| Mathematics thought, which is the essence and soul of mathematics knowledge,is the understanding of the essence of mathematics. And It is the key to improve the individual quality of thinking and mathematical ability by combining mathematical knowledge with learning ability. Also, it is one of the important connotations of mathematical literacy. Classified discussion thought is one of the most important mathematical thoughts in high schools and it is referred to in many chapters in the textbook, which plays a decisive role in the College Entrance Examination. Students’ consciousness of classified discussion is poor in solving problem and they are unclear and subjective while discussing. At the same time, the research now is more likely to pay attention to the study of problem-solving than teaching. This article closely combines the teaching materials with College Entrance Examination knowledge, and it contains a wealth of information on the classified discussion for students in high schools of Shanghai, then it aims to provide valuable reference for the teaching of classified discussion thought.The main contents are as follows:This article studies the current Shanghai high school mathematics textbooks in depth, and excavates fully the knowledge points contained in collection, inequality,function, trigonometric function series plane vector, determinant, analytic geometry,solid geometry, complex, permutation and combination and probability.At the same time, it classifies the same type of exercise and summarizes the reasons leading to classified discussion. Then, the article analyzes Shanghai College Entrance Examination IN recent six years by the classification reasons, and makes statistics with the annual classified discussion items such as types, scores, discussion factors,knowledge carriers in College Entrance Examination every year. And it can draw a beneficial conclusion that the College Entrance Examination often uses function,sequence, analytic geometry, vector, collection and inequality as knowledge carriers in order to examine classified discussion with parameter, the probability of permutation and combination, the formula of class representations, whether or not slope exist for setting line, the discuss about absolute out, the nature of the inequality of the operation, the graphics of the uncertainty, the discussion according to the rest of the class, not the only discussion conclusion. And so on.According to the above research, combining previous studies with my own thirteen years of teaching experience, I put forward five principles of teaching thought and seven teaching strategies about classified discussion of Shanghai high school mathematics. Through the teaching designs, such as concept class, derived class, this article explains how to teach by the classified discussion knowledge. The five teaching principles are the penetration principle, progressive principle, systematic principle, clear principle, the principle of self construction. Seven teaching strategies are as follows:(1) Mine the methods in the classified discussion thought in the textbook, and give some examples by changing some of the examples and exercises into classified discussion by variation.(2) Pay attention to knowledge acquisition process and strengthen the training and cultivation of the classified discussion. Don’t directly define concept teaching and don’t draw a conclusion early about formula,theorem and nature.(3) Make a good summary, then summarize and extract to the ideas and methods of classified discussion. Summarize the strategies in avoiding or optimizing discussion.(4) Strengthen problem-solving guidance and break through the difficulty of classified discussing thought.(5) Take the approach of repetition,master the key points of classified discussion. For the classified discussion emphasis,teaching must be repeatedly carried on different knowledge carriers.(6) Correct the mistakes and strengthen the error-prone points.(7) Pay attention to other mathematical thought and methods. |
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