Logic and intuition are considered as the opposite extremes of teaching geometry, and any teaching method of geometry is to be placed between these extremes. The purpose of this study is to identify the characteristics of logical and intuitive approaches for teaching geometry and to derive didactical implications by taking Euclid's Elements and Clairaut's Elements respectively representing the extremes. To this end, comparing the composition and contents of each book, we analyze which propositions Clairaut chose from Euclid's Elements, how their approaches differ in definitions, proofs, and geometrical constructions, and what unique approaches Clairaut took. The results reveal that Clairaut mainly chose propositions from Euclid's books 1, 3, 6, 11, and 12 to provide the contexts that show why such ideas were needed, rather than the sudden appearance of abstract and formal propositions, and omitted or modified the process of justification according to learners' levels. These propose a variety of intuitive strategies in line with trends of teaching geometry towards emphasis on conceptual understanding and different levels of justification. Specifically, such as the general principle of similarity and the infinite geometric approach shown in Clairaut's Elements, we could confirm that intuition-based geometry does not necessarily aim for tasks with low cognitive demand, but must be taught in a way that learners can understand.

The purpose of the present study is to compare the differences in levels per group of high school students regarding the self-regulated learning factors for mathematics. For this purpose, a self-regulated learning measurement tool was developed and surveys were conducted. And the statistical analysis was completed using the frequency analysis, Kolmogorov-Smirnov normality test, Mann-Whitney U test and the Kruskal-Wallis H test. As a result, it is found that self-efficacy is of statistically significant differences in self-regulated learning levels regardless of the group classifications but test anxiety does not show statistically significant differences in self-regulated learning levels regardless of the group classifications.