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(上接第三期) 三、中学数学中的变换问题 1.这里讨论的“变换”,是指变化转换的意思,含义是较为广泛的。数学中的变换,无非是数的变换、式的变换、图形的变换,以及数形之间的变换,在初等数学中,变换,是联系的纽带,是分类的由来,是化繁为简、化难为易、化未知为已知、化陌生为熟悉的有力手段,是新知识,新方法、新理论的源泉,是解题的有力武器和桥梁。 2。我们研究的变换有如下一些基本类型。 A.在代数中,有恒等变换、同解变换、等值变换,还有代换(包括整体代换、局部代换、循环再生的代换等),这是典型的代数思想的体现,“不等式”则表示一种放缩的变换。
(Continued from the third period) Third, the transformation problem in middle school mathematics 1. The “transformation” discussed here refers to the meaning of the change conversion, the meaning is more extensive. The transformation in mathematics is nothing more than the transformation of numbers, the transformation of patterns, the transformation of graphs, and the transformation between numbers and shapes. In elementary mathematics, transformation is the bond of connection, and it is the origin of classification. It is a powerful means to make difficult, easy, unknown, and familiar. It is the source of new knowledge, new methods, and new theories. It is a powerful weapon and bridge for solving problems. 2. The transformations we studied have the following basic types. A. In algebra, there are identity transformations, homothetic transformations, equivalent transformations, and substitutions (including whole substitutions, local substitutions, substitutions of cyclic regenerations, etc.), which are typical examples of algebraic thinking. Inequality means a scaled transformation.