The Application Of Combination Of Number And Shape In High School Mathematics

The combination of number and shape is a common thinking method,which utilizes and combines the two basic characteristics in mathematics,namely,the intuitiveness of shapes and the accuracy of numbers.The combination of number and shape is able to accurately describe the relationship between numbers and shapes,thereby improving the efficiency of solving problems,even many classic problems.The thought of combining numbers and shapes has always been a hot topic in mathematics teaching research.However,most of the researches focus on mathematics of the entire high school stage,with few on a specific chapter.Therefore,using the literature research method and the questionnaire survey method,this paper takes the “conic section and equation” content in the PEP-edition textbook elective part 2-1 and the National College Entrance Mathematics Volume II(science-oriented)as an example to analyze the application of the combination of number and shape and the grasp of the thought of combining the number and shape by grade-three students in high schools and the teacher’s penetration of it in teaching.The main contents are as follows:First,the paper analyzed the application examples of the combination of number and shape in the parts of conic section and equation definition,geometric properties,and examples and exercises.Second,it sorted out the exam questions related to the conic section and equation in the National College Entrance Exam Mathematics Volume II(science-oriented)in the past five years,and analyzed the examined knowledge points,core qualities,thoughts,etc.as well as the application of the combination of number and shape.It concluded that the combination of number and shape in the conic section is helpful for understanding the concept formation,improving question-answering ability,and cultivating mathematical thinking.Then the questionnaires were distributed.After sorting and summarizing the questionnaires,it is found that the students have the following problems when studying:(1)Most high school students do not have a good understanding of the thought of "combination of number and shape".They simply stay on the shallow surface and use it as a method.(2)When answering the question related to conic section,students often fail to accurately draw the shape,mine the implicit quantitative relationship in the shape,effectively combine the question with the shape,and collecting omplete shape information.Teachers have the following problems in relevant teaching:(1)according to the questionnaire,all teachers agree with the significance of the thought of combining number and shape,but they often ignore its penetration into new knowledge points;(2)they only use the combination of number and shape as a method or question-answering technique,but forget that it is a kind of thought itself;Their teaching idea is solidified,and it is difficult for them to rationally use multimedia tools in teaching.Further,in response to the problems,the following teaching strategies are proposed:(1)Develop teaching goals based on the combination of number and shape content in the textbook;(2)Use information technology to explore the quantitative relationships in shapes;(3)Promote independent thinking and attach importance to cooperation;(4)Incorporate mathematics culture and increase students’ interest in learning;(5)Strengthen the correspondence between numbers and shapes,and break through the difficult knowledge points.Finally,relevant teaching design was carried out.In summary,the paper combined the textbooks and the college exam questions in the past 5 years,and used relevant literature as the research basis to discuss the specific application of the combination of number and shape in the conic section,hoping to provide references for teachers’ teaching.