• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.55-68
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• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• 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.

• 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 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.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.13-28
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• 2003

Practice of proof is considered in, the view of language and meta-mathematics, recognizing the role of proof that is the means of communication and development of mathematical understanding. Linguistic components in proof texts are symbol, verbal language and visual text, and contain the implicit knowledge in the meta-mathematics view. This study investigates the functions of linguistic elements according to Halliday's functional grammar and the rhetoric skills in proof texts in math textbook, teacher's note, and student's written text. We need to inquire into the aspects of language for mathematics learning process and the understanding and use of students' language.

• The Mathematical Education
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• v.48 no.4
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• pp.387-398
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• 2009

In this paper, we investigated the influence of technology, which gave an impact on students through the process of teaching & learning for the proof of an additive law of sine function in the mathematics education for the gifted. We chose students who were taking a course in enrichment mathematics at Science Education Institute for the Gifted in Mokpo National University, and analyzed their processes of a mathematical inference or conjecture, an algebraic description and a proof by visualization using technology. We found the following facts. That is, the visualization using technology is helpful to the gifted students in understanding principles and concepts of mathematics by intuition. Also, it is helpful to ones verifying various cases and generalizing principles. But, using technology can be a factor that disturbs learning of students who are clumsy with operating technology.

• 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.

• School Mathematics
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• v.18 no.4
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• pp.839-856
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• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Wind and Structures
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• v.39 no.3
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• pp.175-190
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• 2024

Aerodynamic shape optimization is very useful for enhancing the performance of wind-sensitive structures. However, shape parameterization, as the first step in the pipeline of aerodynamic shape optimization, still heavily depends on empirical judgment. If not done properly, the resulting small design space may fail to cover many promising shapes, and hence hinder realizing the full potential of aerodynamic shape optimization. To this end, developing a novel shape parameterization scheme that can reflect real-world complexities while being simple enough for the subsequent optimization process is important. This study proposes a machine learning-based scheme that can automatically learn a low-dimensional latent representation of complex aerodynamic shapes for bluff-body wind-sensitive structures. The resulting latent representation (as design variables for aerodynamic shape optimization) is composed of both discrete and continuous variables, which are embedded in a hierarchy structure. In addition to being intuitive and interpretable, the mixed discrete and continuous variables with the hierarchy structure allow stakeholders to narrow the search space selectively based on their interests. As a proof-of-concept study, shape parameterization examples of tall building cross sections are used to demonstrate the promising features of the proposed scheme and guide future investigations on data-driven parameterization for aerodynamic shape optimization of wind-sensitive structures.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.724-729
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• 2001

This paper discusses the composition of the theory of reinforcement learning, which is applied in real-time learning, and evolutionary strategy, which proves its the superiority in the finding of the optimal solution at the off-line learning method. The individuals are reduced in order to learn the evolutionary strategy in real-time, and new method that guarantee the convergence of evolutionary mutations are proposed. It possible to control the control object varied as time changes. As the state value of the control object is generated, applied evolutionary strategy each sampling time because the learning process of an estimation, selection, mutation in real-time. These algorithms can be applied, the people who do not have knowledge about the technical tuning of dynamic systems could design the controller or problems in which the characteristics of the system dynamics are slightly varied as time changes. In the future, studies are needed on the proof of the theory through experiments and the characteristic considerations of the robustness against the outside disturbances.