前面谈到,教学中希望达成的许多目标其实是“不可教”的,越是智慧性高的目标越是不可教。让我们来思考这样的问题:“不可教”的东西往往非常重要,我们该怎么办?以思维为例。数学是思维的体操,数学能力的核心是思维能力,数学教学是思维的教学。我们做过很多研究,诸如思维的内涵,思维的层次,思维的品质,思维的作用,甚至,思维能力的培养。如果我们追问,思维能“教”吗?《教学艺术的基本特征》给出的 As we mentioned earlier, many of the goals we hope to achieve in teaching are actually “unprotected.” The more intelligent and more intelligent the less you can teach. Let’s think about the question: What can not be taught is often very important. What should we do? Take thinking as an example. Mathematics is thinking gymnastics, the core of mathematical ability is thinking ability, mathematics teaching is the teaching of thinking. We have done many researches, such as the connotation of thinking, the level of thinking, the quality of thinking, the role of thinking, and even the cultivation of thinking ability. If we ask, can thinking “teach”? “The basic characteristics of teaching art” are given