用向量法处理立体几何问题的教学效果研究

Studying on the Effect of Solid Geometry Teaching with Vector and Synthetic Methods

向量几何提供了一种认识空间和图形的方法，可使学生初步领略机械化的现代数学思想。学生在解决立体几何问题时，同时运用综合法与向量法两种方法处理问题的学生人数最多，仅使用向量法的人数最少。使用向量法的成功率高于综合法。学生在处理能用两种方法解决的立体几何问题时的错误类型主要有一般性错误与向量错误。向量坐标计算错误是向量错误的主要类型。

Vector geometry provided a new method for studying space and figures, and made for appreciating mechanized thought of modem mathematics. Using an ability test, we want to examine the effect of solid geometry teaching which introduce space vector to deal with some problems concerning metric and positional relations. Through an analysis of written solutions by 368 third grade senior high school students in Shijiazhuang, we found that there were most students who use two methods simultaneously, the students who only use synthetic method, were a few more than them who only use vector method. But the grades of V students were higher than E students＇. We also analyzed two error types-general error and vector error. Logically invalid inference and misinterpreted language were most of general error. For errors related to the concept of vector, coordinates operational mistakes were most.