• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of the Korea Society of Computer and Information
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• v.18 no.7
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• pp.111-123
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• 2013

To verify software vulnerability, the method of conjecturing software structure and then testing the software based on the conjectured structure has been highlighted. To utilize the method, an efficient way to conjecture software structure is required. The popular graph and tree methods such as DFG(Data Flow Graph), CFG(Control Flow Graph) and CFA(Control Flow Automata) have a serious drawback. That is, they cannot express software in a hierarchical fashion. In this paper, we propose a method to overcome the drawback. The proposed method applies various input data to a binary code, generate CFG's based on the code output and construct a HCFG (Hierarchical Control Flow Graph) to express the generated CFG's in a hierarchical structure. The components required for HCFG and progressive algorithm to construct HCFG are also proposed. The proposed method is verified through constructing the software architecture of an open SMTP(Simple Mail Transfer Protocol) server program. The structure generated by the proposed method and the real program structure are compared and analyzed.

• Journal of The Korean Association For Science Education
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• v.38 no.5
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• pp.599-610
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• 2018

The purpose of this study is to analyze mechanistic reasoning in Fabre's inquires and to develop mechanistic reasoning model. To analyze the order of the process elements in mechanistic reasoning, 30 chapters were selected in book. Inquiries were analyzed through a framework which is based on Russ et al. (2008). The nine process elements of mechanistic reasoning that was presented in Fabre's inquires were as follows: Describing the Target Phenomenon, Identifying prior Knowledge, Identifying Properties of Objects, Identifying Setup Conditions, Identifying Activities, Conjecturing Entities, Identifying Properties of Entities, Identifying Entities, and Organization of Entities. The order of process elements of mechanistic reasoning was affected by inquiry's subject, types of question, prior knowledge and situation. Three mechanistic reasoning models based on the process elements of mechanistic reasoning were developed: Mechanistic reasoning model for Identifying Entities(MIE), Mechanistic reasoning model for Identifying Activities(MIA), and Mechanistic reasoning model for Identifying Properties of entities (MIP). Science teacher can help students to use the questions of not only "why" but also "How", "If", "What", when students identify entities or generate hypotheses. Also science teacher should be required to understand mechanistic reasoning to give students opportunities to generate diverse hypotheses. If students can't conjecture entities easily, MIA and MIP would be helpful for students.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.85-108
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• 2009

The purposes of the study were to develop instructional materials based on Freudenthal's guided reinvention principle for teaching proofs and to investigate how the teaching method based on guided reinvention principle affects on 8th grade students' ability to write proofs and learning attitude toward proofs. Teaching based on guided reinvention principle placed emphasis on providing students opportunities to make a mathematical statement and prove the statement by themselves throughout various activities such as exploring, conjecturing, and testing the conjectures. The study found that students who studied proving with instructional materials developed by guided reinvention principle showed statistically higher mean scores on the posttest than students who studied by a traditional teaching method depending onteacher's explanation. Especially, on the posttest item which requested to prove a whole statement without presenting a picture corresponding to the statement, a big difference among students' responses was found. Many more students in the traditional group did not provide any response on the item. According to the results of the questionnaire regarding students' learning attitudes, the group who studied proving by guided reinvention principle indicated relatively more positive attitudes toward learning proofs than the counterparts.

• School Mathematics
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• v.10 no.4
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• pp.537-555
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• 2008

The study aims to analyze elementary school students' understanding of the concept of equality sign in contexts, to reflect the types of contexts for equality sign which mathematics textbook series for $1{\sim}4$ grades on natural numbers and its operation provide, and to invetigate the effects of teaching methods of the concept of equality sign suggested in this research. In order to achieve these purposes, the origin, concept, and contexts of equality sign were theoretically reviewed and organized. Also the error types in using equality sign were reflected. Modelling, discussing truth or falsity of equations, identifying relations between numbers and their operation, conjecturing basic properties of numbers and their operations, experiencing diverse contexts for equality sign, and creating contexts for equality sign are set up as teaching methods for better understanding the concept of equality sign. The conclusions are as follows. Firstly, elementary school students' under-standing of the concept of equality sign varied by context and was generally far from satisfactory. In particular, they had difficulties in understanding the concept of the equal sign in contexts with operations on both sides. The most frequently witnessed error was to recognize equality sign as a result of operations. Secondly, student' lack of understanding of the concept of equality sign came from the fact that elementary textbooks failed to provide diverse contexts for equality sign. According to the textbook analysis, contexts with operations on the left side of the equal sign in the form of $a{\pm}b=c$ were provided excessively, with the other contexts hardly seen. Thirdly, teaching methods provided in the study were found to be effective for enhancing understanding the concept of equality sign. In other words, these methods enabled students to focus on relational understanding of concept of equality sign rather than operational one.