A Research On Problem-solving Of Solid Geometry Of Senior School Students

Solid geometry is not only the classical sections but also the important content of senior high school mathematical curriculum. Space vector provides a new method for solving three-dimensional geometric problems, having an important impact on the study of solid geometry. In this paper, the author will examine the use of Euclidean and vectorial method of senior high school students while solving solid geometric problems, as well as the main errors in the problem solving process. In addition, we will also investigate the students’understanding of the characteristics of the two methods. In order to supply some evidences for the solid geometry curriculum and teaching.In this paper, the author takes a survey on193third grade senior high school students in Shanghai by using test papers, questionnaire, and interview. From the use of the Euclidean method and the vectorial method, we find that,1. There are about58.5%students who use Euclidean method and vectorial method simultaneously, but the students are more familiar with Euclidean method. The scores of V students are higher than E students’ significantly.2. The students tend to use Euclidean method for simple problem, and tend to use vectorial method for difficult problems.3. The different levels of students on the choice of methods is different significantly. Gifted students tend to use vectorial methods while poor students tend to use Euclidean method.The poor students showed relatively low performance on vectorial method.4. The gender differences on the choice of methods is also significant. Male tend to use Euclidean method while female tend to use vectorial methods. But there are no significant differences on the ability of problem-solving.The errors found in both methods are divided into two main categories:general errors and vector errors. In terms of general errors, the errors resulting from logically invalid inference is most for E solvers, and the technical errors is most for V solvers. Vector errors are substantially connected with vector solvers, errors in using coordinates is the most error type. We ask students to answer a questionnaire to investigate their attitudes towards one or the other geometry method. We find that the figure diffculties and complicated thoughts seem to be the strongest characteristics of Euclidean methods. In their opinion, the Euclidean method is difficult but meaningful. The most popular feature of vectorial method seems to be the comfort of methodology, it is simple and convenient. The most disadvantage of vectorial method is that it is prone to make technical errors and errors in using coordinates. Besides, it is difficult for the students to remember the formula.