• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.351-364
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• 1998

This thesis analyzes the nature of proof in the perspective on the philosophy of mathematics. such as absolutism, quasi-empiricism and social constructivism. And this thesis searches for the improvement of teaching proof in the light of the result of those analyses of the nature of proof. Though the analyses of the nature of proof in the perspective on the philosophy of mathematics, it is revealed that proof is a dynamic reasoning process unifying the way of analytical thought and the way of synthetical thought, and plays remarkably important roles such as justification, discovery and conviction. Hence we should teach proof as a dynamic reasoning process unifying the way of analytic thought and the way of synthetic thought, avoiding the mistake of dealing with proof as a unilaterally synthetic method. At the same time, we should make students have the needs of proof in a natural way by providing them with the contexts of both justification and discovery simultaneously. Finally, we should introduce the aspect of proof that can be represented as conviction, understanding, explanation and communication to school mathematics.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.55-68
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• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.35 no.1
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• pp.13-18
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• 2003

This study was done in an effort to evaluate the possibility of recyclability of moisture-proof paper. Because it is difficult to recycle laminated moisture-proof paper, a mixture of styrene-butadiene latex(SB latex) and wax emulsion was used as moisture-proof paper chemicals. A bar coater was applied to make moisture-proof paper and the coated weight was 17 g/$m^2$. The mixing ratios of SB latex to wax emulsion were 85 : 15, 87 : 13, and 90 : 10, respectively. It was observed that the moisture-proof paper treated with SB latex and wax emulsion at the appropriate ratio could be recycled effectively. The moisture-proof paper was similar to base paper in degree of pulping, and there was no significant difference in dispersion between moisture-proof paper and base paper. Most of wax particle which caused the spots during drying process could be removed by flotation process. Tensile strength and tear strength of handsheets made of both moisture-proof paper and base paper after pulping was measured to examine the fiber bonding and no significant difference in mechanical properties was observed.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.33 no.4
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• pp.15-20
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• 2001

The function of the moisture-proof paper is to prevent moisture from adsorbing into the packed goods. Water-vapor transmission rate of the moisture-proof paper should be less than 100g/$m^2$.24hr and the optimum rate would be less than 50g/$m^2$.24hr. In general the moisture-proof paper has been made by laminating polyethylene or polypropylene on top of the base paper. However this kind of moisture-proof paper has a problem in recycling so that it brings about environmental pollution. In general the moisture-proof paper has been made by laminating polyethylene or polypropylene on top of the base paper. However this kind of moisture-proof paper has a problem in recycling so that it brings about environmental pollution. The purpose of this paper was to make moisture-proof paper using the mixture of SB latex and wax emulsion which was recyclable and environmentally friendly. Water vapor transmission rate showed less than 50g/$m^2$.24hr in mixture ratio of 85:15, 87:13, 90:10. Especially the mixture ratio of 87:13 showed the most favorable water-vapor transmission rate. However, the moisture-proof layer was destroyed slightly by folding in packing. It has been observed that there was no close relationship between water-vapor transmission rate of the moisture-proof paper and grammage of the base paper, but the density of base paper had influenced on water vapor transmission rate. It was also observed that the moisture-proof paper could be recycled. The moisture-proof paper was similar to base paper in degree of the pulping, and there was no significant difference in dispersion between moisture-proof paper and base paper. Most of wax particles which caused the spots during drying process could be removed by flotation process. Tensile strength and tear strength of both moisture-proof paper and base paper after pulping were measured to examine the fiber bonding, and no significant difference in physical properties was observed.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.511-528
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• 2010

Students' intuition in formal proof should be expressed as symbols according to the deductive process. The symbol will play a role of the mediation between the intuition and the formal proof. This study examined the evolution process of intuition mediated by the symbol in geometry proof. According to the results first, symbol took the great roles when students had the non-formed intuition for the proposition. The signification of symbols could explain even the proof process of the proposition with the non-expectable intuition. And when students proved it by symbols, not by figure nor words, they could evolute the conclusive intuition about the proposition.

• Research in Mathematical Education
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• v.7 no.1
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• pp.1-10
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• 2003

This research reviewed literatures on proof in mathematics education. Several views of proof can be classified (and identified) such as psychological approach (Platonism, empiricism), structural approach (logicism, formalism, intuitionism) and social approach (ontology, axiomatic systems). All these views of proof are valuable in mathematics education society. The concept of proof can be found in the form of analytic knowledge not of constructive knowledge. Human beings developed their knowledge in the sequence of constructive knowledge to analytic knowledge. Therefore, in mathematics education, the curriculum of mathematics should involve the process of cognitive knowledge development.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.291-298
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• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

• Textile Coloration and Finishing
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• v.27 no.4
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• pp.309-317
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• 2015

This study is the high contraction processing conditions set by the method of the CPB process. And the ultimate goal of this study is the high contraction of the CPB processing test method that can solve the problems of the high-contraction fabric processing method of the current jet dyeing machine. Non-coating process(CPB process) developed by the expression of a soft touch, light weight, functional and to develop excellent breathable nylon fabric. The nylon fabrics established the optimum processing conditions through the high contraction of the various test conditions, the CPB system.(The benzyl alcohol was used as the main constrictor.) At this time, the warp and weft contraction of nylon fabric was about 20%. And it established the constrictor concentration, the treatment temperature, time of a variety of tests. Also non-coating process(CPB process) can develop soft touch, lightweight, excellent air permeability. As a result, we developed a high contraction nylon fabric having a uniform surface. Manufactured fabric is used for Wind-proof and Down-proof.

• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.191-205
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• 2017

The purpose of this study is to investigate the types and characteristics of the Seventh Graders' proofs. Harel, & Sowder's proof schemes were used to analyze the subjects' responses. As a result of the study, there was a difference in the type of proof schemes used by the students depending on the academic achievement level. While the proportion of students using a transformative proof scheme decreased from the top to the bottom, the proportion of students using inductive (measure) proof scheme increased. In addition, features of each type of proof schemes were shown, such as using informal codes in the proof process, and dividing a given picture into a specific ratio in the problem. Based on this, we extracted four meaningful conclusions and discussed implications for proof teaching and learning.

• East Asian mathematical journal
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• v.31 no.4
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.