Middle School Students’ Mathematics "Symbolic" Cognitive Difficulties And Teaching Suggestions

Mathematical symbols simplicity, accuracy, making it an indispensable tool for mathematics, but it is precisely because symbols of simplicity and abstraction resulting in "hard to teach, difficult to learn," the state in teaching. With the deepening of curriculum reform, more and more researchers focus on the important role of symbols in mathematics.On the basis of extensive literature analysis, the symbolic process is divided into three phases of five levels, and as a basis for the preparation of a combined high school textbook content test questionnaire to give high school students in math symbols cognition through the investigation and analysis of data difficulties exist in the process of development:.First, the primary symbolic of levels: 1) understanding of the process of operation mathematical symbols blurred; 2) the use of symbols is not standardized;Second, the significance of operating levels: 1) can not understand the underlying meaning of mathematical symbols under the influence of the understanding and use of symbols, and even confidence lost mathematics learning; 2) lack of relationship between the number of math notation and changes of understanding; 3) use symbolic language and other flexible conversion between mathematical language difficulties.Third, the program operation levels: 1) can not be converted computing and mathematical symbols between; 2) You can not select the appropriate mathematical problems(conventional compact) way to handle mathematical notation; 3) can be used for a variety of ways problem is, you can not select a symbol active expression.Fourth, the interpretation of levels: 1) the potential condition after inadequate understanding of abstract symbols, incomplete grasp; 2) there is no unified system of symbology.On more than symbolic for cognitive difficulties gives the following teaching suggestions: 1) Strict explicit mathematical notation standard use; 2) strengthening symbols’ s history, use of symbols meaning and value of symbols theoretical knowledge of learning 3) focus on symbols meaning of the teaching, and tap the potential significance of mathematical symbols, a complete understanding of the exact meaning of mathematical symbols. 4) abstract symbols concrete; 5) strengthen conversion training mathematical symbol language and natural language between; 6) teaching through multiple representation, strengthen "a given problem," the training; interpretation of levels: 7) emphasis on mathematics teaching choreography, to ensure the integrity, consistency and understanding of the linkages between symbols mathematical notation system;...