Abstract ▼ AI-Helper

In this paper, I review the historical background of "the principle of the permanence of equivalent forms" and sum- marize properties of "the principle of the permanence of equivalent forms" as a kind of heuristic. 1 think that "the principle of the permanence of equivalent forms" can be used effect...

In this paper, I review the historical background of "the principle of the permanence of equivalent forms" and sum- marize properties of "the principle of the permanence of equivalent forms" as a kind of heuristic. 1 think that "the principle of the permanence of equivalent forms" can be used effectively for student's discovery of the algebraic structure. There are three ways of using "the principle of the permanence of equivalent forms" in extending number system - an extension on the base of set theory(SMSC), the formal or axiomatic extrapolation and the inductive-extrapolatory method. All those three methods are mixed up and being used potentially at various levels in current Korean text books. "The principle of the permanence of equivalent forms" is used most effectively in the subject of the exponent. 1 try to present a situation that makes the students find more general definition and cultivate their desirable attitudes for the mathematics in the process of extending the exponent through summarizing the debate between Goel & Robillard(1997) and Tirosh S, Even(1997).