Investigation On The Differences Of The Solid Geometry Problem Solving Strategies In High School Students

The content of solid geometry occupies the important position in high school mathematics teaching. New curriculum standard for the content of solid geometry in high school is a good adjustment. The arrangement in the Compulsory courses 2 and Elective courses C is intended to present a spiral teaching sequence. However, students still have many problems when learning solid geometry, especially failing to grasp the effective strategy for the problem solving and the differences of solid geometry in problem solving under the same learning environment. The purpose of this paper is to summarize solid geometry problem solving strategies, reveal the top students’ problem solving strategies and the underachievers’ "diagnosis and treatment of disease", and provide the basis for improvement of solid geometry teaching and learning. This article focuses on the following questions:(1) What problem solving strategies do the high school students use at the different stages of the solid geometry problem solution?(2) What are the differences between the top students, the medium and the underachiever in the solid geometry problem-solving strategies?The solid geometry problem solving strategy questionnaire for high school students and the corresponding test of solid geometry are compiled on the basis of Hungary’s problem-solving strategies as theoretical basis. Carrying on the investigation and study for the two middle schools in Chongqing and Chengdu school students(313), getting the following conclusions:1. The problem solving strategies high school students used in problem analyzing and planning stage are: digging information strategy and several forms combining strategy. The problem solving strategies high school students used in problem exploration and implementation stage are: problem transformation strategy, classification strategy and special thinking strategy. The problem solving strategy high school students used in problem detection and reflection stage is: detection of reflection strategy.2. The differences between the top students, the medium and the underachiever in the solid geometry problem solving strategies:(1) The differences of the problem solving strategies in problem analyzing and planning stageThe top students are sensitive to the implicit information implied in the question and can turn them to the mathematical conditions; The medium can sometimes noticed the implicit information, but the transformation is not good; While the underachiever is difficult to realize the implicit information, even notice the hidden information, but can’t effectively convert them into the mathematical terms.In the problem analysis stage, if the question has graphics, then the top students and medium will use the graphics to resolve the problem, but most of the underachiever do not have the habit of using graphical solution; If the question does not have any graphics, the top students always draw right the diagrammatic sketch to solve the problem; Similarly, the medium also can draw right the diagrammatic sketch, but sometimes the sketch is inconsistent, while the underachiever do not have the habit of doing sketches.(2) The differences of the problem solving strategies in problem exploration and implementation stageMost of the top students can use the vector method or the geometric method to change the familiar or complex problems right into a familiar and simple one; The medium is below the top students; The underachiever basically have no consciousness.Top students can accurate judgment proposition of true and false, and to find counterexamples to overthrow the topic given false proposition; Medium are basically able to correctly judge proposition true or false, but there is a certain difficulty to cite; And sometimes the underachiever can judge the truth of a proposition, but can’t tran the problem.In general, when students explore the solid geometry problem, most of the students did not classified discussion of consciousness, the level of the overall is low, but there are differences in classification strategy between the top students and the underachiever, the top students’ classification strategy level is higher than the underachievers.(3) The differences of the problem solving strategies in problem detection and reflection stageMost high school students will not consciously check result when solving problems, so top students, medium, and the underachiever have no significant difference at this stage.