High School Students Analyze Geometric Learning Obstacles And Countermeasures

Cartesian geometry is a key and difficult part in senior high school. However, the students have great difficulty in learning it.The writer conducted a survey by questionnaires and conversations among Senior High Two students. The conduct included the following, students' habits, the attitudes and the mentation when they learned this part, students' ability of calculating,their command of the concepts, formulas and principles and the usage of mathematical ways of thinking.This synthesis is based on the data of questionnaires and papers among 320 students. The survey indicates that 76.2 percent of them are not interested in it. 23 percent of them find the complicated and trivial calculation is the biggest barrier. 15 percent of them think there are so many formulas that they can't remember them. 14 percent of them can't use the mathematical ways of thinking. As to the result of papers, the accuracy of the Cartesian geometry problems are 32 percent and 8 percent respectively, which are very low. The writer analyzed the results carefully and referred to large quantities of data and found some problems. First, the students don't have definite learning objectives. They don't have much affection for Cartesian geometry. Second, they pay too much attention to grades and are too anxious when learning Cartesian geometry. Third, the students can't master the basic knowledge well, such as knowledge regarding functions, vectors and triangles, which are included in Cartesian geometry. They have trouble in transferring different aspects of knowledge. Fourth, there are too many concepts and definitions in Cartesian geometry.The students tend to mix them up because they just learn these concepts and definitions by rote. Since they don't understand them fully, the students find it difficult to use them. Fifth, Cartesian geometry needs plenty of calculation, which is related to alphabets and skills. The fact is that students are not skilled at the arithmetic methods and weak in calculating. Sixth, students don't understand the mathematical ways of thinking deeply and thoroughly. They ignore the conditions and solve Cartesian geometry problems by following some mixed models. As a result, they have difficulty in applying the mathematical ways of thinking flexibly.According to the above problems, the writer analyzes the reasons from the aspects of the Cartesian geometry itself, students and teachers. The writer also provides some countermeasures to help. They are as follows. Firstly, it's important to strengthen communication between students and teachers, which is helpful for overcoming the mood of anxiety. Secondly, teachers have to pay attention to the relation among knowledge on different aspects, which can help overcome the students' barrier of transference. Thirdly, teachers have to pay close attention to the students' instant responses in class and make adjustments in time so that the students can overcome the barrier of understanding them. Fourthly, teachers must cultivate the students' ability of calculation so that the students can overcome the barrier of calculating. Lastly, teachers have to explain the mathematical ways of thinking, which can help overcome students' barrier of using them.