Research On The Construction And Application Of The Evaluation Index System Of Geometric Intuitive Ability Of Eighth Grade Students

Geometric intuition ability has played an important role in people’s daily life since ancient times.Most countries in the world pay attention to the cultivation of students’geometric intuition ability,the value of geometric intuition ability in mathematics learning has been affirmed by scholars at home and abroad.In the context of the compulsory education mathematics curriculum standards(2022 edition),which make geometric intuition a core quality in mathematics,and the advocacy of empirical research by our educational community,the empirical research on students’ geometric intuitionistic ability becomes an important topic.However,the current research on geometric intuitive ability mostly starts from its connotation,teaching strategy,status quo investigation and so on,this leads to the lack of some support in the construction of geometry intuitionistic ability curriculum and the assessment of students’ ability.Therefore,this research takes the eighth grade students as the research object,adopts the exploratory factor analysis method,the confirmatory factor analysis method,the analytic hierarchy process method and the literature method and so on research method,in order to enrich the theory research of our country’s geometric intuitionistic ability and provide reference for the practice of geometric intuitionistic ability evaluation,the research results are as follows.Firstly,the evaluation indexes of grade 8 students’ geometric intuitive ability were determined to consist of three level 1 evaluation indexes:"perceive shapes","describe problems using diagrams" and "analyse problems using diagrams".Under the dimension of "perceiving shapes",there are three secondary indicators:"recognising shapes,identifying shapes and abstracting them from concrete objects","analysing the properties of shapes" and "drawing shapes".Under the dimension "Describe problems using diagrams" there are three secondary indicators:"Use diagrams to represent formulas or theorems","Use diagrams to represent data ","Use diagrams to represent real-world situations",Under the dimension of "using diagrams to analyse problems",there are three assessment indicators:"Use diagrams to analyse mathematical problems","Use diagrams to explore problem-solving ideas" and "Use diagrams to solve real-life problems".Secondly,a system of indicators was established and validated to assess the geometric intuitive skills of Grade 8 students:Y=0.30A+0.33B+0.37C.where the symbol A stands for "perceiving shapes",B stands for "using diagrams to describe problems" and C stands for "Y stands for geometric intuitive skills.The current status of Grade 8 students’ geometric intuitive skills was then obtained,with students performing the worst in the area of ’Number and Algebra’and the best in the area of’Statistics and Probability’,while students performed the best in the indicator ’Perceptual Graphs’ and the best in the indicator Students performed best on the indicator "perceive graphs" and less well on the indicators "describe problems using graphs" and "analyse problems using graphs".Finally,in response to the findings,three strategies were proposed to develop students’ geometric intuition:①strengthen students’ training in the translation of the three mathematical languages into each other and improve their ability to use diagrams to describe problems:②strengthen students’ standard training in drawing diagrams so that they can draw diagrams quickly and accurately;③help students to establish the connection between numbers and shapes and strengthen their awareness of the integration of numbers and shapes.