• The Mathematical Education
• /
• v.47 no.2
• /
• pp.221-224
• /
• 2008

The article shows that the concept 'weight' and the concept 'heaviness' give rise to different abstractions in the sense of Piaget and that these two concepts are differentiated by set-theoretic devices. The failure of differentiation of these two concepts 'weight' and the 'heaviness' can cause the failure of learning of the difference between reflective abstraction and empirical reflective abstraction. To explain the Piagetian abstrcation in a classroom, the author suggests to use the concept 'color' instead of the concept 'weigtht'.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.628-635
• /
• 2022

For another study of soft context and soft concept closely related to formal context and formal concept, in this paper, we propose the notions of conditional concepts, decision concepts and soft decision context based on soft contexts. Subsequently, the notions of consistent soft decision context and consistent set are introduced, and some properties for consistent set of soft decision contexts are investigated.

• East Asian mathematical journal
• /
• v.39 no.2
• /
• pp.119-139
• /
• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• Journal of Educational Research in Mathematics
• /
• v.8 no.1
• /
• pp.381-403
• /
• 1998

As a researcher engaged in the mathematical education, mathematics teachers are interested in instructional methods. While it is unlikely that the viewpoints of individual mathematics teachers are reflected in making decisions on instructional purposes and instructional contents, a good many parts of instructional methods on mathematical facts are decided by individual teachers. This means that the role of mathematics teachers is given much weight in the mathematical education. Therefore, the mathematics teachers must not be excluded in all parts of the study of mathematical education. We studied the instructional methods of function concept, a central topic in school mathematics from the following perspectives. First, we examined the characteristics of the three(correspondence-centered, middle, dependence centered) viewpoints about the essence of function concept. And we should that which of them should be the viewpoint of instruction of function concept in school mathematics. Second, we investigated the questions regarding the process of function instruction in school mathematics and presented alternative instruction methods of function concept to solve the questions. Third, we postulated the importance of polynomial function, relating college mathematics in order to present the reason why the polynomial function is importantly treated in functional instruction of school mathematics.

• Research in Mathematical Education
• /
• v.12 no.1
• /
• pp.1-26
• /
• 2008

The concept field is defined as the schema of all equivalent definitions of a mathematics concept. Concept system is defined as the schema of a group concept network where there are mathematics relations. Proposition field is defined as the schema of all equivalent proposition sets. Proposition system is defined as a schema of proposition sets where one mathematics proposition at least is "derived" from the other proposition. CPFS structure that consists of concept field, concept system proposition field, proposition system describes more precisely mathematics cognitive structure, and reveals the unique psychological phenomena and laws in mathematics learning.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.561-572
• /
• 2018

In this paper we consider the concept of statistical causality in continuous time between flows of information, represented by filtrations. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical finance. We give necessary and sufficient conditions, in terms of statistical causality, for extremality of measure in the set of martingale measures. Also, we have considered the extremality of measure which involves the stopping time and the stopped processes, and obtained similar results. Finally, we show that the concept of unique equivalent martingale measure is strongly connected to the given concept of causality and apply this result to the continuous market model.

• Research in Mathematical Education
• /
• v.18 no.4
• /
• pp.289-305
• /
• 2014

The current mathematical education calls for a learning environment from the constructionism perspective that actively creates mathematical objects. This research first analyzes JavaMAL's expression 'move' that enables students to express the agent's behavior constructively before they learn vector as a formal concept. Since expression 'move' is based on a coordinate, it naturally corresponds with the expression of vectors used in school mathematics and lets students take an embodied approach to the concept of vector. Furthermore, as a design tool, expression 'move' can be used in various activities that include vector structure. This research studies the educational significance entailed in JavaMAL's expression 'move'.

• The Mathematical Education
• /
• v.47 no.4
• /
• pp.437-445
• /
• 2008

On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.683-690
• /
• 2013

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.1
• /
• pp.27-36
• /
• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.