The Research Of The Grasp Of Typical Mathematical Problem Solving About High School Students

Studying of mathematical problem is a hot topic in the mathematics education research. The typical mathematical problems have strong representative, so typical mathematical problems are the key of the math studying.Consulting relevant literature, this paper combing existing literatures about math problem solving. We have grasped the research trends, research methods and research results of current question on mathematical problem solving. We show the typical math problems and mathematical problem solving method.According to the needs of research, reference to "the ordinary high school mathematics curriculum standard" and exam outline has carried on the induction and classification of typical high school math problems, and combined with nearly five years, the provinces and cities all over the country mathematics test compiled a set of typical math test. Of 185 students of senior three were tested, research shows that:(1) The students grasp not ideal, the typical mathematical problems in the exam for 116 students, only 3 people including students good grades, and failed to pass the number to 69.(2) The students to master the best in the field of "function", the relevant function domain, parity and periodicity, the topic of master skilled, and the function of zero, and the problems of piecewise function not enough very clear understanding.(3) The students to master in the field of "trigonometric function" relatively well, the same basic relations of the Angle between trigonometric functions, trigonometric functions of image transformation to grasp skilled, and the application of delta transformation, cosine theorem is knowledge.(4) The students to master in the field of "sequence" is not good, the sequence of general term formula are given and the method of series summation to master the unskilled.(5) The students to master in the field of "derivative" is not good, can’t proficient in application of derivative method to study the properties of the function, classification and discuss the lack of the idea of master.Factors that affect high school students for typical mathematical problems solution master are:(1) Students forget the mathematics knowledge, or misunderstand the concept of mathematics;(2) Students can’t accurate identification model, and choose the appropriate problem-solving strategies;(3) Students lack integrity of their thinking;(4) Students lack of reflection after problem.(5) Teachers ignore the solution contains mathematical thinking method.Through interviews with teachers and students, and puts forward several suggestions:(1) For students to study accurately understand and master the basic knowledge of mathematics, makes systematic mathematical knowledge;(2) A thorough understanding process, skillfully applied problem solving method;(3) Attaches great importance to the problem after reflection, help to improve the cognitive structure.Put forward some suggestions for teachers’ teaching:(1) Attaches great importance to the teaching of basic knowledge, improve their science literacy;(2) Pay attention to the interpretation of a typical mathematical problems, pay more attention to the analysis of the problem solving process,(3) Lay emphasis on the analysis of examination, aiming at typical problems in the problem solving design error correction class;(4) Pay attention to in teaching permeate typical mathematical thought and method.