• 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.

• Journal of Information Science Theory and Practice
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• v.9 no.1
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• pp.1-23
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• 2021

This study introduces novel research using Practice Context Models supported by Knowledge Networks and Percolation Theory with the aim to contribute to knowledge management in Proof-of-Concept (PoC) activities. The authors envision this proposal as a potential instrument to identify network structures based on a percolation (propagation) threshold and to analyze the importance of nodes (e.g., practitioners, practices, competencies, movements, and scenarios) during the percolation of knowledge in PoC activities. After thirty months immersed in the natural PoC habitat, acting as observers and practitioners, and supported by an ethnographic exercise and a designer-research mindset, the authors identified the production of meaning in PoC activities occurring in a hermeneutic circle characterized by the presence of several knowledge networks; thus, discovering the 'natural knowledge' in PoC as a spectrum of cognitive development spread throughout its network, as each node could produce and disseminate certain knowledge that flows and influences other nodes. Therefore, this research presents the use of Practice Context Models 'connected' to Knowledge Networks and Percolation Theory as a potential and feasible proposal to be built using the attribution of values (weights) to the nodes (e.g., practitioners, practices, competencies, movements, scenarios, and also knowledge) in the context of PoC with the aim to allow the players (e.g., PoC practitioners) to have more flexibility in building alliances with other players (new nodes); that is, focusing on those nodes with higher value (focus on quality) in collaboration networks, i.e., alliances (connections) with the aim to contribute to knowledge management in the context of PoC.

• Research in Mathematical Education
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• v.27 no.2
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• pp.157-173
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• 2024

Researchers continue to emphasize the centrality of proof in the context of school mathematics and the importance of proof to student learning of mathematics is well articulated in nationwide curricula. However, researchers reported that students' performance in proving tasks is not promising and students are not likely to see the need to prove a proposition even if they learned mathematical proof previously. Research attributes this issue to students' tendencies to accept an empirical argument as proof for a mathematical proposition, thus not being able to recognize the limitation of an empirical argument as proof for a mathematical proposition. In Korea, there is little research that investigated high school students' views about the need for proof in mathematics and their understanding of the limitation of an empirical argument as proof for a mathematical generalization. Sixty-two 11^th graders were invited to participate in an online survey and the responses were recorded in writing and on either a four- or five-point Likert scale. The students were asked to express their agreement with the need of proof in school mathematics and to evaluate a set of mathematical arguments as to whether the given arguments were proofs. Results indicate that a slight majority of students were able to identify a proof amongst the given arguments with the vast majority of students acknowledging the need for proof in mathematics.

• Fashion & Textile Research Journal
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• v.12 no.6
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• pp.755-763
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• 2010

This study was intended to identify the persuasion effects according to social proof message type and product type in the context of online cosmetic advertising. For the experiment, 4 stimuli were developed as experimental stimuli for the 2(social proof message type: attitudinal social proof message, behavioral social proof message)${\times}$2(product type: hedonic product, utilitarian product) factorial design. A total of 160 questionnaires allocating forty students to each group were distributed. The results were as follows. First, behavioral social proof message showed more effective than attitudinal social proof message in advertisement attention, click-through intention and purchase intention. Second, utilitarian product showed more effective than hedonic product in advertisement attention, click-through intention and purchase intention. Third, there was interaction effect according to social proof message type and product type on the aspect of click-through intention.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• Language and Information
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• v.5 no.2
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• pp.1-8
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• 2001

Natural language string sets are known to require a grammar with a generative capacity slightly beyond that of Context Free Grammars. Proofs regarding complexity of natural language have involved particular properties of languages like English, Swiss German and Bambara. While it is not very difficult to prove that Korean is more complex than the simplest of the many infinite sets, no proof has been given of this in the literature. I identify two types of center embedding in Korean and use them in proving that Korean is not a regular set, i.e. that no FSA's can recognize its string set. The regular language i salam i (i salam ul$)^j$ michi (key ha)^k$ essta is intersected with Korean, to give {i salam i (i salam ul$)^j$ michi (key ha$)^k$ essta i $$\mid$$ j, k $\geq$ 0 and j $\leq$ k}. This latter language is proved to be nonregular. As the class of regular sets is closed under intersection, Korean cannot be regular.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.504-512
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• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.55-70
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• 2003

This study investigated tile intuitive level of justification in geometry, as the former step to the aximatization, with concrete examples. First, we analyze limitations that the axiomatic method has in tile context of discovery and the educational situation. This limitations can be supplemented by the proper use of the intuitive method. Then, using the histo-genetic analysis, this study shows the process of the development of geometrical thought consists of experimental, intuitive, and axiomatic steps. The intuitive method of proof which is free from the rigorous axiom has an advantage that can include the context of discovery. Finally, this paper presents the issue of intuitive proving that the three angles of an arbitrary triangle amount to 180$^{\circ}$, as an example of the local systematization.

• ETRI Journal
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• v.35 no.1
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• pp.7-17
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• 2013

The ongoing proliferation of new services, applications, and contents is leading the Internet to an architectural crisis owing to its inability to provide efficient solutions to new requirements. Clean-slate architectures for the future Internet offer a new approach to tackle current and future challenges. This proposal introduces a novel clean-slate architecture in which the TCP/IP protocol stack is decoupled in basic functionalities, that is, atomic services (ASs). A negotiation protocol, which enables context-aware service discovery for providing adapted communications, is also specified. Then, we present how ASs can be discovered and composed according to requesters' requirements. In addition, a media service provisioning use case shows the benefits of our framework. Finally, a proof-of-concept implementation of the framework is described and analyzed. This paper describes the first clean-slate architecture aligned with the work done within the ISO/IEC Future Network working group.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.5
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• pp.525-530
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• 2010

Currently, most context-aware services are built by developers. Some researchers argued that services should be defined by end users, who understand their own needs best. We view that the significance of enabling the user to define his/her personalized services will multiply as our living spaces grow smarter. This paper introduces a novel method called CASPER, which is capable of deriving personalized services from the log of user's activities of daily living. CASPER can generate useful services that even the user may not perceive, mining causality of events in the log. We present the algorithm of CASPER in detail and discuss the result of an experiment which we conducted as a proof of concept.