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數學大綱中明確指出,我們的學校“在教學過程中教師應該通過數學教學使學生建立辯證唯物主義世界觀”。這種“世界觀是觀點和信念底完整體系,這些觀點和信念是我們對於自然界和社會的態度,我們對於行為的表示”(凱洛夫)。世界按其本質來說是物質的,同時自然界被辯證法統治着,恩格斯把它叫做事物的辯證法,而人們的辯證思維方法正是客觀存在的辯證法在人類頭腦裹反映的結果,恩格斯又把它叫做思想上的辯證法,幾何課所進行教學的一切內容當然也不例外的被辯證法統治着,因爲它本身就是反映客觀現實一定侧面的結果。
The outline of mathematics clearly states that our school “in the teaching process teachers should use mathematics teaching to enable students to establish a dialectical materialist worldview.” This kind of “worldview is a complete system of ideas and beliefs, which are our attitudes towards nature and society, and our representations of behavior” (Kalev). The world is material in nature, and the natural world is dominated by dialectic. Engels calls it the dialectic of things, and people’s dialectical thinking method is the result of the reflection of objective existence of dialectics in human minds. Engels called it again. The ideological dialectics and all the contents of the teaching in the geometry class are certainly ruled by dialectic, because it is a result of reflecting certain aspects of objective reality.