• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.313-326
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• 1998

The purpose of this study is to verify the meaning of preformal proof and its didactical significance in mathematics education. A preformal proof plays a more important role in mathematics education, because nowadays in mathematics a proof is considered as an important fact from a sociological point of view. A preformal proof was classified into four categories: a) action proof, b) geometric-intuitive proof, c) reality oriented proof, d) proof by generalization from paradiam. An educational significance of a preformal proof are followings: a) A proof is not identified with a formal proof. b) A proof is not only considered from a symbolic level, but also from enactive and iconic level. c) A preformal proof generates a formal proof and convinces pupils of a formal proof d) A preformal proof is psychologically natural. e) A preformal proof changes a conception of what is a proof. Therefore a preformal proof is expected to teach in school mathematics from the elementary school to the secondary school.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.385-402
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• 2001

The purpose of this study is to conceptualize 'proof' school mathematics. We based on the assumption the following. (a) There are several different roles of 'proof' : verification, explanation, systematization, discovery, communication (b) Accepted criteria for the validity and rigor of a mathematical 'proof' is decided by negotiation of school mathematics community. (c) There are dynamic relations between mathematical proof and empirical theory. We need to rethink the nature of mathematical proof and give appropriate consideration to the different types of proof related to the cognitive development of the notion of proof. 'proof' in school mathematics should be conceptualized in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof 'proof' has not been taught in elementary mathematics, traditionally, Most students have had little exposure to the ideas of proof before the geometry. However, 'proof' cannot simply be taught in a single unit. Rather, proof must be a consistent part of students' mathematical experience in all grades, in all mathematics.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• The Mathematical Education
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• v.43 no.4
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• pp.381-390
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• 2004

In this study, we conceptualized the ‘preformal proof’, which is a transitive level of proof from the experimental and inductive justification to the formalized mathematical proof. We investigated concrete features of the preformal proof in the historico-genetic and the didactical situations. The preformal proof can get the generality of the contents of proof, which makes a distinction from the experimental proof. And we can draw a distinction between the preformal and formal proof, in point that the preformal proof heads for the reality-oriented objects and does not use the formal language.

• 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.

• The Mathematical Education
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• v.37 no.1
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• pp.55-72
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• 1998

We prove many statements in middle and high school mathematics, so it is necessary to have some method for understanding the modes of proof. But it is hard to discuss about the modes of proof without knowing logics. Venn-diagrams can be used in a great variety of situations, and it is useful to the students unfamiliar with logical procedure. Since knowing a mode of proof that could be used may still not guarantee success of proof, it is also necessary to illustrate many cases of proof strategies. To achieve the above reguirements, (1)Even though intuition, the modes of proof used in middle school mathematics should be understood by using venn-diagrams and the students can use the right proof in the right statement. (2)We must illustrate many kinds of proof so that the students can get the proof stratigies from these illustrations. (3)If possible, logic should be treated in middle school mathematics for students to understand the system of proof correctly.

• Education of Primary School Mathematics
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• v.4 no.1
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• pp.63-73
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• 2000

The purpose of this paper is to address He possibility of the teaching of 'proof' in elementary mathematics, on the assumption that proof in school mathematics should be used in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. 'Proof' has not been taught in elementary mathematics, traditionally. Most students have had little exposure to the ideas of proof before the geometry. However, 'Proof' cannot simply be taught in a single unit. Rather, proof must be a consistent part of students' mathematical experience in all grades. Or educators and mathematicians need to rethink the nature of mathematical proof and give appropriate consideration to the different types of proof related to the cognitive development of a notion of proof.

• 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.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.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.11-22
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• 2003

In this paper, we investigate the types and roles of ancient mathematical proof by exploring Gu-Jang-Sal-Sul. Gu-Jang-Sal-Sul is a ancient Chinese mathematics book. Types of proof contained in Gu-Jang-Sal-Sul are enactive proof and intuitive proof and the role of proof is explanation. And we suggest social background of proof in Gu-Jang-Sal-Sul topographically, culturally, and logically.