The Comprehension And Application Of Mathematical Formulas And Rules Of Middle School Students Of Grade Eight

In this paper, the author takes a survey on students' comprehension and application of mathematical formulas and rules by using questionnaire and interview. 670 Middle School students of Grade 8 are involved in this investigation which focuses on the following seven aspects such as self-cognition, cognitive characteristics, restrictions, bilateral application, transfer phenomena, derivation of characterization and flexible application. From the survey the author obtain the following results:a. Most of students reflect that formulas about geometry form are the most difficult to master, especially the area formula of sector.b. Most of students can understand the general characteristics of formulas and rules whose truth and universality students have the same cognition on. By contrast, students have some cognitive deviations of formulas and rules' instrumentality and conciseness.c. Students pay little attention to the restrictions of formulas and rules. When they using these formulas and rules to solve problems they often ignore or misuse the restrictions. In the survey, the author find that different restrictions can cause different degrees of attention.d. Conclusively, students apply better formulas than theirs inverses and different formulas can makes significant differences. From the results of survey, we can find that the master of the inverse uses of power multiplication of the same base is better than the other formulas'.e. The phenomena of negative transfer occurred in the learning of formulas and rules is becoming common and serious. It appears obvious in the study of distribution in multiplication. To some degree, it is inevitable to occurring negative transfer since many students can only reach to the understanding level of instrumentality but not relation.f. There is a large gap between Ideal and actual effect of students' cognition of the necessity of deriving or proving formula and rule.g. Students are deeply effected by the thinking set. They have poor flexible ability in the application of complete square formula.At the end of this paper, the author makes some suggestions about teaching and writing textbooks according to the results of this research. Some subsequent research topics are raised and also some deficiencies of this paper are given.