• Journal of KIISE
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• v.45 no.3
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• pp.211-223
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• 2018

In this paper, we propose a robot-centered direction relation representation and the relevant reasoning methods for indoor service robots. Many conventional works on qualitative spatial reasoning, when deciding the relative direction relation of the target object, are based on the use of position information only. These reasoning methods may infer an incorrect direction relation of the target object relative to the robot, since they do not take into consideration the heading direction of the robot itself as the base object. In this paper, we present a robot-centered direction relation representation and the reasoning methods. When deciding the relative directional relationship of target objects based on the robot in an indoor environment, the proposed methods make use of the orientation information as well as the position information of the robot. The robot-centered reasoning methods are implemented by extending the existing cone-based, matrix-based, and hybrid methods which utilized only the position information of two objects. In various experiments with both the physical Turtlebot and the simulated one, the proposed representation and reasoning methods displayed their high performance and applicability.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.

• East Asian mathematical journal
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• v.26 no.4
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.507-522
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• 2009

In general, we do fold paper and unfold, it remain paper traces. We can be obtained by using rectangular paper, a mathematical fact and the program had a combination. Depending on the direction of the rectangle, folding paper in the form of variety shows valley and ridge signs of the appearance of this paper. By using (0,1)-code and (0,1)-matrix, we study four kinds of research. Therefore, traces of this view upside down rectangle folding paper how to fold inductive reasoning ability of the code and explore the relationship of traces. Finally, the mathematical content and program development can practice in the field.

• Human Ecology Research
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• v.51 no.6
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• pp.591-602
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• 2013

This paper aims to explore the role of the home economics subject in helping high school students preparing for an independent aged life and to develop problem based teaching plans toward this goal. Contents related to the elderly in the high school home economics and technology 2007 and 2009 revised curricula were analyzed, and elderly-related contents in other subject areas (the 2009 revised curricula of ethics, public health, and social studies) were also comparatively analyzed to determine the identity of the home economics subject in relation to preparation for independent aging. Based on these analysis, five subjects and teaching plans were presented: the aging society and population changes, the characteristics of the elderly, individual preparation for aging, care of the elderly, and welfare services for the elderly. The ultimate objectives of the lessons were, through critical reasoning, to inquire into the causes of current problems the elderly face so that teenagers can understand aging societies and the elderly and to seek reasonable alternatives for teenagers as they prepare for successful and independent aging, increasing their problem-solving abilities in choosing the best course of action by considering the ripple effect of consequences of each of those alternatives. Suggestions on what direction elderly-related education should take in the future, and what roles teachers should take are also provided.