• Communications of Mathematical Education
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• v.8
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• pp.17-32
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• 1999

본 논문의 목적은 Cabri II 를 이용하여 형식적이고 연역적인 증명수업 방법의 대안을 찾는 데 있다. 형식적인 증명을 하기 전에 탐구와 추측을 통한 발견과 그 결과에 대한 비형식적인 증명 활동을 강조한다. 역동적인 기하소프트웨어인 Cabri II 는 작도가 편리하고 다양한 예를 제공하여 추측과 탐구 그리고 그 결과의 확인을 위한 풍부한 환경을 제공할 수 있으며, 끌기 기능을 이용한 삼각형의 변화과정에서 관찰할 수 있는 불변의 성질이 형식적인 증명에 중요한 역할을 한다. 또한 도형에 기호를 붙이는 활동은 형식적인 증명을 어렵게 만드는 요인 중의 하나인 명제나 정리의 기호적 표현을 보다 자연스럽게 할 수 있게 해 준다. 그러나, 학생들이 증명은 더 이상 필요 없으며, 실험을 통한 확인만으로도 추측의 정당성을 보장받을 수 있다는 그릇된 ·인식을 심어줄 수도 있다. 따라서 모든 경우에 성립하는 지를 실험과 실측으로 확인할 수는 없다는 점을 강조하여 학생들에게 형식적인 증명의 중요성과 필요성을 인식시킬 필요가 있다. 본 연구에 대한 다음과 같은 후속연구가 필요하다. 첫째, Cabri II 를 이용한 증명 수업이 학생들의 증명 수행 능력 또는 증명에 대한 이해에 어떤 영향을 끼치는지 특히, van Hiele의 기하학습 수준이론에 어떻게 작용하는 지를 연구할 필요가 있다. 둘째, 본 연구에서 제시한 Cabri II 를 이용한 증명 교수학습 방법에 대한 구체적인 사례연구가 요구되며, 특히 탐구, 추측을 통한 비형식적인 중명에서 형식적 증명으로의 전이 과정에서 나타날 수 있는 학생들의 반응에 대한 조사연구가 필요하다.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.653-674
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• 2023

The development of mathematical problem solving ability and the making(transforming) mathematical problems are consistently emphasized in the mathematics curriculum. However, research on the problem making methods or the analysis of the characteristics of problem making methods itself is not yet active in mathematics education in Korea. In this study, we concretize the method of deductive problem making(DPM) in a different direction from the what-if-not method proposed by Brown & Walter, and present the characteristics and phases of this method. Since in DPM the components of the problem solving process of the initial problem are changed and problems are made by going backwards from the phases of problem solving procedure, so the problem solving process precedes the formulating problem. The DPM is related to the verifying and expanding the results of problem solving in the reflection phase of problem solving. And when a teacher wants to transform or expand an initial problem for practice problems or tests, etc., DPM can be used.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.159-178
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• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• Journal of The Korean Association For Science Education
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• v.26 no.1
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• pp.88-98
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• 2006

The purpose of this study was to analyze the process of scientists' science knowledge generation by employing four creative scientists as participants. Raw protocols were collected by an intensive interview method and then analyzed by a psychological modelling procedure. The present study showed that the process of knowledge generation divided into the processes of inductive, abductive, and deductive thinking. Furthermore, the inductive process in simple and operative observation was involved in the processes of generating a question, conjecture/prediction, designing an operational method, operation, and simple observation. Also, the abductive process had two components; question generation, and hypothesis generation which consisted of analyzing questions, searching explicans, and constructing hypothesis. Finally, the deductive process involved inventing abstract test methods, inventing abstract criteria, inventing concrete test methods, inventing concrete criteria, collecting results, and evaluating hypotheses and stating conclusions.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.8
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• pp.78-85
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• 2018

In this study, we investigated the cases where there were many opinions in the judgment of the cause of ignition in the case of 20 cases of frozen warehouse fire that occurred in 2017.The research methodology is the scientific fire survey method prescribed by the NFPA 921 CODE. Scientific fire investigation method is fire investigation method by logical reasoning through hypothesis setting, minimizing errors in judgment of ignition source. On the other hand, unscientific fire investigation methods cause many errors by the intervention of irrational factors such as subjective estimation, reasoning judgment, etc. This eventually leads to the problem of human and material responsibility and academic deterioration. In particular, fire not seen as compared to sighted fire makes more errors in ignition sources in the cause investigation. In this study, we set the hypothesis A and hypothesis B based on the review of the fire investigation report and the field survey on the fire case of the cold storage warehouse front line that occurred at ** city ** Mart in 2017.The set hypothesis was tested by the NFPA 921 code. This analytical method will be constructed by NEW Paradigm as a source of fire that is not seen in the future and a source of ignorant fire.In addition, the experimental data of this study will be used to inform the manufacturer and operator of the refrigeration warehouse and serve as basic data for fire prevention.

• KSBB Journal
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• v.10 no.5
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• pp.499-509
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• 1995

PU.1, a tissue-specific transcription activator, binds to a purine-rich sequence(5'-GAGGAA-3') called PU box. The PU.1 cDNA consists of an open reading frame of 816 nucleotides coding for 272 amino acids. The amino terminal end is highly acidic, while the carboxyl terminal end is highly basic. Transcriptional activation domain is located at the amino terminal end, while DNA binding domain is located at the carboxyl terminal end. Activation of PU.1 transcription factor is supposed to be accomplished by the phosphorylation of serine residue(s). There exist 22 serines in the PU.1. Five(the 41, 45, 132$.$133, and 148th) of the serines(plausible phosphorylation site by casein kinase II), are the primary targets of interest in elucidating the molecular mechanism(s) of the action of the PU.1 gene. In this study, PU.1 cDNA coding for the five serine residues(41th AGC, 45th AGC, 132$.$133th AGC$.$TCA, and 148th TCT), was mutated to alanine codon(41th GCC, 45th GCC, 132$.$133th GCC$.$GCA, and 1481h GCT), respectively, by Splicing-Overlapping-Extension(SOE) using Polymerase Chain Reaction(PCR). And each mutated cDNA fragments was ligated into pBluescript KS＋ digested with HindIII and Xba I, to generate mutant clones named pKKS41A, pRKS45A, pMKS132$.$133A, and pMKS148A. The clones will be informative to study the "Structure and Function" of the immu-nologically important gene, PU.1.