Vector Applied Research In Secondary School Mathematics Teaching And Problem-solving

Vector is one of the important concepts in modern mathematics. Vector has educational value,cultural value and practical value.In the production practice vector is in a wide range of applications. Vector is the cohesion point between elementary mathematics and the higher mathematics. This article standing out the instrumental of vector in high school math is written to study the application in vector teaching and solving. This article is from the curriculum standards and the basic conclusion of learning theory, analyzing the history,and the necessity of vector introducing in high school:Help students feel the value of mathematics applications. Help students further understand the math operations, develop operational capacity. Help students to master an effective way to deal with the problem geometry. Broaden the problem-solving ideas. Help students to connect with the higher education. Next this article finishes knowledge structure and teaching application of vector. This article made detailed classification to elaborate the application in the high school mathematics in the form of examples and comments, including vector concepts and operations, the vector application of algebra,trigonometry, plane geometry, analytic geometry, solid geometry,and series. Then it carries on the investigation and analysis the teaching and learning of the present situation of vector in the way of questionnaire and testing.Questionnaire investigates of vector master degree of the senior high school students from the concept, operation and application of vector in order to accurately understand the master degree of the application of vector in high school students and to put forward some teaching improvement measures. This article comes to the following conclusions through the questionnaire of high school students:Abstract vector of knowledge by some students found to be generally difficult to understand; The high-school pupil is not deep to understanding the difference between vector operation and number operation; High school students cannot convert the variety of vector representations in volume of more flexible methods; Application of the vector concept is in a low level in high school students; Can not reflect the relationship between the appropriate number and location in proper vector model. Connecting the final research results, vector of teaching at the current stage is to make the following improvement measures, in the hope of affording lessons that merit attention of vector teaching research:The process of the concept introducing should be based on the students' knowledge background.. Using counterexamples is to deepen the understanding of concepts. The process of teaching concept should pay attention to highlight key characteristics, control unrelated features. Great attention must be paid to physical background, the analogy to digital operation, geometrical significance and the analogy to multiple representation. Vector application emphasize the tool role of vector as solving realistic problems and mathematical problems.