• Communications of Mathematical Education
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• v.32 no.3
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• pp.275-296
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• 2018

The purpose of this study is to investigate the change of gaze and the change of the proof learning achievement after learning the analytic method for proof to mathematical gifted students using eye tracking technique. In order to complete the purpose of this study, a mixed method research was used, that is a combination of quantitative and qualitative research methods. Quantitative analysis was conducted based on the data obtained through the eye tracker, and qualitative analysis was also done using post interview data to make up for the quantitative analysis. The subjects of this study were 8 mathematical gifted 3rd grade middle school students in the gifted education center. The conclusions of this study are as follows. First, the learning of analysis leads to a change of gaze in the proof learning of students. The students, after learning the analysis, moved their gaze from the bottom to the top when solving the proof problem, and the occupancy rate of the gaze to the bottom of the proof was higher than the higher part. Second, the change of gaze caused by the learning of the analysis have a correlation with the achievement of the proof learning and it can be seen that the method learning improves the achievement of the proof learning of the students.

• Education of Primary School Mathematics
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• v.16 no.2
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• pp.123-145
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• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• 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.

• The Journal of Bigdata
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• v.7 no.1
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• pp.1-14
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• 2022

The proof-of-work consensus algorithm used by most blockchains is causing a massive waste of computing resources in the form of mining. A useful proof-of-work consensus algorithm has been studied to reduce the waste of computing resources in proof-of-work, but there are still resource waste and mining centralization problems when creating blocks. In this paper, the problem of resource waste in block generation was solved by replacing the relatively inefficient computation process for block generation with distributed artificial intelligence model learning. In addition, by providing fair rewards to nodes participating in the learning process, nodes with weak computing power were motivated to participate, and performance similar to the existing centralized AI learning method was maintained. To show the validity of the proposed methodology, we implemented a blockchain network capable of distributed AI learning and experimented with reward distribution through resource verification, and compared the results of the existing centralized learning method and the blockchain distributed AI learning method. In addition, as a future study, the thesis was concluded by suggesting problems and development directions that may occur when expanding the blockchain main network and artificial intelligence model.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.17-28
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• 2008

이 논문은 중학교 기하 영역의 수업에 대한 학생들의 성취도가 낮은 것을 관찰하고, 그에 대한 고민으로 교육과정을 분석하고, 수학교육의 질적 접근을 위한 교수 실험을 통해 실제 중학교 과정에서 운용되는 논증기하 교육의 문제점과 그 대안을 탐색하고자 하였다. 본 연구에서는 교사가 반드시 갖춰야 할 지식으로 Shulman(1986)이 제시한 교과 내용 지식과 교수학적 내용 지식, 그리고 교육과정 관련 지식을 받아들였으며, 중학교 기하 영역에서 이런 지식을 갖추기 위해 교사가 폭넓은 고민을 하여 수업의 개선점을 찾는 과정을 보여주고 있다. 연구를 통해서 학생들에게 명제를 지도할 때 주의할 점과 학습자에게 증명을 하도록 제시하는 방법상의 문제점, 그리고 이등변삼각형의 지도에서의 그 증명이 갖는 의미를 잘 이해하여 학생들에 증명 학습에 진정한 도움이 될 수 있는 방향을 탐색하였다. 그리고 절차만을 학습시키는 현행 작도 수업을 개선하기 위한 여러 시도와 등변사다리꼴의 학습에서와 같이 학생들이 수학 용어를 되돌아보는 수업이 필요성을 탐색하여, 많은 교수 실험을 통한 교육과정의 바람직한 개정을 제안하였다.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.359-374
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• 2014

Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.

• 한국어정보학회:학술대회논문집
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• 2016.10a
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• pp.79-84
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• 2016

본 연구는 전문기관에서 생산되는 검증된 문서를 웹상의 수많은 검증되지 않은 문서에 자동 주석하여 신뢰도 향상 및 심화 정보를 자동으로 추가하는 시스템을 설계하는 것을 목표로 한다. 이를 위해 활용 가능한 시스템인 인공 신경 정리 증명계(neural theorem prover)가 대규모 말뭉치에 적용되지 않는다는 근본적인 문제를 해결하기 위해 내부 순환 모듈을 단어 임베딩 모듈로 교체하여 재구축 하였다. 학습 시간의 획기적인 감소를 입증하기 위해 국가암정보센터의 암 예방 및 실천에 대한 검증된 문서들에서 추출한 28,844개 명제를 위키피디아 암 관련 문서에서 추출한 7,844개 명제에 주석하는 사례를 통하여 기존의 시스템과 재구축한 시스템을 병렬 비교하였다. 동일한 환경에서 기존 시스템의 학습 시간이 553.8일로 추정된 것에 비해 재구축한 시스템은 93.1분 내로 학습이 완료되었다. 본 연구의 장점은 인공 신경 정리 증명계가 모듈화 가능한 비선형 시스템이기에 다른 선형 논리 및 자연언어 처리 모듈들과 병렬적으로 결합될 수 있음에도 현실 사례에 이를 적용 불가능하게 했던 학습 시간에 대한 문제를 해소했다는 점이다.

• Annual Conference on Human and Language Technology
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• 2016.10a
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• pp.79-84
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• 2016

본 연구는 전문기관에서 생산되는 검증된 문서를 웹상의 수많은 검증되지 않은 문서에 자동 주석하여 신뢰도 향상 및 심화 정보를 자동으로 추가하는 시스템을 설계하는 것을 목표로 한다. 이를 위해 활용 가능한 시스템인 인공 신경 정리 증명계(neural theorem prover)가 대규모 말뭉치에 적용되지 않는다는 근본적인 문제를 해결하기 위해 내부 순환 모듈을 단어 임베딩 모듈로 교체하여 재구축 하였다. 학습 시간의 획기적인 감소를 입증하기 위해 국가암정보센터의 암 예방 및 실천에 대한 검증된 문서들에서 추출한 28,844개 명제를 위키피디아 암 관련 문서에서 추출한 7,844개 명제에 주석하는 사례를 통하여 기존의 시스템과 재구축한 시스템을 병렬 비교하였다. 동일한 환경에서 기존 시스템의 학습 시간이 553.8일로 추정된 것에 비해 재구축한 시스템은 93.1분 내로 학습이 완료되었다. 본 연구의 장점은 인공 신경 정리 증명계가 모듈화 가능한 비선형 시스템이기에 다른 선형 논리 및 자연언어 처리 모듈들과 병렬적으로 결합될 수 있음에도 현실 사례에 이를 적용 불가능하게 했던 학습 시간에 대한 문제를 해소했다는 점이다.

• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04b
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• pp.619-621
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• 2002

MLP(multilayer perceptron)는 기존의 패턴인식 방법에 비해 몇 가지 이점을 제공하지만 학습에 비교적 많은 시간을 요구한다. 이 점은 화자증명 시스템의 인식방법으로서 MLP를 사용할 경우 등록시간이 길어지는 문제를 발생시킨다. 본 논문에서는 기존의 시스템에서 채택한 화자군집 방법을 응용하여 MLP 학습에 필요만 배경화자 수를 줄임으로써 화자등록 시간을 단축하는 방법을 제안한다.