"Transformation" is a common method to solve problems. The means and methods of "transformation" are diverse and flexible, which are not only related to the content and characteristics of practical problems, but also related to students' cognitive structure. Mastering the "transformation" strategy is not only conducive to solving problems, but also conducive to the development of thinking. Teaching should not only aim at students' ability to solve various problems in textbooks, but also aim at students' experience and active application of "transformation" strategies. Having the initial "transformation" consciousness and ability will play a very positive role in future study and problem solving.
Second, the transformation of the learning foundation
(A) knowledge base-the cornerstone of strategy learning
High-rise buildings have sprung up, so has the application of transformation strategies. "Transformation" is a strategy to turn new problems into old problems and complex problems into simple problems, so that the original problems can be solved. In fact, what method is used to carry out the transformation and how to solve the problems after the transformation all need a certain knowledge base, otherwise the problems cannot be solved. It can be seen that a certain knowledge base is the cornerstone of "transformation" strategy learning.
(B) the ability base-a powerful lever for strategic learning
Strategy learning needs not only a certain knowledge base, but also a certain ability base. Psychological research shows that ability is the basic condition for people to acquire knowledge and master skills, and the combination of various abilities is needed to complete any activity. Therefore, students' existing ability foundation can be said to be a powerful lever for strategy learning.
1. Ability to observe, imagine and operate:
Learning geometric figures is inseparable from keen observation and spatial imagination, as well as the ability to operate on this basis.
2. Transfer and reasoning ability: Because "transformation" is to transform one kind of problem into another, students should have the ability of transfer and reasoning from the perspective of transformation or popularization. Therefore, when teaching "transformation" strategy, we should guide students to reason correctly, realize transformation and solve problems effectively. Of course, we should learn from examples, so as to solve more practical problems.
3. Ability to seek difference and innovation: Everyone has the idea of seeking difference and the impulse to innovate. In fact, transformation is also an important strategy, but when we really solve the problem, we need to determine the specific transformation goals and methods.
4. Ability to collect and process information: Modern society is an information society. The ability to collect and process information is an essential learning ability and an important criterion to measure a person's ability. Therefore, it is also an important ability foundation for students to learn transformation strategies.
Third, the transformation strategy.
1, which is transformed by analogy and association.
Analogy is a kind of reasoning method that compares two research objects and infers that they may be the same or similar in other aspects according to their similarities or similarities in some aspects. Therefore, when learning new knowledge, using analogy in time can turn unfamiliar problems into familiar ones, which will help students better accept new knowledge and consolidate old knowledge.
2. Realize the transformation by combining numbers with shapes.
The idea of the combination of number and shape is to make full use of "shape" to express a certain quantitative relationship vividly. In other words, it is a mathematical thinking method to help students understand the quantitative relationship correctly by making some line graphs, number graphs, rectangular area graphs, polymers, etc. , so as to make the content of the problem concrete and visual, so as to turn complex problems into simple ones.
3. Realize the transformation with the idea of substitution.
Substitution thought is an important thinking method in mathematics teaching. The essence of replacement is to change the form of the topic, but not the essence of the topic. When we encounter a difficult problem, we can replace some conditions or problems in the problem with another form equivalent to its content, so as to realize the smooth transformation of solving ideas and achieve the purpose of solving problems.
4. Use the hypothesis method to realize the transformation.
In primary school mathematics, it is often difficult for students to solve thinking problems. Therefore, teachers should pay attention to teaching students how to solve problems in the teaching process, thus improving students' thinking ability. Hypothesis often plays a key role in solving problems. Hypothesis is to turn abstract problems into more specific problems, which makes the quantitative relationship clearer and makes it easier to grasp the path of solving problems.
5. Use existing knowledge to realize transformation.
Turning unfamiliar problems into familiar ones is a common way of thinking in solving problems. Problem-solving ability is actually a kind of creative thinking ability, and the key of this ability lies in whether you can observe carefully and apply what you have learned in the past to turn unfamiliar problems into familiar ones. Therefore, as a teacher, we should dig deep into the factors of quantitative change, make use of the knowledge we have learned, and make efforts to abstract the teaching materials to an acceptable level for students, so as to reduce the strangeness when contacting new content and avoid psychological obstacles caused by changes in the research objects, which can often get twice the result with half the effort.
6. Use reasonable questions to realize transformation.
Teachers divide a complex problem into several small problems whose difficulty is synchronous with students' thinking level by setting questions reasonably, and then analyze and explain the relationship between these small problems, so as to serve the whole by mastering local knowledge. For example, for a concept, you can set questions around the following angles: the composition of the concept; Sub-concepts involved in the concept; The extension of the concept; The connotation of the concept; Definition and negation of concepts; The relationship between concepts; The application of concepts and some constructive problems designed by concepts. There should be a certain gradient between questions in order to inspire students' thinking in teaching.
Simplification of complex problems is the most commonly used thinking method to solve mathematical problems. A problem that is difficult to solve directly is transformed into a simple problem and solved quickly through in-depth observation and research.