The transformation between positive thinking and reverse thinking is to create a reversibility in the process of students' psychological activities, from a one-way A→B thinking mode that only works in one direction to a two-way (or reversible) A? B-mode thinking.
The reversibility of thinking is a positive psychological activity, which has a correct influence on the development of students' thinking activities. Practice has proved that reverse thinking can be formed at the same time as positive thinking.
In teaching, people's thinking activities are generally in a certain direction. In teaching, students should be actively encouraged to leave one way of thinking freely and move towards another way of thinking, thus forming a multi-directional thinking direction.
New teaching is an important link for students to learn and master new knowledge, and students' learning methods are formed with the teaching process of teachers in new teaching. If the teacher only pays attention to the cultivation of students' positive thinking while imparting knowledge, but ignores the cultivation of students' reverse thinking, it will inevitably lead to the one-way thinking activities of students and will also imprison the development of thinking.
Transformation of definition
It is one of the effective means to form two-way (reversible) thinking that students appear simultaneously in the forward narrative and reverse narrative defined by mathematics.
For example:
Theorem: The angle of the vertex at the center of the circle is called the central angle.
Inverse theorem: the vertex of the central angle is on the center of the circle.
In teaching, students should be trained to consciously look at every mathematical definition and law from a mathematical perspective, seeing both its positive narrative and its reverse narrative, so as to master knowledge flexibly. For example, judge whether the reciprocal of 25 is 2 12. This is an inverse problem. If students have a "two-way" understanding of the concept of "reciprocity", the problem will be easily solved. Of course, some definitions are irreversible, which will be described in detail later. Pay attention to the influence of reverse practice.
Practice is the digestion and absorption of what students have learned, and it is also a means for students to adjust their thinking activities with self-awareness. Therefore, the form of practice plays an inestimable role in developing students' thinking quality. Then, how to make students consciously or unconsciously form the transformation of positive and negative thinking in practice. In practice, this often happens. When we finish an example for students and then give several questions that are contrary to the example, students will get the correct answer soon, and the correct rate is relatively high. If the known and unknown examples are reversed, many students will be at a loss when giving several "inverse" questions, and the correct rate is very low. It can be seen that the thinking that occurs in the transformation from the forward problem to the reverse problem is not unimpeded, and some unexpected obstacles will be encountered. The existence of these obstacles is the unique attribute of reverse thinking at work. In the reverse way of thinking, thinking is not necessarily just repeating the original way. The way from a to b can be different from the way from b to a, but the movement direction is opposite. For example, "natural numbers and zeros are integers", whereas "integers are natural numbers and zeros" is not true.
Generally speaking, the way of positive thinking is unique, while the way of reverse thinking is multi-directional. The existence of this feature causes students' thinking obstacles in inverse problems and makes students feel difficult in inverse propositions. In teaching, if we pay attention to this and explain this problem to students on appropriate occasions, it will greatly reduce the obstacles for students to solve problems.