• Journal of the Korean Graphic Arts Communication Society
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• v.24 no.2
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• pp.69-78
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• 2006

Proofing is one of the inspection operations of printing and can be considered a process control step. The three main kinds of proofs are press proofs, photomechanical proofs, and digital proofs. Photomechanical and digital proofs are also generally refered to as "off-press" proofs. Off-press color proofs are more economical than press proofs. Digital proofs offer fast production time along with a much lower cost per page. Hard-copy digital proofs can be output using thermal transfer printers, ink jet printers, and color laser copiers, as well as dye sublimation and electrophotographic technology. Ink jet method is commonly using because of the reasonal price. But ink jet system is difficult to reproduce an exact color proof. This research was carried out for the purpose of optimization of ink jet color proofing, using two kinds of ink jet printers with 6 colors (C, M, Y, K, mC, mM) and 4 colors (C, M, Y, K) system.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• The Mathematical Education
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• v.57 no.3
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• pp.215-229
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• 2018

Despite the importance of learning to do mathematical proofs, researchers have reported that not only secondary school students but also undergraduate students have difficulties in learning proofs. In this study, we introduced a new toll for learning proofs and explored the reliability and the validity of peer assessment on proofs. In the course of a university in Seoul, students were given weekly proof assignments prior to class. After solving the proofs, each student had to assess other students' proofs. The inter-rater reliabilities of weekly peer assessment was higher than .9 over 90 percent of the observed cases. To examine the validity of peer assessment, we check whether students' assessments were similar to expert assessment. Analysis showed that the equivalence has been quite high throughout the semester and the validity was low in the middle of the semester but rose by the end of the semester. Based on these results, we believe instructors can consider the application of peer assessment on proving tasks as a tool to help students learn.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.299-314
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• 2008

The purposes of this study were to investigate what attitudes students have toward learning proofs and what difficulties they have in learning proofs, and to examine how the use of dynamic geometry software, the Geometer's Sketchpad, helps students' proof learning. The study involved 117 9th graders in 2 high schools. According to questionnaire data, over 50 percent of the total respondents(116) indicated negative attitudes toward learning proofs, on the other hand, only 16 percent of the total respondents indicated positive attitudes toward the learning. Memorizing and remembering many kinds of theorems, definitions, and postulates to use in proving statements was the most difficult part in learning proofs, which the largest proportion of the total respondents indicated. The study found that the use of the Geometer's Sketchpad played positive roles in developing students' understanding of proofs and stimulating students' interests in learning proofs.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.43-54
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• 2003

In this article we study various proofs of Heron's formula, extract some didactical ideas from these proofs, and didactically enlarge Heron's formula. In this paper we in detail introduce five different proofs from various articles and textbooks, and suggest our proof of Heron's formula. Enlarging this proof we are able to prove Brahmagupta's formula and generalized convex quadrangle's area formula.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.33-48
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• 2002

In this article we study various proofs of Euler's theorem(the number of faces of any polyhedron, together with the number of vertices, is two more than the number of edges), from these proofs extract some mathematical ideas. In this paper we in detail introduce eight different proofs from various articles and textbooks.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.93-108
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• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.65-77
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• 2008

In this paper we study new proofs and generalization of Haga theorem in paper folding. We analyze developed new proofs of Haga theorem, compare new proofs with existing proof, and describe some difference of these proofs. We generalize Haga second theorem, and suggest simple proof of generalized Haga second theorem.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.225-240
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• 2015

In this study, we investigated the representativeness of proofs in school mathematics, based on the extension of the midpoint connector theorem for the quadrilateral. To this end, we considered a variety of quadrilateral and proved their extensions of the midpoint connector theorem, and identified the relationships between them, therefore seemed that the proof in school mathematics has a representativeness. On the other hand, in the survey based on this information, students were found only some types of quadrilateral and completed easily the proofs for each quadrilateral they found, but students tended to use other proof or mathematical concepts, if the target figures changes in despite of proving the same mathematical fact. Thus, students were more difficult to figure out the relationship between the proofs. From these facts, we know that students are poorly understood the representativeness of proofs to understand the relationship between concrete proofs and to generalize it, though they are able to proof to the specific figures. Therefore it can be seen that the proof activity needs to be done with organic and semantic.