• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.499-524
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• 2015

In the present study, we propose four participating $8^{th}$ grade students' genetic decomposition of congruent transformation and investigate the role of their dragging activities while understanding the concept of congruent transformation in GSP(Geometer's Sketchpad). The students began to use two major schema, 'single-point movement' and 'identification of transformation' simultaneously in their transformation activities, but they were inclined to rely on the single-point movement schema when dealing with relatively difficult tasks. Through dragging activities, they could expand the domain and range of transformation to every point on a plane, not confined to relevant geometric figures. Dragging activities also helped the students recognize the role of a vector, a center of rotation, and an axis of symmetry.

• Journal of Korea Society of Industrial Information Systems
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• v.4 no.3
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• pp.90-94
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• 1999

To prevent the congruent output of the digital psuedo-random transformation from giving the same randomness, a transformation of seemingly random deterministic process, called Chaotic transformation, is introduced. Passing through a Chaotic transformation, each event(descriptor) will produce chaotic random sequences. haotic transformation is designed on the basis of deterministic chaos function and also can be realized by simple hardware like shift registers. The circuit of chaotic transformation implemented with the shift registers is presented and the chaotic behavior of suggested circuit is explained with the characteristics of saw-tooth function with the chaotic behavior.

• The Mathematical Education
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• v.17 no.2
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• pp.1-13
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• 1979

This study aimed at studying the sequence of the Figure Transformation Learning, inquiring relationship among these transformations and then researching whether there is the difference of the learning ability or not between by teaching them as it is independent and by teaching them as it is contains. (Hypothesis 1) It may be more effective to teach The Sequence of Transformation Learning by beginning with peculiar field, ending with general field than vice versa At the result of verification-C $R_{M}$=2.59, 0.005$R_{M}$=5.19, p<0.005-significant difference appeared. It is proved more effective to teach the Figure Transformation Learning the way it contains than the way it is independent. Synthesizing two hypothesises of the above, the conclusion is following The Figure Transformation Learning should be taught by beginning with peculiar field. ending with general field (congruent transformationlongrightarrowsimilar transformationlongrightarrowprojective transformationlongrightarrowtopological transformation). To teach it the way it contains is more effective.ive.

• The Mathematical Education
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• v.46 no.3
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• pp.273-292
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• 2007

The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

• Economic and Environmental Geology
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• v.45 no.2
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• pp.89-104
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• 2012

The solubility of aluminum for two Andisol profiles formed on pyroclastic materials and basaltic rocks from Jeju Island, Korea was investigated. It is found that high organic carbon content and $Al_{pyrophosphate}/Al_{oxalate}$ ratios in the A horizons, suggesting the substantial amounts of reactive Al are associated with organic matter, whereas the low organic carbon content and the $Al_{pyrophosphate}/Al_{oxalate}$ ratios in the Bo horizons indicate that a major part of the reactive Al should be bound inorganically. The differential FT-IR spectra following acid-oxalate dissolution and heating up to 150 and $350^{\circ}C$, and transmission electron microscope (TEM) observation confirm that imogolite is in the Bo horizon. Our results of equilibration experiments demonstrate that the Al solubility in the Bo horizon for Andisols can be clarified by the congruent dissolution model for imogolite-type material (ITM), rather than by the simultaneous equilibrium with both ITM and Al hydroxy-interlayered aluminosilicate. With results from dialysis and aging procedures, it is noted that the formation of a proto imogolite sol showing its transformation to imogolite, which supports the congruent dissolution of ITM primarily controlling the Al solubility of Andisols in Jeju Island, Korea.