• The Mathematical Education
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• v.53 no.1
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• pp.41-55
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• 2014

In recent years, there has been increasing interest in the pedagogical importance of counter-examples that contradict statements about mathematics education research and the curriculum revision process for high school mathematics courses. Using a literature research method, this study analyzed views about counter-examples according to a method of approach to statements and the classification of counter-examples and their criteria. The study also described the learnability of the content of counter-examples presented in Korean secondary school mathematics textbooks. The results showed that generating many counter-examples enables learners to understand mathematical concepts exactly, construct links between mathematical contents, and have flexible thoughts about mathematical objects. Considering the learnability of counter-examples, the contents of counter-examples in school mathematics textbooks are needed for mathematics teachers and students to generate numerous counter-examples and verify the justification of generating counter-examples in various manners.

• School Mathematics
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• v.15 no.4
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• pp.743-758
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• 2013

This paper analyses the examples of polygons taken in the 1st grade middle school mathematics textbooks. We analysed generic examples, non-examples and counter-examples represented in these textbooks. And also we classified and analysed with examples of the concept and the application of a procedure. We analysed the differences of methods among these textbooks representing the same concepts or procedures. The findings from the analysis showed that these textbooks mostly make use of generic examples. The examples of concept and procedure vary depending upon the textbooks. Also, many textbooks haven't properly represented various positions and figures of polygons. Textbooks need to represent various and appropriate examples in order to expand the example space of the students.

• International Journal of High-Rise Buildings
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• v.11 no.3
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• pp.145-156
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• 2022

Application examples of computational fluid dynamics (CFD) in the planning stage of high-rise buildings are introduced. First, we introduce examples of applications in the environmental field. The pedestrian wind environment was one of the earliest practical examples of CFD. CFD was also employed to validate the heat island mitigation measures proposed as part of the new construction plan. Second, application examples of wind-force evaluations are introduced. Prediction examples are presented for the peak wind pressure around a complex-shaped building and the wind force evaluation for a base-isolated building. The results prove that the results of the proper execution of CFD are equivalent to those of the wind tunnel experiment. As examples of CFD applications of other issues related to high-rise building planning, we introduce snow accretion on outer walls and high-temperature exhaust from emergency generators. Finally, the future prospects for the use of CFD are discussed.

• Journal of the Korean Institute of Educational Facilities
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• v.13 no.3
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• pp.37-47
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• 2006

The conservation or practical use of a lot of closed schools which occurred from 1982 all over the country by governmental policy has been becoming important concerns to local resident and community with economical and administrative interest. A lot of examples, sold or rented to public institutions or a person, which have been using by welfare facilities for inhabitants, facilities for education, youth, company, culture and art, and other use, could be found. It could be said that the process of user's participation of these examples is very high, that is, a lot of examples of our surrounding is applied with ecological concept have participated by most users and local residents directly to architectural repair and renewal process, and practical use. In this background, I choose total five examples more than one by Chungbuk, Chungnam, Jeonbuk, Jeonnam district to investigate examples of closed schools applied ecological architectural concept and I researched reconfiguration of site, change of exterior or interior material, application of ecological system, and role as local community.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.401-416
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• 2013

There has been increasing interest in recent years in the pedagogical importance of counter-examples that focuses on pedagogical perspectives. But there is no research that undergraduate students' generating counter-examples and proposing the true statements. This study analyze 6 undergraduate students' response to interview tasks and the process of their generating counter-examples and proposing true statements. The results of interviews are that the more undergraduate students generate various counter-examples, the more valid they propose true statements. If undergraduate students have invalid understanding of logical implication and generate only one counter-example, they would not propose true statements that modify the given statement, preserving the antecedent. In pre-service teacher's education and school mathematics class, we need to develop materials and textbooks about counter-examples and false statements.

• Korean Journal of Cognitive Science
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• v.11 no.2
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• pp.19-35
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• 2000

Learning by examples has proven to be an efficient method in mastering various subjects including programming languages. This study hypothesizes that the number of examples and the type of examples are two significant dimensions that influence the performance of learning programming languages by examples. A set of experiments was conducted to investigate the impacts of the two dimensions in the domain of JAVA programming. The results showed that providing two examples is more effective than providing only one example even though significantly more explanations are attached to the single example. Among the 'two-example' groups, the group that was given functionally similar examples performed better than those with functionally dissimilar examples. Explanations for these results are provided in this paper based on the behavioral patterns of individual subjects in terms of time and frequency. This paper concludes with the implications of the study results for the development of effective tutoring systems for programming languages.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.401-417
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• 2005

Skemp supposed that it is effective to use both examples and non-examples when new concepts which are upper level than learner's schema are introduced. The purpose of this research is to develop a practical process of teaching geometrical concepts based on Skemp's assumption. For this, the related literatures are reviewed and the Korean textbooks(4-ga, 4-na) are analyzed with respect to method of concept formation. The analysis to]Is that the textbook just explains Properties of concepts or present definitions, instead of giving the chance of inquiry. So we design and apply six step process of teaching geometrical concepts to 4th graders focused on students' inquiry using both examples and non-examples.'rho result turns out that using examples and non-examples is highly positive to concept formation.

• Journal of KIISE:Software and Applications
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• v.31 no.7
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• pp.859-868
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• 2004

We propose a method of selecting initial training examples for active learning so that it can reach high accuracy faster with fewer further queries. Our method is based on the assumption that an active learner can reach higher performance when given an initial training set consisting of diverse and typical examples rather than similar and special ones. To obtain a good initial training set, we first cluster examples by using k-means clustering algorithm to find groups of similar examples. Then, a representative example, which is the closest example to the cluster's centroid, is selected from each cluster. After these representative examples are labeled by querying to the user for their categories, they can be used as initial training examples. We also suggest a method of using the centroids as initial training examples by labeling them with categories of corresponding representative examples. Experiments with various text data sets have shown that the active learner starting from the initial training set selected by our method reaches higher accuracy faster than that starting from randomly generated initial training set.

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.17-30
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• 1996

In ergodic theory cutting and stacking constructions have been used to obtain a variety of important examples of transformations on the unit interval. We examine the example constructed by J. von Neumann and Kakutani and then apply the method used in the construction of Chacon's transformation to make examples that are weakly mixing but not mixing.

• Research in Mathematical Education
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• v.23 no.1
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• pp.1-12
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• 2020

In this case study, a professor was observed to investigate use of instructional examples when teaching the Intermediate Value Theorem in a calculus course. Video-recorded lessons were analyzed with constant comparison to video-stimulated recall interviews and field notes. The professor employed multiple instructional examples, which was initiated by students and modified by the professor. The professor asked students to build non-existing examples as an informal proof of the Intermediate Value Theorem and assessment of students' previous knowledge. Use of incorrect examples on instructional purpose can be an appropriate way for formative assessment as well as a bridge between informal and formal proofs in college mathematics.