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在数学教学过程中,加强对学生的思维训练是改革数学教学,提高教学质量的最根本的途径。“思维”是人类特有的,是人有意识的、能控制的认识活动。“思维过程”是一种信息的转换、加工、分析、存储、输出的过程。学生的学习就是这种思维过程。由于每一个学生在学习过程中,对信息处理的水平的不同,从而出现了学习成绩的差异。如何提高学生的信息处理水平呢?下面提出的思维程序是值得提倡的。我们知道,人们要认识进而掌握一个事物的本质及其运动规律,必须从它的正反两个方面去认识、去分析(即“是 A 如何?不是 A 又如何?”),如果一个学生学习数学过程中,对每一个概念、定理、公式都能从正反两个方面去进行分析、理解,明确相应的结论,这对于掌握数学知识、增强解题能力都是极其有利的。这种从正反两个方面去分析求解的思维过程就是所谓的“正向思维”过程与“逆向思维”过程。
In the process of mathematics teaching, strengthening the thinking training of students is the most fundamental way to reform mathematics teaching and improve teaching quality. “Thinking” is unique to human beings and is a conscious and controllable cognitive activity. The “thinking process” is a process of information conversion, processing, analysis, storage, and output. Student’s learning is this kind of thinking process. As each student in the learning process, the level of information processing is different, so there is a difference in academic performance. How to improve the student’s information processing level? The thinking program proposed below is worth promoting. We know that people need to understand and grasp the nature of a thing and its law of motion. It must be understood and analyzed from its positive and negative aspects (that is, “How is A? Is not A?”) if a student learns In the mathematics process, each concept, theorem, and formula can be analyzed and understood from both positive and negative sides, and the corresponding conclusions can be clearly defined. This is extremely advantageous for mastering mathematics knowledge and enhancing problem-solving abilities. This kind of thinking process from the positive and negative aspects of analysis and solution is the so-called “positive thinking” process and “reverse thinking” process.