"in mathematics ... we find two tendencies present. On the one hand, the tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material that is being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects one studies, a live ra...

a central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. in this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. the main stages of the modeling process are represented as fuzz...

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

In gb, the importance of phrase-structure rules has dwindled in favour of nearness conditions. Today, nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet, while the formal theory of phrase-structure grammars is quite advanced, no formal investigation into the prop...

This paper explores universal relations, i.e., meta-mathematical concepts that mathematicians seem to employ in all domains of mathematical reasoning. This paper presents precise mathematical definitions for three universal relations: isomorphism (type identity), essential property , and isoonticity . Although no formal explanation is given as to how universal relations expedite mathematical re...