An Investigation On The Representation Of The Function Of High School Students

Many researchers begin to pay attention to problem representation for the value of teaching with the development of cognitive psychology. The core to settle a problem is problem representation, while problem representation is directly related to the degree of difficulty and the speed of problem solving. Therefore, studying the tendency and the transformation of problem representation has special meanings to teaching students in accordance with their ability and has a certain practical significance to improve the students’ ability to solve problems.Firstly, this study summarized the connotation of problem representation through literature research, including the definition and types of general representation, and the definition and types of mathematical problem representation. Then based on the results of previous studies, the study made the problem representation be divided into four aspects, including the word representation, the abstract representation, the image representation, the mixed representation, which formed the theoretical basis of this study. So, This research put forward three problems to be solved.Next, based on the questionnaire survey, the paper studied the students’tendency of problem representation. The conclusion showed that the different grade, different types of classes, and students of different genders had different tendency of problem representation.Then, the author studied the correlation between students’ ability of problem representation and their grades. The results indicated that the correlation of math grades and mathematical problem representation is close. The conclusion is that the excellent group, the medium group and the difficult group have the opposite significantly, which means the higher score the student gets, the stronger ability the student will be.Finally, according to the test results, the paper analysed the characterization of each question. And combining with the results of interviews, the paper studied the transformation included the word representation to the abstract representation, the word representation to the image representation, and the text representation to the mixed representation. And according to the research results, the paper proposed the corresponding teaching suggestions.