The Study Of The Second Year Students In The Senior High School About Understanding Curves And Equations

Mathematics Teaching in China attaches great importance to "double base", focusing on basic knowledge and basic skills training for students in mathematics, but not to understand of mathematics .However, the understanding of mathematics teaching is so weak in China that it is one of the current urgent problems in educational reform. The concept of the curve and the equation is the core of the concepts of analytic geometry, but also the concept which is hardest to understand for high school students. The research of understanding the curves and equations could be a breakthrough the understanding of mathematics teaching.In this paper, I study the following issues:(1) How do the Second Year Students in the Senior High School to understand the concept of curves and the equations?(2) Which difficulties will be encountered after learning the concept of the curves and the equation?(3) Are there any differences between male students and female ones to understand the concept of the curves and the equations? And what are the differences?My investigation and interviews of some Second Year Students in the Yong Jia Senior High School and the 11th Senior High School showed that right understanding of the concept of the curves and the equations is based on the operations that students keep on doing exercises on the curves and the equations. Through reflection and the abstract, the students gradually develop their own concepts on the curves and the equations. Therefore, the learning of the function and its image, and the equation of a straight line is the base of the learning of the curves and the equations. The practice students usually do is also the necessary conditions of understanding the concept of curve and the equation.The difficulties that the understanding of the curves and the equations are faced by students are mainly the following points:1. Most students can not understand the concept of the curve and the equation by the way of the mapping although the mapping is one of the main ideas in mathematics. By the way of doing exercises, and perception that they have before, and imitating their teachers, and rotting some examples, students access to the initial experience, form operation pattern, but did not format the structure pattern that reflection is needed.2. Most students can not apply the concept of curves and the equations to solve problems in real life. They can not solve the conic problem by their corresponding equations, and also they can not solve the equation by their corresponding curves.The paper also show that there are significant differences about understanding the concepts of the curves and the equations between the boys and the girls. The boys'level of understanding the concept is higher than the girls'. When the degree of difficulty increases, the gap between the boy and the girl will become increasingly large .But Girls in memory, patience, calculation has certain advantages.