• Kyungpook Mathematical Journal
• /
• v.53 no.1
• /
• pp.25-35
• /
• 2013

In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

• The Pure and Applied Mathematics
• /
• v.2 no.2
• /
• pp.163-172
• /
• 1995

G.Lumer [8] introduced the concept of semi-product space. H.M.El-Hamouly [7] introduced the concept of fuzzy inner product spaces. In this paper, we defined fuzzy semi-inner-product space and investigated some properties of fuzzy semi product space.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.63-66
• /
• 2002

As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany(GO). In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Sostak[SO1], to the interval-valued fuzzy setting and study its fundamental properties for some extent.

• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.11-23
• /
• 2022

In this paper, the concept of pseudo - complementation on a generalized almost distributive fuzzy lattices (GADFLs) is introduced as a fuzzification of the crisp concept pseudo - complementation on a generalized almost distributive lattices. It is also established a one - to - one correspondence between the pseudo - complemented GADFL (R, A), R with 0 and the left identity element of R.

• The Mathematical Education
• /
• v.47 no.2
• /
• pp.197-219
• /
• 2008

Unlike ordinary situations, deifinitions play a very important role in mathematics education in schools. Mathematical concepts have been mainly acquired by given definitions. However, according to didactical intentions, mathematics education in schools has employed mathematical concepts and definitions with less strict forms than those in pure mathematics. This research mainly discusses definitions used in geometry (promising) course in primary schools to cope with possibilities of creating misconception due to this didactical transformation. After analyzing problems with potential misconceptions, a survey was conducted $\underline{with}$ 80 primary school teachers in Jeju to investigate their recognitions in meaning of mathematical concepts in geometry and attitudes toward teaching. Most of the respondents answered they taught their students while they knew well about mathematical definitions in geometry but the respondents sometimes confused mathematical concepts of polygons and circles. Also, they were aware of problems in current mathematics textbooks which have explained figures in small topics (classes). Here, several suggestions are proposed as follows from analyzing teachers' recognitions and researches in mathematical viewpoints of definitions (promising) in geometric figures which have been adopted by current mathematics textbooks in primary schools from the seventh educational curriculum. First, when primary school students in their detailed operational stage studying figures, they tend to experience $\underline{a}$ collision between concept images acquired from activities to find out promising and concept images formed through promising. Therefore, a teaching method is required to lessen possibility of misconceptions. That is, there should be a communication method between defining conceptual definitions and Images. Second, we need to consider how geometric figures and their elements in primary school textbooks are connected with fundamental terminologies laying the foundation for geometrical definitions and more logical approaches should be adopted. Third, the consistency with studying geometric figures should be considered. Fourth, sorting activities about problems in coined words related to figures and way and time of their introductions should be emphasized. In primary schools mathematics curriculum, geometry has played a crucial role in increasing mathematical ways of thoughts. Hence, being introduced by parts from viewpoints of relational understanding should be emphasized more in textbooks and teachers should teach students after restructuring this. Mathematics teachers should help their students not only learn conceptual definitions of geometric figures in their courses well but also advance to rigid mathematical definitions. Therefore, that's why mathematics teachers should know meanings of concepts clearly and accurately.

• School Mathematics
• /
• v.3 no.2
• /
• pp.373-399
• /
• 2001

The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.4
• /
• pp.859-868
• /
• 2007

The present paper deals with the ordering problem for how to teach mathematical concepts successfully. Main object is the concept of continuous functions which is fundamental in analysis and topology. At first, the theoretical organization of this concept is investigated through several texts in related field, calculus, analysis and topology. And next, the historical order for this concept from the viewpoint of problem-solving is considered. Based on these two materials, we suggest a lecturing organization order in order to establish a balanced unification of three concepts - intuitive, logical and formal concepts.

• The Pure and Applied Mathematics
• /
• v.14 no.4
• /
• pp.289-306
• /
• 2007

We define and study a concept of $H^f-space$ for a map, which is a generalized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration $E_{\kappa}{\rightarrow}X$ induced by ${\kappa}:X{\rightarrow}X'\;from\;{\epsilon}:\;PX'{\rightarrow}X'$, we can obtain a sufficient condition to having an $H^{\bar{f}}-structure\;on\;E_{\kappa}$, which is a generalization of Stasheff's result [17]. Also, we define and study a concept of $co-H^g-space$ for a map, which is a dual concept of $H^f-space$ for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg's result [6].

• Journal of Educational Research in Mathematics
• /
• v.10 no.1
• /
• pp.85-102
• /
• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

• Bulletin of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.27-30
• /
• 1984

The concepts of the numerical range of an operator on a Hillbert space and on a Banach space were introduced by Toeplitz in 1918 and Bauer in 1962 respectively. Bauer's paper was concerned only with finite dimensional Banach spaces, but the concept of numerical range that he introduced is available without restriction of the dimension [1, 2]. In this paper, we define a C-algebra spatial numerical range of an operator on C-algebra valued inner product modules introduced by Paschke [4], and give analogous results on these modules as those on Banach spaces.