Second Year High School Students' Understanding Of Mathematical Formulas And Theorems And Its Influence On Mathematical Learning

In this paper, the author takes a survey on second year high school students' understanding of mathematical formulas and theorems and its influence on mathematical learning by students' tests, teachers' questionnaire and students' interviews. From the survey, the author obtains the following results:1. Second year high school students' understanding situation of mathematical formulas and theorems:(1) Most second year high school students' understanding of the formula and theorem of calculating the sum of arithmetic progressions and geometric progressions stays on the second level----Concept Level, less on the fourth level----Analysis Level, then on the third level----Comprehension Level, last on the first level----Calculation Level; (2) 46.41% of second year high school students' understanding of the Sine Theorem stays on the Concept Level, and 43.14% of students arrives at the Comprehension Level; (3) Second year high school students have obstacles on understanding the Cosine Formula, and only 16.34% of students reaches the Comprehension Level.2. Second year high school students have no difference on the understanding levels of the two series summation formulas. They understand better on the Sine Theorem than on the Cosine Formula.3. The number of times of teachers'proving in the class is few. The mathematical language cannot be easily understood by the students. The number of teaching designs based on the history of mathematics is not very much. The students do not understand the role of proof well. These factors impact the understanding of students of mathematical formulas and theorems.4. The understanding of mathematical formulas and theorems has some positive impact on mathematical learning:(1) Students located in the different understanding levels of formulas and theorems have significant differences in problem-solving ability (p<<0.01), and the understanding levels are significantly related to the problem-solving ability; (2) Students lying in the different understanding level of formulas and theorems have significant differences in restriction condition (p=0.009). At the end of the paper, through this research's conclusions and found, the author gives some suggestions on teaching and writing textbooks, and points out the study's limitations and reconstructs the follow-up research topic.