Research On The Current Situation Of High School Students Using The Idea Of Combining Numbers And Shapes To Solve Ellipse Problem

"Number" and "form" are two closely related objects of study in secondary school mathematics.The standard states: "Mathematics is a science of quantitative relationships and spatial forms." Under the requirements of the new curriculum standards,teachers should not only attach importance to the transmission of knowledge,but also to the teaching of mathematical ideas.The idea of combining number and form,as one of the important mathematical ideas,plays an important role in mathematics education.Analytic geometry represents a combination of algebraic and geometric methods of thinking,and has an irreplaceable role in developing students’ careful thinking and overall understanding of the subject matter.In the GCE Analytical Geometry questions,the requirements for thinking skills and the combination of number and shape methods of thought are high,resulting in students not scoring very well.Therefore,in teaching,training students to complete their answers to analytic geometry quickly and accurately within the limited time available is a topic that teachers must face in teaching analytic geometry.The main research questions in this paper are:(1)What is the current situation of students using the idea of combining numbers and shapes to solve elliptic problems?(2)What is the current situation of boys’ and girls’ use of the idea of combining numbers and shapes in solving elliptic problems? What are the differences?(3)Are there any differences in the use of number and shape combining ideas in solving problems between students with different grades in mathematics? Firstly,by reading the works of experts and scholars on the theory of combining number and shape,and on the basis of a clear definition of the meaning of combining number and shape,and by carefully studying the requirements of the senior secondary mathematics curriculum standards,we determined the dimensions of the various levels of combining number and shape;then we prepared test questions on students’ application of combining number and shape and a questionnaire on their main performance,and finally processed the data obtained from the test questions and the questionnaire.The data obtained from the test questions and questionnaires were finally processed to analyse the current level of students,and to analyse whether there were differences between male and female students and students with different grades in the application of the idea of combining numbers and shapes to solve elliptical problems.The results of the survey showed that:(1)the overall level of students’ number and shape combination ideas was good.Among all the subjects,only one person did not reach Level 1,the rest of the students reached Level 1,less than one-third of the students were at Level 1,about one-fourth of the students were at Level 2,and more than one-third of the students were at Level3;further analysis of the current situation revealed that the students’ problems were: the basic knowledge was not solid,the transformation of numbers and shapes was not accurate;the awareness of using the idea of combining numbers and shapes to solve problems was not strong;the arithmetic At the same time,the survey found that students who had reached Level 3 were more active in their thinking and were able to integrate their knowledge,combine numbers and shapes,and choose the best method to solve problems.(2)There is a significant difference between the overall scores of the sophomore students in numerical and figurative thinking in terms of gender,and the overall mean score of boys is higher than that of girls;there is no significant difference between the mean scores of each level in terms of gender,but the percentage of boys who are at level 3 is significantly higher than that of girls.(3)Significant differences exist between students with different grades in self-perceptions in terms of overall grades,there are no significant differences in Level 1 and Level 3,there are significant differences between students with good grades and those with failing grades,and between students with passing grades and those with failing grades in Level 2,and there are no significant differences between students with good grades and those with passing grades.Based on the above findings and the collation and analysis of the questionnaires,this study also puts forward several teaching suggestions: cultivate creative thinking and strengthen the awareness of combining number and shape;consolidate basic knowledge and strengthen the accurate combination of number and shape;pay attention to the norms of problem solving;and summarise and reflect on the ideas of problem solving in a timely manner.