Spinoza의 Ethica에 나타난 수학 내용 분석 및 그에 따른 교과서의 ‘삼각형의 세 각의 합’ 내용 고찰

Abstract

In the field of mathematics education, there is a growing interest in Spinoza in relation to the study of affect. This is because his philosophy provides clues about the close relationship between affect and cognition. However, Spinoza can also be explored in relation to contents of school mathematics. Spinoza's main writing, <Ethica>, is not only written in a mathematical form, but also contains a variety of mathematics at the level of school mathematics, and the mathematical contents occupy an important place in his philosophical explanations like that all modes including affect are inevitable. In this article, in order to examine how contents of school mathematics support Spinoza's philosophical claims, the mathematical contents of <Ethica> were analyzed, focusing on the relationship with the main idea of the part including the contents. As a result of the analysis, it was noted that the proposition that 'the sum of the three angles of any triangle is equal to 2 right angles', a traditional theme of school mathematics, was mentioned repeatedly to help somebody understand Spinoza’s concept of the ‘Necessity’. Relatedly, how this proposition is handled in school mathematics textbooks was examined in terms of the context mentioned in <Ethica>. Through these results, the humanities aspect of school mathematics and the need of mathematics education as a humanities education were discussed.