학교수학에 나타난 닮음의 의미에 대한 고찰

Abstract

The 2015 textbooks on school mathematics explain ‘the meaning of similarity’ as ‘figures that are stretching or shrinking at a constant rate’. The method of ‘stretching or shrinking at a constant rate’ can be interpreted in various ways. When interpreting the meaning as ‘the ratio of the length of the corresponding side and size of the corresponding angle are invariant’, the ‘meaning of similarity’ and ‘property of similar figure’ falls into the recursive argument. In order to find an alternative, the Euclid’s ‘Elements’ and Clairaut’s ‘Elements of geometry’ were compared with contents that are related to the similarities. Based on this, the 2015 textbooks were analyzed. Since the method of ‘stretching or shrinking at a constant rate’ was not clarified, the possibility of the recursive argument was confirmed. In order to avoid the recursive argument, a search for a manner to specify the ‘the meaning of similarity’ based on Clairaut's approach is necessary. ‘The meaning of similarity’ can be avoided in the recursive argument by interpreting the meaning of ‘stretching or shrinking at a constant rate in the horizontal and vertical directions’. In particular, it was confirmed that it is possible to intuitively develop similarity in school mathematics.