• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.105-120
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• 2011

This research intends to analyse how mathematically gifted 8th graders (age 14) discover and proof the properties on the sum of face angles of polyhedron. In this research, the problems on the sum of face angles of polyhedrons were given to 36 gifted students, and their discovery and proof processes were analysed on the basis of their the activity sheets and the researcher's observation. The discovery and proof processes the gifted students made were categorized, and levels revealed in their processes were analysed.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.111-127
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• 2004

In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.717-725
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• 2009

We show that to every real polynomial of degree n, there corresponds a certain basis for the space of polynomials of degree less than or equal to (n-1). As an application, we give a new proof for the existence and uniqueness of the partial fraction decomposition of a rational function.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.527-537
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• 2004

This paper deals with the asymptotic behaviour for the semi-linear differential systems x' (t) = A(t)χ + f(t, x). We give a detailed proof of known generalization of Coppel's result about the above mentioned system.

• The Mathematical Education
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• v.63 no.1
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• pp.105-122
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• 2024

This study analyzed the research trends of 101 articles published in prominent international mathematics education journals over 24 years from 2000, when NCTM's recommendation emphasizing argumentation was released, until September 2023. We first examined the overall trend of argumentation research and then analyzed representative research topics. We found that students were the focus of the studies. However, several studies focused on teachers. More studies were examined in secondary school than in elementary school, and many were conducted in argumentation in classroom contexts. We also found that argumentation research is becoming increasingly popular in international journals. The representative research topics included 'teaching practice,' 'argumentation structure,' 'proof,' 'student understanding,' and 'student reasoning.' Based on our findings, we could categorize three perspectives on argumentation: formal, contextual, and purposeful. This paper concludes with implications on the meaning and role of argumentation in Korean mathematics education.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.455-467
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• 2008

We need to reflect the establishment of meaning and level of 'proof and argumentation in middle school mathematics'. It should be considered as human activity through communication in community. Thus, we should design instruction from this standpoint. From this point of view, we had been operated 'Geometry Inquiry Class' aimed at middle school students in eighth grade for two years to improve current geometry class in middle school. In this study, we will observe how individual students' original proof schemes are developed and accepted to the class through the process of mutual negotiation between the teacher and students. The episode with four phases begins with the initial proof schemes students have offered. Through the negotiation of class participants, it gives birth to the proof scheme unique to the current geometry classroom. Why do we pay attention to the process? It is because we think that the value of this type of instruction lies in the process of communication and mutual understanding and mutual reference, not in the completeness of the final product. This is the very appropriate proof in the middle school mathematics classroom.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.489-503
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• 2008

It is not an easy matter to develop problems which help students understand mathematical concepts correctly and precisely. The aim of this paper is to review the merits and demerits of three problem types (i.e. one answer problems, multiple choice problems and proof problems) and to suggest some points that should be taken into consideration in problem making. First, we presented the merits and demerits of three types of problems by examining actual examples. Second, we discussed some examples of misleading problems and the ways to make desirable ones. Finally, on the basis of our examination and discussion, we suggested some points that should be kept in mind in problem making. The major suggestions are as follows; i) In making one answer problems, we should consider the possibility of sitting a solution by wrong precesses, ii) In formulating multiple choice tests which are layered for their easiness of grading, we should take into account the importance of checking whether the students are fully understanding the concepts, iii) We may depend on the previous research result that multiple choice tests for proof problems can be helpful for the students who have insufficient math background. Besides those suggestions, we made an overall proposal that we should endeavor to find ways to implement the demerits of each problem type and to develop instructive problems that can help students understanding of math.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1061-1066
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• 1996

We will give an example which is a normal Hausdorff countable dense homogeneous space but not a densely homogeneous space. Next, we will give a proof for the fact that every nondegenerate component of densely homogenous spaces is open and densely homogeneous.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.867-874
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• 1995

Linear invariance is closely related to the concept of uniform local univalence. We give a geometric proof that a holomorphic locally univalent function defined on the open unit disk is linearly invariant if and only if it is uniformly locally univalent.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.653-655
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• 2006

We give a simple proof of the statement that if T is a bounded linear operator on a complex HIlbert space then T is Fredholm if and only if ${\pi}(T)$ is not a TDZ, where ${\pi}(\cdot)$ is the Catkin homomorphism.