A Study On The Cognition And Application Of Mathematical Beauty Among Grade Eight And Grade Nine Students In Shanghai

When it comes to mathematics,the first reaction of most students is that it is difficult and boring.Because of the complex process of mathematical deduction and abstract presentation form,many students can not feel the fun of learning mathematics.By combing the mathematical beauty contained in the mathematical principles in the mathematics textbooks of grade 7 in Shanghai,this study provides more possibilities for front-line teachers to infiltrate the mathematical beauty in teaching.The test paper is used to investigate students' cognition and application of mathematical beauty,so that students can more intuitively realize the beauty of mathematics.In future study,they will more consciously think about mathematical content from the perspective of mathematical beauty.This study constructs a three-dimensional research framework of mathematical beauty from three aspects:the content,the form and the type of mathematical beauty.Content dimensions include: mathematical principles and mathematical problem solving;Form dimensions include:concise beauty,symmetry beauty,unified beauty and singular beauty;Performance types are divided into types 1-4 according to students' cognition and application.Through the interviews with experts and teachers and the analysis of predictive test,the test paper that can measure the cognition and application of mathematical beauty of students in grade8 and grade 9 is finally developed with high reliability and validity.There are 51 mathematical principles in the Shanghai mathematics textbooks for the seventh grade,among which 41 contain unified beauty,29 contain concise beauty,14 contain symmetrical beauty and only 4 contain bizarre beauty.The current situation and characteristics of students' cognition and application of mathematical beauty in grade 8 and 9 are as follows:(1)More than 80% of the students in grade 8and grade 9 can recognize the beauty of simplicity,among which the cognition of beauty of simplicity is biased towards whether the mathematical principle can simplify problem solving.(2)Eighth and ninth grade students have a good cognition of the beauty of symmetry.About 80% of them can recognize the beauty of symmetry,but only about 50% of them belong to the type 4 of beauty of symmetry,which indicates that students have a bad application of beauty of symmetry.The cognition of symmetry of graphs is better than that of algebra.(3)About 20% ofthe eighth and ninth grade students' cognition and application types of unified beauty are type 1,among which more than half of the students prefer unified beauty in terms of form and method.The use of unified beauty in solving problems also tends to think from the superficial form.(4)The number of students in grade 8 and 9 who can perceive the fantastic beauty is less than 20%,and the cognitive characteristics of the fantastic beauty tend to think from the perspective of sensibility and lack of rational analysis.