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一、数学教学难点的反思数学中的教学难点,通常出现在新知识、新方法、新模式上。从数学思想的角度看,这“三新”正是数学思想迅速丰富、大步跳跃的地方。因此,数学教学难点可以认为是数学思想比较抽象、较为复杂或转折较大的一种表现。所谓数学思想,是指体现在数学基础知识、基本方法中的本质思想,诸如假设思想、对应思想、转化思想、分合思想、比较思想、分类思想、代数思想等,它们都是唯物辨证法中联系与转化、运动与发展等基本思想的具体化、数学化的体现。
I. Reflections on the Difficulties of Mathematics Teaching Difficulties in mathematics often arise in new knowledge, new methods, and new models. From the perspective of mathematics thinking, this “three news” is where mathematics ideas are rapidly enriched and strides. Therefore, the difficulty in mathematics teaching can be considered as a relatively abstract, complex or turning-over of mathematical thinking. The so-called mathematical thinking refers to the essential thoughts embodied in basic knowledge and basic methods of mathematics, such as hypothetical thoughts, corresponding thoughts, transformed thoughts, disjunctive thoughts, comparative thoughts, classification thoughts, algebraic thoughts, etc., which are all materialistic dialectical methods. Contact and transformation, movement and development and other basic ideas, the embodiment of mathematics.