• The Mathematical Education
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• v.59 no.2
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• pp.113-130
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• 2020

The purpose of this study is to analyze how well middle school students understand space geometrical concept related to a cylinder. To this end, we developed the test tool based on prior research and examined 433 middle school students in November and December, 2018. And in March 2019, we interviewed 4 students who showed some type of errors. The difference in the correct answer rate of the questions by the grade and gender was tested, and the error type was analyzed based on the student's responses to the questions to evaluate the spatial reasoning ability. The results of this study are as follows. First, the difference by graders was not statistically significant in the questions evaluating spatial visual ability. On the other hand, in the case of the two questions for evaluating spatial measurement ability and spatial reasoning ability, the difference in the correct answer rate between the 7th graders and 8th is not significant, but the difference between lower graders and 9th was significant. Second, there was no significant difference in the spatial geometric ability of all girls and boys participating in this study. Third, analyzing the student's error type for an item which assessed spatial reasoning ability, we found that there are various error types in relation to visual, manipulative, and reasoning errors.

• Korean Institute of Interior Design Journal
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• no.40
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• pp.34-41
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• 2003

A purpose of this study is to comprehend a concept of 'Open Space', realization of a deconstruction, presented in his works, based on a deconstruction and surrealism Coop Himmelblau's philosophical contemplation and to look into how this concept is interpreted in spaces. A concept of 'Open Space' is functioned as not a singular meaning but a multiple meaning accompanied with other formative ingredient and contemplation, scientific paradigm and a realation with a surroundings. The concept of 'Open Space' in their architentural space is applied. First, the space openness that represents to the extreme a concept 'Open Space', as a 3D designing ways that demolishes a structure and outgrows an ex siting thinking pattern, represents multiple grade spaces and an anti-gravity space. In a material, using glass and iron provides a spacial transparency and through this, visibly liberal sense that an interior and exterior is felt as an unification. Second, an non-expressive box pattern repulses to a spatial rank nature, outgrowing an uniform geometrical system, through demolishing a geometrical system, an edge and fold pattern. This is, as an anti-gravity, dynamic a typical structure, outgrowing an orthogonal system, interpreted as a composite meaning without division in spatial area. Third, the collage is used to represent a complexity and pluralism in representing 'Open space'. The collage that forms a image through combining a fragmentary elements into being a space change, composite constitution and spatial amusement. Thus, It is worthwhile to study how the collage that forms a diverse shape will be developed making what impact as an age and surroundings changed. As we contemplate in former part, Coop Himmelblou has deployed 'deconstruction beyond deconstruction' realm as just their midterm concept in their works like the words 'The architecture must climb', the deconstructive architect. A studying for their works reflecting the 'Open Space' concept based on deconstruction must be lasted and this enables us to comprehend space concept containing an architecture and interior design.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.