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### High school students learn math problem solving three main strategies

In order to make the recall, Lenovo, guess the direction more clearly, more lively, further increasing the effectiveness of exploration, we must have some problem-solving strategies.
All problem-solving strategy is the basic starting point of scientific learning method of "transformation", that is, into problems faced by one or several easy to answer new questions, with the adoption of the new title of the study, found that the original problem-solving ideas, and ultimately achieve the objective of solving the original problem.
Based on this understanding, problem solving strategies are commonly used: the familiar, simple, intuitive, and specialization, generalization, integration, indirect, and so on.
First, be familiar with strategy of the so-called strategy, is when we are confronted with is not previously exposed to strange when, trying to turn it into solutions have been or are familiar with the topic, so as to make full use of existing knowledge, experience or problem-solving mode, successfully solving the original problem.
In General, the familiarity with the subject, depends on the awareness and understanding of the topic itself. Structure analysis and answers to any questions, containing conditions and conclusions (or question) two aspects. Therefore, in order to take strange into familiar questions, problem conditions, conclusions can transform (or problems) and to work harder on their contact.
Commonly used approaches are:
(A) basic knowledge, fully associative memories and questions:
According to polyA's view, until the problem is resolved, we should make the associations and memories with the original issues of the same or similar types of knowledge and, making full use of similar problems, methods, and conclusions, so as to solve the existing problems.
(B), Omni-directional, multi-perspective analysis of the meaning of:
The same math problem can often be different sides and angles to get to know. Therefore, based on their knowledge and experience, adjust the angle to analyze the problem, help to better grasp the meaning, find their own problem-solving directions.
(C) appropriate auxiliary element:
In mathematics, the topic of the same material, often can have a different form of conditions and conclusions (or problems), there are also a variety of contact. Therefore, the proper construction of auxiliary elements, helps to change topics in the form of communication conditions and conclusions (or the conditions and problems) the relationship, the strange into familiar questions.
Solving mathematical problems, and the auxiliary elements are many and varied, a common structural graphics (point, line, surface and volume), the construction algorithm, construct polynomials, structural equation (s), the construct coordinate system, construction sequence, structural determinants, structural equivalence proposition constructs counterexamples constructed mathematical models, and so on.
Second, simplified policy of the so-called simplified strategy, is when we are confronted with is a complex, hard to start when, trying to transform into one or several simple and easy with new problem, through the study of new problems, inspire problem-solving ideas, to simplify the complex, solve the original problem.
Added to simplify is familiar with and play. Generally speaking, we are often more familiar or easier for simple problems familiar.
Therefore, the practical solution, combining these two strategies are often the only focus is different.
Problem solving, ways of the implementation of the simplification strategy is multifaceted, mastering the studying law of middle school students: sought link between classification review discussion, simplify the known conditions, proper decomposition results.
1, sought link between mining implied conditions:
Structure of complicated questions, its background and theory, mostly consists of several simple basic questions, by a combination of removing intermediaries constitute of.
Therefore, starting from the causal relationship of the topic, seeking possible intermediaries and implied conditions, break the topic down into a set of interrelated series title, is an important way to realize complex questions simple.
2, classification review discussion:
In mathematics, the complexity of problem-solving, mainly lies in its conditions, conclusions (or questions) contains a wide range of difficult to identify possible cases. For this type of question, select the appropriate classification standard, the original problem is decomposed into a set of parallel Direct help simplify complex issues.
3, simplifying the known conditions:
Some math problems, conditions are relatively abstract and complicated, not easy to start. At this time, some known conditions may wish to simplify problems, even putting aside for the time being, despite, consider a simpler problem first. Such a simple question, to answer the original question, can often play the role of go-between.
4, the right decomposition conclusion:
There were problems, major difficulties of solving, abstraction from the conclusion, it is difficult to direct links and conditions, then, may wish to imagine conclusions can be reduced to a few relatively simple parts in order to conquer and solve the original problem.
Third, Visual strategies:
So-called Visual strategy, that is, when we're faced with is an abstract, elusive topic, try to convert it to vivid, direct specific questions, so that by virtue of the image to grasp the problem of things and linkages between the various objects, find the original problem-solving ideas.
(A), chart, Visual:
Some mathematics, abstract, complex and added difficulties to the understood meaning, often due to abstraction and complexity of the topic, make it difficult for normal thinking to the end.
For this type of topic, with chart viewing, analysis the meaning of diagram, or table, helps to visualize the abstract content, organized the complex relationship, thought to have relatively specific backing, deep thinking, find clues to solve problems.
(B), graphics, Visual:
Some involve relationship problems, using algebraic methods to solve, the roads tortuous and rugged, large amount of calculation. At this time, may wish to use a graphic intuitive, geometric analysis of the number of questions relating to the right and broaden basic Chinese learning method to solve problems, identify simple and rational way of solving problems.
(C), image visualization:
Many involve relationship problems, image and function is closely related to the flexible use of image visualization, often to simplify the complex, get simple, ingenious solution.
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