fluency, flexibility, originality). The finding showed that mathematical creativity was different between students with greater clarity. And mathematical creativity in tasks was different. So I questioned the possibility of analysis of students' the mathematical creativity in mathematical areas. According to the evaluation system of mathematical creativity of this research, mathematical creativity was proportional to the fluency. But the high fluency and flexibility was decreasing originality because it was easy for students to solve multiple solution tasks in the same ways. So, finding of this research can be considered to make the criterion in both originality in rare and mathematical aspects.

• The Mathematical Education
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• v.58 no.1
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• pp.55-77
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• 2019

Textbooks play a very important role as a medium for implementing curriculum in the school. This study aims to analyze tasks for mathematical competencies in the high school 'mathematics' textbooks based on the 2015 revised mathematics curriculum emphasizing competencies. And our study is based on the following two research question. 1. What is the relationship between core competencies and mathematical competencies? 2. What is the distribution of competencies of tasks for mathematical competencies presented in the textbooks? 3. How does the tasks for mathematical competencies reflect the meaning of the mathematical competencies? For this study, the tasks, marked mathematical competencies, were analyzed by elements of each mathematical competencies based on those concept proposed by basic research for the development of the latest mathematics curriculum. The implications of the study are as follows. First, it is necessary to make efforts to strengthen the connection with core competencies while making the most of characteristics of subject(mathematics). Second, it needs to refine the textbook authorization standards, and it should be utilized as an opportunity to improve the textbook. Third, in order to realize competencies-centered education in the school, there should be development of teaching and learning materials that can be used directly.