Investigation And Research On Thinking Level Of Plane Vector Of 11th-grade High School Students

Vector not only has profound mathematical connotation and rich physical background,but also is a powerful mathematical tool and a bridge between geometry and algebra.Based on van Hill's theory,this paper studies the students' plane vector thinking level,which not only enriches the research of plane vector and van Hill's theory,but also provides some help for the teaching and learning of plane vector,which has certain theoretical value and practical significance.For plane vectors,firstly,according to van Hill's theory,this study divides them into four thinking levels,ranking from low to high: Level 1(vision),level 2(analysis),level 3(informal deduction)and level 4(formal deduction).Secondly,based on the in-depth study of teaching materials and the suggestions of mathematics education experts and math teachers,the test paper to test students' thinking level is carefully designed.First,52 students were pre tested.According to the shortcomings of the pre-test,the questions were modified appropriately to determine the final test paper.Then,207 11th-grade high school students from two schools were formally tested.Finally,the main conclusions are as follows:(1)The thinking level of 11th-grade high school students is mainly concentrated on Level 2 and level 3,of which level 2 is the most.It shows that most students can carry out simple plane vector operation after learning.The proportion of people from level 1 to level 4 is 6%,46%,35% and 13% respectively.The overall thinking level of students presents a normal distribution.(2)The proportions of students from level 1 to level 4 in key middle schools are4%,30%,46% and 20% respectively,and the proportions of students from level 1 to level 4 in ordinary middle schools are 9%,61%,24% and 6% respectively.There is a certain gap in the thinking level of the students in the two middle schools.The key middle schools have the most students at Level 3,and the ordinary middle schools have the most students at level 2.(3)There is no significant difference in the level of thinking between male and female students.Although there are some differences between male and female students in Level 3 and level 4 in keyhigh school,it is not obvious.The proportion of boys in keyhigh school at level 4 is 25%,while that of girls is only 16%.The proportion of boys in keyhigh school at level 4 is a little more than that of girls.In order to better understand the characteristics of students' thinking level,I also interviewed some teachers and students.The interview results show that the research conclusion basically conforms to the students' actual thinking level.Finally,based on the research conclusion and interview results,some teaching suggestions are put forward.