Study On The Features Of Naturality Of Mathematical Problem-solving In Middle Schools

Polya proposed in his book how to solve problems that teachers should help students solve problems in accordance with its natural tendency.Subsequently,Professor Shan Zun who comes from China also repeatedly emphasized in his book problem-solving research that the solutions should be natural. In addition, in the papers of mathematics teaching in recent years, a growing number of scholars and first-line teachers have mentioned that problem solving should be natural.However, after reading the literature it can be found that different people have different opinions. Therefore, it is necessary to discuss the connotation of naturality of problem-solving, including its features, and the degree of understanding of first-line teachers on the naturality of problem-solving, as well as the recognition of its features.Based on literature analysis and interviews, this paper discusses and understands the connotation and features of naturality of problem-solving, analyzing the factors that affect the naturality of problem-solving with a multi-perspective.After a summary of literature it can be found that the features of naturality of problem-solving mainly include: following the students’ thinking, focusing on using universal properties and methods, grasping the essence of problems and introducing complementary elements rationally.And then through interviews with the first-line expert-oriented teachers, it founds that intuition, on the basis of reference answers, simple problem-solving steps,integration of mathematics history are the features of naturality of problem-solving which have a high recognition.It carries out by using the questionnaire containing the above eight factors. The questionnaire data shows that the first-line teachers have higher recognition with regard to the features.Based on the questionnaire, it carries out comparison of the differences of problem solutions between teachers and students, and it founds that the process of problem-solving of teachers and students has a higher match.Finally, this paper provides three revelations are(1)problem-solving should based on the principles of nature;(2)a problem with multiple solutions needs to choose the optimal one;(3)continuous pursue natural solutions. Hope this study can provide elicitation and help for the problem-solving teaching of teachers.