• Journal of Information Processing Systems
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• v.11 no.2
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• pp.184-204
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• 2015

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 1996.06c
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• pp.679-684
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• 1996

The work was aimed at realize the problem of seed processing . Solving this problem it was ascertained that the existing mathematical methods are reliable enough, but they are used practically very seldom. The work offers to use the expert system technology which allows to solve problems connected with practical knowledge of experts in the region of investigation effectively. The method of knowledge structuring and analizing as well as technique of knowledge acquisition which is necessary for realization of this technology are worked-out in the work. As the result applying the worked-out method the prototypes of the expert system (ES) are created : -ES " Sieves " ; research prototype for the sieve choice for the seed sorting machines -ES " Diagnostics " ; displaying prototype for the technological determination of action disrepair of seed sorting machines.

• East Asian mathematical journal
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• v.34 no.4
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• pp.537-548
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• 2018

An integrated approach has been regarded as important in mathematics education. The ultimate ideal of mathematics education is the development of whole person in students. However, mathematics education has not been successful in achieving this ideal. The purpose of this article is to identify an integrated approach to secondary mathematics education in order to achieve the ideal of the whole person. In particular, Ideas for an integrated approach for mathematical activities are sought. This study starts with analysis of recent attempts to integrate knowledge and attitude of mathematics education. Finally, some suggestions for the cultural and institutional conditions in which these integrative ideas can be effectively realized in secondary school.

• The Mathematical Education
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• v.42 no.5
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• pp.647-672
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• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.

• Research in Mathematical Education
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• v.11 no.2
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• Research in Mathematical Education
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• v.8 no.1
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• pp.39-58
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• 2004

The School of Mathematical Sciences at University Sains Malaysia has offered a laboratory course on the integration of hand-held technology into the teaching and learning of mathematics since the beginning of the 2001/2002 academic year. This inquiry-based course highlights the explorations and application of mathematics in a data rich modeling environment. In addition, the course addresses several issues related to the effective integration of such technology into the mathematics curriculum. This paper discusses the appropriate use of graphing technology to present mathematical concepts and to support student's understanding in a student-centered learning environment, shares knowledge on the new mathematics that was made possible by hand-held technology, and summarizes student reactions to this innovative learning mode.

• Research in Mathematical Education
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• v.25 no.1
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• pp.65-89
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• 2022

Despite its recognition in the field of mathematics education and mathematics, students' understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers' judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.45-56
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• 2014

Modern society demands leaders who are trained with competence to not only approach knowledge but also create new knowledge by comprehensively understanding and applying it, and a leader with character and commitment to share one's ideas with others and be able to accept criticisms. In response to these societal changes, universities are increasingly adopting 'small group discussion-based classes with an attempt to develop and strengthen communication skills through reading, writing and speaking. This paper seeks to introduce a case of a math lecture, where discussion-based class was applied to mathematical education, requiring practical problem-solving through an argumentative thought process.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.95-106
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• 2005

This paper is investigated conception and methodology of data selection, cleaning, integration, transformation, reduction, selection and application of data mining techniques, and model evaluation during procedure of the knowledge discovery in database (KDD) based on Mathematics. Statistical role and methodology in KDD is studied as branch of Mathematics. Also, we investigate the history, mathematical background, important modeling techniques using statistics and information, practical applied field and entire examples of data mining. Also we study the differences between data mining and statistics.

• The Mathematical Education
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• v.39 no.2
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• pp.145-150
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• 2000

In this paper, we study the subject-matter knowledge related to the problem about rational exponent with negative bases. From the school mathematics point of view, we first investigate the meaning of the extensions of the number systems. We analyze the intrinsic meaning involved in the (-8)$^{1}$ 3) through the natural interpretation of rational exponent with negative bases by the complex number. we explain why it is important for a teacher to have the subject-matter knowledge in order to detect and correct student\`s mistake and misunderstanding.