• The Mathematical Education
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• v.57 no.4
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• pp.353-369
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• 2018

This study started with the following questions. Suppose that students do not accept various forms of geometric series tasks as the same task. Also, let's say that the approach was different for each task. Then, when they realize that they are the same task, how will students connect the different approaches? This study is a process of pro-actively confirming whether or not such a question can be made. For this purpose, three students in the second grade of high school participated in the teaching experiment. The results of this study are as follows. It also confirmed how the students think about the various types of tasks in the geometric series. For example, students have stated that the value is 1 in a series type of task. However, in the case of the 0.999... type of task, the value is expressed as less than 1. At this time, we examined only mathematical expressions of students approaching each task. The problem of reachability was not encountered because the task represented by the series symbol approaches the problem solved by procedural calculation. However, in the 0.999... type of task, a variety of expressions were observed that revealed problems with reachability. The analysis of students' expressions related to geometric series can provide important information for infinite concepts and limit conceptual research. The problems of this study may be discussed through related studies. Perhaps more advanced research may be based on the results of this study. Through these discussions, I expect that the contents of infinity in the school field will not be forced unilaterally because there is no mathematical error, but it will be an opportunity for students to think about the learning method in a natural way.

• Journal of the Ergonomics Society of Korea
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• v.7 no.2
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• pp.31-44
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• 1988

If an error occurs in the automatic mode when the advanced teleoperator system performs a task in hostile environment then the automatic mode changes into the manual mode. The operation by the control program and the operation by a human recover the error in the manual mode. The system resumes the automatic mode and continues the given task. It is necessary to improve the manual mode in order to make the best use of a man-robot system, as a part of the human interface technique. Therefore, the error recovery task is performed by combining the operation by the control program representing autonomy of a robot and the operation by a human representing versatility of a human operator effectively in the view point of human factors engineering. The geometric inverse kinematics is used for the calculation of the robot joint values in the operation by the control program. The singularity operation error and the parameter operation error often occur in this procedure. These two operation errors increase the movement time of the robot and the coordinate reading time, during the error recovery task. A singularity algorithm, parameter algorithm and fuzzy control are studied so as to remove the disadvantages of geometric inverse kinematics. And the geometric straight line motion is studied so as to improve the disadvantages of the operation by a human.

• IE interfaces
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• v.12 no.2
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• pp.305-311
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• 1999

Robot task program is needed to control and manage a Robot without explicitly describing the robot program by user which includes commands, procedures, geometric and signal data in the detail level. To use the Robot task program, a computer system is required to convert the Robot task into the Robot program, which can be understood by the Robot. In this paper, the systemic method for automatic generation of explicit Robot programs (ERP) from task-level commands is described. Specifically, a 3-step procedure including Robot task decomposition, task synchronization and ERP generation is presented.

• 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.

• Journal of the Ergonomics Society of Korea
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• v.9 no.1
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• pp.21-27
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• 1990

Teaching Expert System/World Coordinate System(TES/WDS) was proposed to improve robot motion control. First, precise coordinate reading for getting the inherent data about position and posture of task objects was performed throgh the integrated image and fuzzy processing. Second, singularity and parameter limitation problems in getting the motion data about position and posture of robot in macro motion were solved by proposed geometric algorithm. Third, the unnecessary robot motion was also removed by the Robot Time and Motion (RTM) method and the Multi-Geometric Straight-Line Motion (MGSLM) method in micro motion. This results demonstrated reduction of the average teaching task time according to task order.

• East Asian mathematical journal
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• v.36 no.4
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• pp.493-513
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• 2020

The reason for this study is that the learning content of geometric construction in school mathematics is very insufficient. Geometric construction not only enables in-depth understanding of shapes, but also improves deductive proof skills. In school mathematics education, geometric construction is a very important learning factor, and educational significance is very high in that it can develop reasoning skills essential to the future society. Nevertheless, the reduction of geometric construction learning content in Korean curriculum and mathematics textbooks is against the times. Therefore, the purpose of this study is to analyze the transition of geometric construction learning contents in middle school mathematics curriculum and mathematics textbooks. In order to achieve the purpose of this study, the following studies were conducted. First, we analyze the characteristics of geometric construction according to changes in curriculum and textbooks. Second, we develop a framework for analyzing geometric construction tasks. Third, we explore geometric construction tasks according to the developed framework. Through this, it is expected to provide significant implications for the geometric areas of the new middle school curriculum that will be developed in the future.

• Research in Mathematical Education
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• v.18 no.1
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• pp.41-54
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• 2014

This study investigated the visual-mental capability of pre-service and in-service mathematics teachers as well as academicians making a career change to mathematics teachers with regard to manipulations of two geometric shapes (from 2- to 3-dimensional). Moreover, it investigated whether there are differences between the visual-mental capability of these participant groups. Findings illustrate that most of the participants demonstrate an adequate visual capability relating to the task dealing with a cube. Conversely, very low percentage of participants manifested a visual-mental capability in a task requiring the identification of a solid resulting from rotation of a square page, whose diagonal serves as the rotation axis. The study indicates that learners' high visual view should be developed in order to enhance their visual-mental capability.

• The Journal of Korea Robotics Society
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• v.3 no.2
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• pp.106-111
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• 2008

This paper presents a decentralized coordination for a small-scale mobile robot teams performing a task through cooperation. Robot teams are required to generate and maintain various geometric patterns adapting to an environment and/or a task in many cooperative applications. In particular, all robots must continue to strive toward achieving the team's mission even if some members fail to perform their role. Toward this end, given the number of robots in a team, an effective coordination is investigated for decentralized formation control strategies. Specifically, all members are required first to reach agreement on their coordinate system and have an identifier (ID) for role assignment in a self-organizing way. Then, employing IDs on individual robots within a common coordinate system, a decentralized neighbor-referenced formation control is realized to generate, keep, and switch between different geometric shapes. This approach is verified using an in-house simulator and physical mobile robots. We detail and evaluate the formation control approach, whose common features include self-organization, robustness, and flexibility.

• School Mathematics
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• v.18 no.4
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• pp.819-838
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• 2016

This research analyzed proportional reasoning abilities of the 5th grade students who learned only the basis of ratio and rate and 6th grade students who also learned proportion and cross product strategy. Data were collected through the proportional reasoning tests and the interviews, and then the achievement of the students and their proportional reasoning strategies were analyzed. In the light of such analytical results, the conclusions are as follows. Firstly, there is not much difference between 5th and 6th grade students in the achievement scores. Secondly, both 5th and 6th graders are less familiar with the geometric, qualitative and comparisons tasks than the other tasks. Thirdly, not only 5th graders but also 6th graders used informal strategies much more than the formal strategy. Fourthly, some students can't come up with other strategies than the cross product strategy. Finally, many students have difficulties in discerning proportional situation and non-proportional situations. This study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: focusing on letting students use their informal strategies fluently in geometric, qualitative, and comparisons tasks as well as algebraic, quantitative, and missing value tasks focusing on the concept of ratio and proportion instead of enforcing the formal strategy.

• Research in Mathematical Education
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• v.16 no.1
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• pp.31-50
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• 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers' proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers' mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners' levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.