Preliminary Curriculum Research On Solid Geometry In Senior High School Based On Van·Hiele Theory

The course of geometry is responsible for improving students' spatial imagination ability and logical reasoning ability,and cultivating students' core literacy of logical reasoning,mathematical abstraction and intuitive imagination.Learning geometry in senior high school plays an irreplaceable role in the establishment of students' geometry knowledge system.With the help of the theory of geometric thinking level proposed by Van hill and his wife,this paper establishes the evaluation index of geometric thinking level,analyzes the curriculum standard and the knowledge points in high school mathematical geometry textbooks,compiles the test paper,investigates the students' geometric thinking level,and obtains some conclusions.This study uses the methods of literature analysis and content analysis to have a general understanding of the research status,analyze the curriculum standards and teaching materials,and statistically analyze the students' learning results with mathematical measurement and statistical analysis.It focuses on the following questions:(1)what is the distribution of geometric thinking level embodied in the curriculum standards and teaching materials?(2)Is the geometric thinking level reflected in the knowledge points contained in the textbook consistent with the curriculum standard?(3)Is the arrangement of teaching materials in line with the law of students' development?(4)What are the characteristics of the distribution of students' geometric thinking level?(5)Whether the students' geometric thinking level meets the requirements of the curriculum standard?The conclusions of this study are:(1)23% of the knowledge points in the curriculum standards belong to the analysis level,while only 6% of the knowledge points in the teaching materials belong to this level;33% of the knowledge points in the curriculum standard belong to the non-formal deduction level,and 42% of the knowledge points in the teaching materials belong to this level;44% of the knowledge points in the curriculum standard belong to the formal deduction level,while 52% of the teaching materials belong to this level.(2)The geometric thinking level embodied in the knowledge points in the textbook is consistent with or higher than the requirements of the curriculum standard.(3)The knowledge presentation in the textbook meets the principle from easy to difficult and from simple to complex.The geometric thinking level presented by the knowledge points is basically from low to high,which is in line with the development law of students' geometric thinking level.(4)Most of the students' geometric thinking has reached the level of non-formal deduction,and nearly half of the students' geometric thinking has reached the level of formal deduction.A total of 127 students participated in the survey,of which 11 were at the level of intuition and analysis,accounting for only 8.7% of the total number of people surveyed,59 were at the level of non-formal deduction,accounting for 46.5%of the total number,and 57 were at the level of formal deduction,accounting for44.9% of the total number.(5)Most of the students met the requirements of visual level and analysis level in the curriculum standard,about 55% of the students met the requirements of non-formal deduction level,and about 45% of the students met the requirements of formal deduction.Most of the students have met the requirements for mastering the basic characteristics of spatial graphics in the curriculum standards,have a good grasp of the positional relationship between points,lines and planes,have a weak memory of the concept of individual geometric graphics,and have a general grasp of the calculation formulas of surface area and volume of geometric graphics,There is a lack of understanding of the proof and reasoning of propositions and the sufficient and necessary conditions required to prove a conclusion.Students are very lack of the ability to use the definition,nature and theorem of graphics to solve other problems.