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(一) 对于一道数学題,教师經常可以通过适当地变更問題的条件和結論,或变更問題的內容和形式,拟造出一些新的数学題来,这种工作称为数学題的拟造。任何一道数学題,都蘊涵着一定的数量間的相依关系或图形性貭問的相依关系。在解題的时候,还要运用一些特定的邏輯关系和思維方法,通过数学題的拟造,甚至是最簡单的拟造,都能使我們对其中的关系有更深刻的认識并对所运用的方法能更透彻地掌握。恩格斯在自然辯証法中曾說:“数学上各种形态的轉变,并不是一种无聊的游戏,它是数学科学最有力的杠杆之一。”这話不仅对于数学定律和公式等的变形是正确的,对于数学問題的变形和拟造也同样是正确的,近代数学有些部門正是在对旧有的問題进行內容和形
(1) For a math problem, teachers can often create new math problems by appropriately changing the conditions and conclusions of the problem or changing the content and form of the problem. This kind of work is called the creation of a math problem. Any mathematics question implies a certain number of dependencies or graphical interdependence. When solving the problem, we must also use some specific logical relationships and thinking methods. Through the creation of mathematical problems, or even the simplest of them, we can make a deeper understanding of the relationship between them and the The methods used can be more thoroughly mastered. Engels said in the dialectics of nature: “Mathematical changes in various forms are not a kind of boring game. It is one of the most powerful levers in mathematics science.” This is not only a distortion of mathematical laws and formulas, etc. Correctly, it is also correct to distort and make mathematical problems. Some departments of modern mathematics are precisely carrying out the content and shape of the old problems.