Research On Improving The Ability Of Geometric Problem Solving In Senior High School

According to the new High School Mathematics Curriculum Standard, the high school mathematics teaching should pay attention to improving students’ ability of mathematical thinking, which is one of the basic goals of mathematics education [1]. Students are required to master the relevant knowledge and skills. More importantly, they should be able to reflect on the methods of mathematical thinking in the process of solving the problems. The idea of the combination of the number and the pattern is a very important mathematical thought, the essence of which is the combination of the abstract mathematical language with visual image and the key of which is the reciprocal transformation between algebraic problems and graphics. As a result, it can make the algebra geometry and in turn.The essence of the analytic geometry is to study geometry with algebraic method.Therefore, in the teaching process, great importance should be attached to the connection between the number and the pattern. Students should be instructed to find out the mutual relation and inner link between the two, based on which they can identify the types and characteristics of graphics, thus solving the problems.The author herself made a research on liberal art students of one senior high school in Jiangyin City, Jiangsu Province from 2012 to 2014 and found that they are commonly deficient in the ability of reading the picture, afraid of analytic geometry psychologically and emotionally. In this case, the author observed students’ reaction in class, collected their homework, and analyzed their mathematical thinking revealed in their homework. Moreover, the author sorted out some typical problems and introduced the core idea of combining the number and the pattern to improve students’ problem-solving skills. Last but not least, the author cared more about students’ emotional changes to develop their interest in analytic geometry as well as mathematics in general. The findings are as follows: Firstly, the liberal arts students fail to thoroughly understand the essence of combining the number and the pattern and flexibly apply it to practice. Instead, they focus more on the pattern but can’t draw the picture accurately so that it’s easy for them to make mistakes. Secondly, liberal arts students are psychologically allergic to learning analytic geometry. Based on the analysis of these findings, the author put forward her personal thoughts and suggestions.