Research On The Thinking Level Of Geometry Transformation Of Senior High School Students

In the study of mathematics,students' thinking ability is particularly important.Nowadays,more and more scholars begin to pay attention to students'mathematical thinking.As an important logical thinking ability,geometric transformation thinking has gradually won the attention of many scholars in the field of mathematics education.However,at present,the study of this thinking is still in the primary stage,and many conclusions are not comprehensive and perfect.Therefore,based on the previous research.this research will be supplemented and expanded to investigate the geometry transformation thinking of senior two students after learning the contents of ellipse,so as to realize the following analysis:(1)The current situation of high school students' thinking level of geometric transformation.(2)The thinking confusion and typical mistakes of current senior high school students in geometric transformation.(3)The difference of thinking level of geometric transformation between different groups of senior high school students.In this study,Van Hiele's theory is selected as the theoretical basis,and ellipse is selected as the test medium.Through reading and sorting out the new curriculum standard,teaching materials,supplementary books and extracurricular literature,a set of test paper for the level of thinking of geometric transformation is designed,which is suitable for senior two students.It focuses on the test of students' ability of geometric transformation,such as horizontal transformation,similar transformation,expansion transformation and coordinate transformation.After pre-test and continuous improvement,the Cronbach's alpha of the test paper is 0.758,and the KMO value in KMO and Bartlett test is 0.705.The test paper has high reliability and validity.Alter having the perfect test tools,this study chooses 195 students from four classes in a high school in K city to test,and finally recovers 183 test papers,including 150 valid test papers.Through the qualitative and quantitative analysis of these 150 valid test papers,the following conclusions are obtained:(1)Most of the students' thinking level of geometric transformation is focused on level 3 and level 4,and with the improvement of the requirements of students' thinking level,the average score of students' test is decreasing.In addition,there is a close relationship between the development of students' thinking level of adjacent Van Hiele geometric transformation,and the development of lower level is the basis of the development of higher level.(2)Students generally have a vague understanding of the concept of "geometric transformation".Their thinking development is relatively smooth from level 1 to level 3.Their thinking development on level 4 is a little bumpy.Their thinking development on level 5 is relatively difficult.The main problems existing in their thinking development are:1.Details error;2.Transformation process error;3.Transformation knowledge error;4.Weak ability of independent inquiry(3)There is a significant correlation between the level of students' geometric transformation thinking and their arts and science classes,their usual performance and gender,and the level of students' geometric transformation thinking has the following rules;science class>arts class>art class,students with high scores at ordinary times>students with low scores at ordinary times,boys>girls.Finally,the author puts forward five teaching suggestions according to the problems of students in this test,hoping to help students develop to a higher level of thinking.